Кэнт, Кларк

(Clarke Cant) - известный в своё время эксперт по блэкджеку, сошедший с игровой сцены примерно в 2003 году. Но на пике своей популярности он был постоянным автором многих статей и публикаций. И несмотря на очень язвительный и пренебрежительный стиль общения, его расчёты всегда воспринимались с уважением. Кларк Кэнт, в соавторстве с Полом Кином (Paul Keen), изобрели систему счёта C-K Count (она же Precision Count). А также Кларк Кэнт написал онлайн-книгу по блэкджеку, "Blackjack Therapy" (2000). Ниже приводится полный текст этой книги, исключительно ради сохранения его для истории.


Blackjack Therapy

By Clarke Cant


Dedicated to Paul Keen, Craig Glossner, Harvey Cannon and Joe Perales.

This work is text only and lacks normal footnotes and bibliography to avoid format problems for readers who may be downloading this document with the wide variety of alias servers and formats they may be using on a casino trip. Print editions will include these items, but there should be adequate information, in text, to provide readers with source information. Copyright © 2000 Clarke Cant, a registered penname and alias.


Table of Contents:

Chapter 1, entry points.

Chapter 2, basic strategy fast and easy; your first step in advantage is couponomy.

Chapter 3, the Blackjack Formula revised and revisited.

Chapter 4, the truly optimal bankroll, to infinity and beyond.

Chapter 5, Psi Blackjack is Limited

Chapter 6, Bangers and other tasty tricks to do to a casino

Chapter 4A, The rest of chapter 4 – patience rewarded

Chapter 7, Shuffle Tracking to the Limits, how to use the blackjack formula for ST too.

Chapter 8, Amazing health tips and tests of your attitudes to health. Yes too plans to build a muscle relaxer and blood cleanser.

Chapter 9, how to beat those feared shuffle machines (and why they are probably illegal too).

Chapter 10, Why I believe in Anarchy, Chaos and human progress.

Chapter 11, Uston +/-, Zen, and Victor APC count indexes.

Chapter 12, Moving on up…how high is the blackjack sky and how to safely climb on up

APPENDIX A - Ruin and Distribution

APPENDIX B - Showing the maximum profit and BJF for continuous shuffle machine games

APPENDIX C - Estimating Bankroll Requirements


Chapter 1, entry points.


There are four situations that will be discussed below that are typical of people using this book and beginning or restarting their adventure in advantage play in blackjack. This discussion may seem off topic but it is vital to go over these life situation suggestions to get over the greatest obstacle we may have, how to get over the fact that money we win did not fall from the sky, or is somehow undeserved, by going over some of the traps, we may face if we are:

Homeless or near homeless

Living a normal middle class life but having to justify our playing

Wealthy but overcoming inhibitions to now taking the edge on the casinos

A past card counter that is re-entering the fray and reclaiming the edge.

No matter how low life has gotten you down you can start now almost, but you must take a hard look at all the traps….I have had to deal with them all…


If you are homeless or near homeless you will be thankful that places exist that will provide free meals or a place to stay for a few nights,  until you get “back on your feet.” Prepare to be shocked to find out however how huge the disincentives are for such missions and agencies, far more than the “old welfare as we knew it,” to help you, and how likely they are to, through obvious and deliberate neglect, to keep you trapped, where your painful status is money in the bank for such places and you are their cashcow.

A good place to start is by access I have had to the online version (via some nice hacker types) of a publication first brought to public attention by Chuck Harder, of For the People (forthepeople.org),  who obtained access to the 1991 print edition of a publication for congressional aides to aid constituents, called, Cash and Non-Cash Benefits for People of Limited Incomes.

(The moral question of what the federal government is doing by giving tax dollars to groups that also solicit from the public is not too far removed from what would happen if Compaq and IBM were allowed to hold telethons to subsidize their bids to sell servers to the Pentagon.)

The reembursement rates and calculated equivalent costs, for the same services in the normal business world will shock you. Here are the latest figures I have to date for the moneys that the federal government is required to pay to any charity (whether the charity even likes it or not) serving meals to the needy that qualifies or participates in any USDA or other food programs in the USA.

Breakfasts $1.65

Lunches $2.65

Dinners $3.15

Such compares on the low to median side for such meals at typical fast-food outlets across the USA. Cost equivalents will be made however to reflect the advantages such groups have over private enterprise. Such programs are sold to the public in the excuse that the cost to the taxpayer is less than the old welfare system, while the total taxpayer impacts and total costs to society of such activities are ignored.

To begin with, at least 60% of all such foods are donated, with costs being typically 50% of what you pay in  restaurant. The equivalent costs become:

Breakfast $2.15

Lunch $3.45

Dinner $4.10

25% is normal wages where at least 80% of the servers and preparers being some sort of voluntary person, who may actually be in some sort of rehab program. The first raises the equivalent to:

Breakfast $2.48

Lunch $3.98

Dinner $4.73

The rehab people, those in some sort of program no doubt, are entitled to be paid at minimum wage, which may or may not be paid them, are usually 60% of the staff, which now adjusts the figures, if kept for rehab services by the agency to:

Breakfast $2.73

Lunch $4.38

Dinner $5.20

The tax impact of the donations of food, in tax deductions and direct tax credits, matches the value of the donated food in full and  amounts to another 50% of that original price:

Breakfast $3.54

Lunch $5.70

Dinner $6.78

Another 40% of the original price comes in additional private donations of cash:

Breakfast $4.21

Lunch $6.76

Dinner $8.35

And then you can add still more for direct grants from the federal government over and above these program costs, but by now you can see we are not eating at the Circus-Circus buffet at all, but may be headed to the Bellagio. Now can you believe it that these same missions, may demand $1 for some meals, taking food stamps illegally (typical of the Union of Gospel Missions) or trying to get regulars to assign their food stamps to them (typical of the Salvation Army).

The same holds true for the similar reembursement that is paid for bed space each night of between $18 and $22. For $58.30 you could stay at the most expensive Motel 6 locations in the USA, San Francisco or New York City. Here the multipliers are similar staffing and largely donated blankets and sheets etc.

At each, very pointedly you will be asked to leave your belongings too in very unsecured spaces, such as demanded to leave your backpack away from you because of supposed fire hazards, before you partake of such “services.” The real purpose of such and proof of keeping people trapped, even though it is not consciously done, the incentives are certainly followed, can be found in virtually every other issue of the Salvation Armies, Battle Cry, magazine. About that often you will find some article about someone forced by some life crisis to seek help and losing whatever little belongings they have while in shelter, and then deciding that it was all part of some plan by Jesus to get them to give up their addiction to things and turn to him.

The states get in the act too, which I will not detail except  in one example. You can manage quite well with good budgeting to survive on food stamps. If you are issued paper stamps you will find the change quite handy. You may have even read how Anthony Curtis once credited couponomy with his initial survival when he first decided to become a professional gambler. In one conversation with Paul Keen, quoted by him to me, he also added that food stamp change, after being laid off from one bar-back job helped too. Well every so often a county or state will switch over to an ATM like system, where some racist walking stereotype from some studio call will be shown on TV saying, “I likes this new card system so much because now my kids won’t have to go hongry if the stamps are stolen.” BS

If you are probably in this situation you probably will have to use such services for a time. But don’t fall for being offered to go into some rehab program or bible training program. You will be working for free in some thrift store without any wage and hour protection. You will not likely be placed in anything resembling AA or the like either, just fed that religion. You certainly will not be allowed to gamble in any way shape or form. As little as $4 can be enough to begin optimal play with Basic Strategy and playing bet $1, win $2 coupons, and letting your money build. You perhaps should keep to state employment agencies for such things as day labor to get cash in your pocket, apply for paper stamps, and try to avoid the temp agencies—both they and the state offices will require long hours waiting for a job, but less of the money paid for you will be yours in the temp agencies and the temps have a tendency to put drunk and other dangerous workers to you out on “tickets” because they know damn well that such people if injured will flunk any drug tests and they will not have to pay the medical bills. You can get hurt working with such “expendables.”

Try to get a bicycle and campout if you can to get away from such pressures and save expenses. Don’t teamup with anyone else, in that the “heybros” are likely just trying to make sure you are a boozer or druggy too, to make sure you become their alternate reserve supplier of physcoactives. A used bicycle can not only pay for itself in transportation savings quickly, but you would be surprised at the rate you find spare change on the streets with one. Tents, such as the $12.95 A frame found at Wal-Mart often will do. Also develop skills at dumpster diving. Food can be found at 7-11s and Circle Ks that is only slightly expired and will outlast the computer you are reading this on. Clothing can be found at virtually any laundromat—which is where that odd sock goes….Shave any beard (it is amazing how far down some street people get to where they want to be IDed as homeless and hassled) you may have and keep your hair short but not in any atypical style. Keep clothes clean and try to stay away from clothing giveaways unless you like dressing in bizzare polyester or are an extra in some new Austin Powers movie (and take note of the above where the hidden agenda of the missions, even when not conscious of it, may “dress you funny.”). Later on, during early Januarys, you can find working last years computers behind offices, especially phone sales companies and real estate offices. Bike parts are easy – especially in Laughlin – except in Las Vegas, to find (the drivers are often DUI or feel because they have a juice job on the strip they have a right to target joggers and bicyclists and anyone else who is in better shape then they and threatens their self-image.).

Now before you start thinking that this is bizzare to discuss, after all how many of you are this broke, you should consider this as a good example of how to think about the hidden costs of playing hunches or not being able to understand how basic and count strategies rate different playing recomendations. The money paid out by the government and by donors is hidden in a shell game where each contributor is tricked into thinking he is getting a bargain because others are also paying in, not seeing how a contributor donating food is also himself a tax-payer and the like. The same fallacies can hit when not splitting 8s (as is recommended by John  Patrick in several writings on blackjack) does result in 2 losing new hands, but 2 hands that lose less than the original 16. Other similarly sneaky points will be made in the same way, in this text.

Similar concerns will haunt you if you are a more typical member of the middle class and still have it together.  Blackjack Attack, by Don Schlesinger, and his SCORE articles, can give the impression that you shouldn’t play until you have $5K or $10K, or until your expected value per hour is higher than your job earnings. Even if you are playing instead of on a normal job, this is misleading. You should look toward playing as the start of a new business like any other new business venture that is going to take a little time and a lot of hard work to turn to the black. You also have to deal with spouses and normal expenses and the unique viewpoint where a dollar won today may not really be yours to spend for sometime. Right from the start you are going to have to have good estimates of your expected value and your required bankroll. Another major hurtle is looking at the relatively meaningless term, advantage, when hands to double or Schlesinger’s DI (still not as meaningful), is a far better way to rate games (hands to double, or HD as given here is not the same as the H0 that Brett Harris uses either). The experiences of Stuart Perry, writing in, Blackjack Diary, are perhaps indicative of this. You most of all have to directly confront just who you are trying to justify your playing to.

Your day to day and hourly experiences of play are simply meaningless compared to the expected value you have while playing, even in the best games. You have to be stubborn to the point of being compulsive to reach success, to play long enough to win, only having the math, and not results, to go by, until far down the road. While I believe that things like remote viewing and psi sense exist, these are not the same as spousal intuition and you will have to often explain things. You also have to be absolutely firm about not talking about your advantage play in any casino situation and stopping people from viewing your legitimate concerns as “paranoia” (actually they are the clinically paranoid ones in that there really are “boots under the bed,” here, and they are the ones refusing to deal with actual reality). Such people can really screw you over when they try to prove that you are “worried over nothing” and insist on talking in the wrong places.

For the wealthy, which can be very relative in terms of the casinos you play and etc., and players known for their formerly losing play, there are limits to what tactics you can apply. Couponomy, which is suggested in the next chapter as an introduction to advantage play and seeing how your bankroll runs up and down is not going to be available to you. You are limited by having to stay within the playing styles and profiles that you  have already established.  Many of you are going to have to jump into games that are not as good as those available to others because of that. You have to look at yourself as an income rather than investment player: you will not have as much oportunity to seek out games that provide quick bankroll growth, but will be able to find games that can give you high dollar returns. The difference will be explained in chapter 4.

The biggest problem is that you will have already been profiled by the casinos as gambling to meet non-monetary goals. Suddenly leaving a game because conditions are not as good for maintaining your advantage is likely to be interpreted as “your pockets going empty,” by the casinos. Your increase in skill, suddenly playing at least basic strategy for example, is not as serious a problem as you might think however. A casino is more likely to give you breathing space in that a player who bets black chips, and plays basic strategy, and maybe tries to count but appears to be bad at it, appears to be much more profitable than a $5 bettor who plays basic strategy. The $5 chip basic player will be viewed as not necessarily giving up enough money to “pay the rent on that chair,” while the same percentage appearing to go to the casino, but from a $100 chip player, is more than enough to get the casino to comp you to room, food and beverages. The same cover for your play can come from exploiting the comps in other ways. When a game goes bad try to make a little more unreasonable demand than usual. You not only can create an excuse to leave that is unrelated to playing conditions, but you can gauge more accurately the pit’s attitude toward you by the tone and manner of their yes or no.

For the player who has left the game for awhile there are changes that are very subtle. Every game will tend to appear to be better than it really is, with the trend toward moving initial game observation to the staff monitoring the overhead cameras (the sky) than from the pit bosses. Shoe games that a player would never play as recently as 5 years ago, may be the best games around you, with the revelations of shuffle tracking. Tell play is nearly totally gone, while front loading (the attempt at detecting the quick inadvertent exposure of the dealer’s hole card) is perhaps more doable than ever—with the countermeasures that have been taken to stop players exploiting bangers (my own term), which has itself replaced playing the warps. Trying to form teams is different now that the trend is away from more complex counts to unbalanced systems where true counting is optional. You are going to be puzzled over the new terms that have cropped up: such as bjmath.com popularizing the use of the term, “system tags,” for card values. These are the most troublesome perhaps.

Computers have advanced forward over the years where older ways to estimate your edge, such as the Blackjack Formula revision given here, will seem archaic, until you consider the risks involved in having your own computer with you, and the shear meaninglessness of the extra precision that these advances have brought. Some people have recognized this point, such as Arnold Snyder in his revised edition of Blackbelt in Blackjack, where he shows how to simplify the indexes for the hilo count, with very little impact (though in my opinion the true edge concept carries the concept too far). There are also newer studies showing that there is limited impact in what would seem to be drastic overbetting; though it is more proven than ever that using bet sizes of twice your optimal bet will reduce your gains to zero, long term, and you will absolutely wipeout at bet sizes any more than this, and that an optimal bet is well optimal for your long term gains—there will be some controversial discussion of ways to estimate optimal bankroll requirements in Chapter 4, that point-out how some famous books have miss-used normal statistical methods.

Consider these comments however most of all to get over the idea that money you can win from blackjack is somehow the result of magic of some sort, simply because the causal link between the way you play and the money you gain is so spread out over so many hands, or that in any way you should have less respect for money that you win, as compared to money from your usual career. Chapter 10 will cover these issues which go back to the roots of statistics; back to people like Cardano and Fibinacci who originated such concepts.


Chapter 2, basic strategy fast and easy, couponomy is your first step in advantage.


Basic strategy will give the plays that you will be making most of the time. This chapter will show you how to learn basic in less than 30 minutes after reading this chapter. It will do so by starting with conventional charts and then presenting study aides, based on the outlines in the charts, that you will be able to easily recall in casino play. Then there will be betting guidelines for playing the various coupons that casinos circulate. This will give you an initial edge that will also show you how your bankroll will typically go up and down as you play. Even when you are using more advanced methods your bankroll will still rise and fall in much the same way. First we start with a conventional chart of an approximate basic for all games; refinements for different numbers of decks and specific hands are omitted. Most of the gains that are given up are already part of the adjustments that will come with using a count system.

“h” is hit; “s” is stand; “$” is split; “g” is surrender “s” before a number is a hand that has an ace that counts as 11; “d” is double down.


Your hand            dealer upcards

        *                   2       3       4       5       6       7       8       9       X       A

       s18                s        s       s        s        s        s       s       h        h       h

        16                 s       s        s        s       s        h       h       h       h       h

        15                 s       s        s        s       s        h       h       h       h       h

        14                 s       s        s        s       s        h       h       h       h       h

        13                 s       s        s        s       s        h       h       h       h       h

        12                 h       h       s        s       s        h       h       h       h       h

Double downs

        11                 d       d      d       d        d       d       d       d        d       h

        10                 d       d      d       d        d       d       d       d        h       h

          9                 h       h      d       d        d

Soft Double Downs      


        A7                h       d      d       d        d

        A6                h       d      d       d        d

        A5                h       h      d       d        d

        A4                h       h      d       d        d

        A3                h       h      h       d        d

        A2                h       h      h       d        d

        Omitting 88, AA which are always split (in basic) and XX which is always stand (in basic), here are the pairs

        99                $       $      $       $        $       s       $        $        s       s

        77                $       $      $       $        $       $   …..see above for 14….

        66                h       $      $       $        $ …….see above for 12 …..

        33                h       h      $       $        $       $       h        h        h       h

        22                h       h      $       $        $       $       h        h        h       h


Surrender comes in two flavors when the dealer has a ten card or an ace as the upcard. Early surrender lets you giveup half your bet, rather than risking it all, before there is any checking for whether the dealer has a blackjack, or if the hole card is drawn after the players play their hands. Late surrender is still giving up half your bet, rather than playing out the hand, but is playable only when it is determined the dealer will not/does not have a blackjack. Doubling down after splitting a pair is often allowed on the first two cards after you split a pair (this text is not an elementary text but like the title indicates therapy for the playing problems you may have after reading other texts. If this information is a little new to you perhaps you should come back after reading, Blackbelt in Blackjack, by Arnold Snyder; Basic Blackjack, by Stanford Wong; or Beat the Dealer, by Edward Oakley Thorp.). They all give good explanations of simply playing and other tips about basic strategy. This material is mainly to speed up using basic.


Early Surrender:                                    Late Surrender:


  “your hand”      dealer upcards              your hand       dealer upcards


       *                  X       A                          *              9       X       A

    17                   s       g                          16               g       g       g  but not 8,8

    16                   g       g                          15                       g

    15                   g       g

    14                   g       g                  Doubling allowed after splitting add

    13                   g       g                   these splits:

    12                   g       g                          your hand        dealer upcards

      8                            g                          *            2       3       4       5       6       7  

      7                            g                         66           $

      6                            g                         44                                      $       $

      5                            g                         33           $       $

                                                               22           $       $


Now please forgive me if the charts are slightly shifted in this version. The charts are done by hand to leave as little formatting in the textfile as possible so that this can be viewed and printed out etc., as per the opening statement. The key to this system for learning basic should still be clear however, though you may wish to work in your own computer to lineup the charts better. What is next is to look at the outlines for each section of the above charts, by only marking the changes, from what we do normally with a hand, rather than having h, s, d, etc.


“your” hand     dealer upcards

       *                2 3 4 5 6 7 8 9 X A

      s18                                  # # #

        16            # # # # #

        15            # # # # #                           notice the skull with cap outline?

        14            # # # # #

        13            # # # # #

        12                  # # #

        11             # # # # # # # # #                   notice the gun shape of the hard

        10             # # # # # # # #                      double downs?

         9              # # # # #

        A7               # # # #

        A6               # # # #                             notice the chart goes over one step for

        A5                  # # #                             every two down for the soft double

        A4                  # # #                             downs? This is our soft double

        A3                     # #                             “stairway.”

        A2                     # #

         99           # # # # # . # #       Pairing 9s you pair 2 through 9 except

         77           # # # # # #            you leave a gap for the 7 upcard.

         66              # # # #

         33                 # # # #    .

         22                 # # # #              Pairing 6s through 2s is shaped like a box with the lid slid back.


For late surrender:               9 X A                      For early surrender:  X A

                                    16     # # #                                              17         #

a “T” shape                 15        #                                                  16      # #

                                                                                                   15      # #

                                                                                                   14      # #

                                                                                                   13      # #

                                                                                                   12      # #

                                                                                                     8         #

                                                                                                     7         #

                                                                                                     6         #

                                                                                                     5         #

and a shape they would call a King Author’s Tournament at the Excalibur: a pikeax.


The added pair splits would be:

 your hand       dealer upcards

                        2 3 4 5 6

                66   #           

                44            #  #

                33   # #    

                22  # #

like a figure waving us to keep running in baseball or to follow him, over the hill in some battle.

There you have it. A simple shape system like this can help you visualize the basic strategy tables in the casinos. Once you recall the overall shapes you have memory clues to recall the full charts. I have taught several friends how to play basic strategy in less than ½ hour with this system. This system is now enough to go on to the first way you can get an edge in playing: couponomy.

T-hop posting on bjrnet.com , showed me some points that I have incorporated into these recommendations. Details on how this chart was prepared will be given later in the chapter on optimal bankrolls. T-hop reminded me that the bankroll units were below the number of units where normal distributions are used:

The games are coded: C, for craps; R, for roulette; and BJ, for blackjack. The parenthesis gives the number of units you should have.  As an example, betting bet 5, win 7 coupons, in craps, requires 8 units, or $40. Coupons that are multiples of others are omitted. Expectation is given as fractions of a dollar, just before the parenthesis:


Type of coupon:

Bet $1, Win $2       C .479 (3)    R .421 (4)   BJ .469 (4)

Bet $2, Win $3       C .465 (7)    R .368 (8)   BJ .463 (8)

Bet $3, Win $4       C .451 (10)  R .316 (14) BJ .457 (12)

Bet $4, Win $5       C .437 (14)  R .263 (22) BJ .451 (16)

Bet $5, Win $6       C .423 (17)  R .210 (35) BJ .445 (20)

Bet $3, Win $5       C .944 (5)    R .790 (6)   BJ .932 (6)

Bet $5, Win $7       C .916 (8)    R .684 (12) BJ .92 (10)


The bet$5, win $7 entry for roulette shows you that you are making just a little over 68 cents everytime you bet one of these coupons at say the Stardust or Riviera casinos in Las Vegas Nevada. That means that this coupon is the same as a check written to you for 68 cents, in the long run, every time you play one. As little as $4, as promissed in the first chapter, is enough to get you started (for craps even $3) with almost the same element of ruin as optimal betting will have once you begin counting and setting your bankroll for the best relationship between ruin and the growth of your bankroll. I won’t say that these tables are totally optimum in that the number of expected hands to double the lower unit bankrolls is often less than 30 bets, which is below the number of trials where statisticians use the standard normal curve to approximate things like possibility of ruin. The tests used instead are called “T” tests. You should still have elements of ruin of less than 16%. Your element of ruin can be lower by continuing to bet the lower denomination coupons, such as any, bet $1, win $2, coupons, by adding the coupons that require more money as your bankroll (even this sort of mini-bankroll) grows. It is suggested that most players, except the wealthy players mentioned above, should play as many coupons as possible, and keep track of their results for awhile, if nothing else just to establish, or reestablish, the “feel” of riding the ups and downs of blackjack play. Perhaps some of you should even consider establishing yourself outside of Nevada, to obtain out of state identification (or OOSID) to play such coupons. It is easy to get coupons that will add about $140+ to your winnings in Las Vegas, per week, at the time of writing. Reno Nevada coupons are sparce indeed, as Reno casinos try to make the downtown less friendly to the type of homeless who give being homeless a “bad name.”


Chapter 3, the Blackjack Formula, revised and revisited.


My penname, Clarke Cant, began in 1980, when I went to the GBC bookstore, in Las Vegas, and I heard someone in back tell Howard Swartz, “you know sometimes the math of blackjack seems to be such a waste. There is so much effort put into analysis of what is still a game.” I didn’t know who said it, but it sounded like GBC’s founder leading someone to their car out back.

Tom, who used to hold down the title of blackjack expert, before they hired Paul Keen, told me, “that was Stanford Wong you just missed going out the back.”

I wrote a letter later to Wong concerning a free newsletter offer that he had, added this phrase (paraphrased here):

“You ought to know that the math of blackjack is an example of sampling and partition theory that has applications in particle physics, where the mass of virtual particles changes their interaction with others, much the same way blackjack changes when dealt from a single deck, and then dealt with the same rules from a shoe…”

I didn’t know then but this technique was actually new in physics and would later be used at the CERN supercollider to estimate the mass of vector bosons.

When I got the envelope from Wong, my signature of my real name was garbled, when read by Wong, into Clarke Colbey(?) in the address. I realized just how bad my handwriting was. I was also teased by a friend about my libertarian views, and how my handwriting often varried the same way Lenin’s or Kant’s did. Hmm, Clarke Cant—and the name stuck.

One of the sample newsletters was only a month old and mentioned a new book by Arnold Snyder called, The Blackjack Formula and gave some examples from it. I wrote Arnold a letter pointing out that one example was wrong in that betting gains will not rise past a certain point, where otherwise you would have an impossible situation where betting gains were more for staying and playing through negative counts, than you would have table hopping.

Snyder wrote back that I was the second to point this out, Griffin (Peter, author of the Theory of Blackjack) was the first, and that he was the first only because his envelope was on top in the Snyder mailbox at home. Also enclosed was a comp copy (then selling for $100) of the Blackjack Formula. An exposition of that method of estimating your possible winning using a counting system is given in this chapter.

Years later he wrote several pieces in his magazine, Blackjack Forum, about the development of that original book. Bits of explanation were also scattered in several letters to me about difficulties in doing a California startup, when I wrote him about the difficulties in doing a Texas publishing startup, and had sent a prior version of this book to him, originally intended to be a companion to his Blackjack Formula. Later I received a permission letter from him to include the formula in my Clarke Cant Blackjack Utilities, published in 1985 as shareware for the Atari 8-bit (6502 based) home computers, and copyrighted with the Library of  Congress. He also gave permission to use his Algebraic Approximation paper on deriving indexes directly from the effects of removal tables from Theory of Blackjack. His permission was included in the paperwork I sent the LoC and can be obtained, along with his letters about sharing the original manuscript, by anyone willing to send the LoC the copying fees (one controversy down but more fun to come). I only asked that my real name not be disclosed from anyone requesting my paperwork.

When the Blackjack Formula was first written there was little computer power available for all the simulations possible today. But virtually any game could be estimated for its return with most common calculators. The formula was also a bit more accurate than even Arnold gave it credit and with a little tweaking can be applied to today’s games with almost as much accuaracy as a 50 million hand simulation, and can still give results that are more than accurate enough to set your bankroll requirements to an accuracy that would not be noticably different for any player’s experiences.

But mostly I wanted to see this classic revised and updated because, as powerful as today’s simulators are, there are times in entering the casinos, and staying in their rooms, that we don’t want to have our computers with us ( and subject to being seized with all of our private details on their hard drives). The best example I can think of is the experience of a friend in the US Forestry Service, whose wife was doing contract programing for IGT, and had their laptop with them.

In a southshore Lake Tahoe casino, a malfunction occurred in one video poker bank of machines while he and his wife had their laptop out, waiting for their table in the coffee shop. His wife had been talking about working for IGT.  He almost lost his daughter over the incident in that when the charges of violating Nevada’s device law were dropped, his hard drive had still been “gone over,” and nude photos of his daughter were found. His family had been nudists for generations and some family vacation photos were on the hard drive.

Each component of the blackjack formula will be discussed; some of those bigger pieces will be mentioned before some of the ingredients in that piece are explained to avoid cluttering details. This sort of top down explanation will be easier to understand. That means however that some variables will be given before they are labeled or explained. Be patient therefore as you read through this chapter and some of the others. Most labels will be explained, as will changes from the original formula. …all will come out in the wash…


BJF=Blackjack Formula result; BJF=BA+PA+RA+SA

BA=betting advantage

PA=playing advantage

RA=rule adavantage

SA=starting advantage

H=spread, in this use it is the ratio of your average high bet to your waiting bet and is based on playing all hands and not table hopping.

P=number of players to your left; the original formula used the total number of players. This change is made to note how “depth charging effects,” from Snyder’s Blackbelt in Blackjack, compensate for playing with others at your table.

N=number of decks

LH=the upper limit of where your spread can be entered directly. If the ratio of your average high bet, to your waiting bet, is higher, use LH for calculating the BJF and your actual spread for things like your bankroll estimates.

BE=betting efficiency which is virtually the same as the correlation between the count you are using and the effects of removal for the type of game you are playing. There will be details on how to estimate this later.

SQR=square root

LH=38*[C-(P/30*N)]^2/SQR(N); the original formula used 20*N. Spreads that are more than this exagerate your edge. Use LH also if you are table hopping out when you don’t have an edge in the games you play.


Your BA is then:



The PA estimate of your playing expectation, for using playing indexes rather than basic strategy, is something that Snyder termed an example of his “jazz mode” of doing math. The formula is:



C is the fraction of cards remaining undealt when the dealer shuffles. The formula overall is more accurate with this estimate, rather than using an estimate for C based on the number of cards when the dealer begins his last round, which you might think of when you consider the simple fact that betting gains only come from the cards seen before the last round.  Many elements of the BJF are not precise in themselves but where errors thankfully tend to cancel themselves out. This is one example of this.


CC=correlation coefficienct

IP= inner product


The inner product is the sum of each individual count value (or tag being the more up to date term) multiplied by the effect of removal, going card by card value. For the betting CC these values, tweaked at bit by Arnold Snyder, give good results for most games:


Ace       2       3       4       5       6       7       8       9       X (used here for all tens)

-.61      .38    .44    .55    .69    .46   .28      0    -.18    -.51


Add in the tens effect 4 times; there are 4 tens per suit.

For Hi Opt I these are the inner products:


Card      effect of removal  Hi Opt I card value             inner product term

Ace         -.61                                 0                                0

 2             .38                                 0                                0

 3             .44                                 1                               .44

 4             .55                                 1                               .55

 5             .69                                 1                               .69

 6             .46                                 1                               .46

 7             .28                                 0                                0

 8              0                                   0                                0

 9            -.18                                 0                                0

 X           -.51                                 -1                               .51 *4=2.04


The inner product is: IP=4.18

The CC formula is: CC=IP/SQR(SSE*SSP)


SSE=sum of the squares of the effects of removal, in this case SSE=2.818

SSP=sum of the squares of the values of your point count; for Hi Opt I SSP=8

For Hi Opt I the CCis just over .88; your BE is thus rounded to .88

The CC is not used directly for estimating the PE, but is used in a formula that Arnold Snyder has stated several times came from his jazz mode of doing math, with a model that made Peter Griffin cringe, but which gives very good estimates never the less. Snyder developed predictive effects of removal that derive from an count Griffin developed to give optimal single parameter results with values ranging up to 180. Here we have another instance of a math model that gives good results but in no way is precise in its ingredients, and which also gives results which are accurate enough that no one will ever be able to feel any impact of their errors.

These special effects of removal are:

Ace       2       3       4       5       6       7       8       9       X

.25       .3      .43    .62    .85    .61   .58     .22   -.26   -.90


SSE= 5.508

IP=6.11     CC=.920447984,  OK that is a little more digits than the formula is accurate to, but what the hell.

The final PE is: PE=[1.405-(1-CC)]*CC/2


Everybody raise their hands who got .61 (rounded) for the PE for Hi Opt I.

The playing advantage now has all of its ingredients. I hope you can see how much easier it was to explain working from the top down rather than getting lost in some of the details.

The playing advantage requires some adjustment for some rules (just wait til we go into explaining a variable V we will use too). Bustout is an option that the Riverside in Laughlin used to have on some 6 deck shoes, where you would bet on a hand busting in one hit by using your counts infinite deck (later, be patient) index for insurance This rule adds a whopping 8/7 to your PA. If your game doesn’t include insurance (boo on the Cal-Neva in Reno Nevada for not having it) you subtract 1/7 of the PA. You can add 1/7 of the PA if your games has late surrender (well the Cal-Neva did have it for awhile). This late surrender gain presumes that you are at least using the “Fab 4” indexes that Don Schlesinger popularized (I usually use more).

Another adjustment is Snyder’s RA, or rule advantage, for more general reductions (usually)  in your gains from rule changes. Your playing advantage is reduced for things like being limited in your double downs in d10 games (be patient) or when the dealer hits soft 17s.


Your SA is your starting advantage, or lack thereoff, as you begin playing a fresh shuffle (which is not the same thing as aproaching a continous shuffle machine unless it is just after new cards are put in, provided of course that the machine is allowed to cycle through a few times and it helps if the cards are “washed” by being spread about randomly before being loaded).

SA=DA+V; V is the variation from what used to be called standard strip rules but is now labeled DOA s17, which is double downs allowed on any first two cards, except the first two cards after the first hit when you split cards, and that the dealer stands on all 17s.


The Blackjack Formula originally gave V tables for 1, 2, 4, 6 deck games, but the advent of shuffle tracking has complicated things. Many times shuffle trackers in their play are playing segments that are odd deck sizes that wouldn’t be easy to fit into such tables. This either requires nearly 100 columns (which would resemble a certain…well skip it) or the solution here of 2 major columns and interpolation between them. Both the one deck and infinite deck Vs start at zero and change with each rule changes as given below:

              One deck V         Infinite deck V  explanation (excuse?)


No d11        -.81                 -.73              cannot double on 11

No d10       -.52                  -.45              cannot double on 10

No d9          -.132               -.076            cannot double on 9

No sd         -.131                -.083         cannot soft double-- want Pappy’s excuse?

No $A         -.16                  -.18              cannot split aces (not asses)

No nonA$    -.21                -.25               cannot split the others either

No re$        -.018              -.039              cannot split again

Re$A           +.03                +.08             do it again to that ace I drew

DA$              .14                  .14     this is the flavor if your game is otherwise DOA, double after splitting.

DA$ 11 only  +.07               +.07             occasionally in Puerto Rico (where NY democrats go to find spare voters who get Musicals written about them)

DA$ 10 only +.05               +.05              but seriously if 10s but not 11s (obviously you add these if your flavor is in a d10 place where you can only double if you have at least a 10)

DD3+         .+.24                 +.22            can double after taking a hit

2to1 BJ     +2.32                +2.25           If this is only with one suit of ace or ten divide by 4; if this is in a matching suit divide by 4; if this is with a specific ace and ten divide by 16 (or go ask Stanford Wong and bug him—just kidding)

h17           -.19                   -.22              dealer stands on most 17s but hits soft 17s


These rules don’t fit the above chart:

Later surrender, abreviated LS usually, is +.022 in one deck, and +.069 in all multideck s17 games. LS in h17 games is +.036 in one deck and +.088 in all multideck games.

Early surrender—just a reminder, this is before the dealer is able to check whether they have a potential blackjack, is +.62 in all s17 games, and +.71 in all h17 games.

The rest of these V modifications apply to all 17 flavors and all numbers of decks:

Redouble, adds +.4 to your Vs. In this rule you can double your bet again (4X your original bet) if your double down card still gives you a double down recommended hand. This is just the rule if your double on a 9 draws a 2.

21 pushes a dealer blackjack adds +.17 if it allows ties with a dealer’s tenup blackjack and another .17 if you can tie an aceup blackjack as well (which only happens in games which take no dealer hole card until the players are finished with their options).

ReDA$ adds +.6; a test if you are understanding the abreaviations. It is a rare rule indeed.

ReDA$ just aces; which is the above when you can soft double and redouble if you split aces.

Joker declare in blackjack is where the pack has one or more jokers that you declare the value of when they are drawn as one of your first two cards. It adds: +4.2/joker/N

22 counts as 21 with coupon now I really mean ask Stanford Wong. His explanation is not too clear in Basic Blackjack. The sources of these tables are Basic Blackjack, Theory of Blackjack and some of my own simulations (and snide remarks).  Actually this is from a one time coupon in the north shore of Lake Tahoe so there is little to worry about. The rule actually adds 14.6% of your bet with each coupon use.

To use this information to determine the V for your game add the infinite deck values and then the values that apply to one deck.. V1 would be your one deck figure, while Vi would be your infinite deck figure. Your final V is:


That concludes the initial way to estimate advantage, the next chapter 4, will detail estimates of expected value and optimal betting. Pappy’s excuse reffers to Pappy Smith, father of the owner, and the real founder of Harold’s Club, sadly missed in Reno (club and man). He more or less originated limiting doubling down to 10 or 11 only, to allegedly protect service men from throwing their money away doubling more, during WWII.


Chapter 4, the truly optimal bankroll, to inifinity and beyond. (or my 1982 views on bankroll)


I couldn’t resist saying that.

Actually advantage is not a very good way to rate games. Advantage implies some simple game like the biased coin flip that analysis of optimal betting was first based on. When I first started playing, back in 1977, the only way to approach bankroll estimates was to follow a proportional betting scheme and hope for the best. The Blackjack Formula is just one approach to estimate your gains per hand too. But you should know my feelings from the first part of chapter 3 and my poor forestry service friend. There is even a quirk to the BJF that makes for higher accuracy in estimating gains than in estimating advantage.

The BJF based formula for G, or gains per hand is:

G=AB*BJF/100 (the 100 is there to convert from a percentage to a decimal figure)

AB is the average bet per hand; pr is the probability of making your average high bet. The probability of your high bet is based upon your betting optimization (the best work on this is by Brett Harris as given in his count booklets and his numerous archived postings on bjmath.com), mainly at what true count you raise your bets at. It also has to involve the probability of that true count, which itself is derived from the number of decks in the pack and the depth of the shuffle point, in conventional games, and with continuous shufflers it is either dependant on the usual delay in the reapearence of cards or the relative depth you choose to use (be patient). Sources for such information would have to start with Snyder’s book series on Beating the _decks, where a separate book was written for 1,2,4,6 and 8 deck games, or a simulator that can give you a probability of a given true count, given the number or decks in the pack and conventional shuffle point.

If you are jumping your bets between a high bet and low bet, your average bet is:


If you are using a proportional betting schedule that calls for different bets at each true count you expand out and:


A similar set of formulas is derived from  Wong’s Proffesional Blackjack for calculating standard deviation per hand. Once  G and sd are found for one hand approximations can be used from the same book, or similar mentions in Theory of Blackjack by Peter Griffin, to adjust for math measures such as variance and covariance between hands, if you typically play more than 2 hands. Blackjack Attack by Don Schlesinger is useful here too, but the famous Chapter 10 will comein for harse words over its overly timid safety dancing recommendations for your bankroll.

The simple formula for sd is…


In the formula for proportional betting schedules the H and pr terms expand as:

H1^2*pr1+H2^2*pr2…..,+H^2*prn; we take the sum, multiply by the FBV and take the SQR.

Fortunately FBV, or flat bet variance is mostly tied to the probability of your double downs and for virtually any game is:

1.2 for d10 games where you can double on 10 and 11 only,

1.28 for DOA games, and

1.32 for DA$ games,

with very little if an variation for other sets of rules, the only exception to which is in the rare DA$d10 games (I knew I had that entry for a reason) go ahead and use FBV=1.32

I first developed my own estimates of required bankroll back in 1982, in the first version of this book that Arnold Snyder talked me out of publishing. I was very impressed with the Blackjack Forum Articles on the Gwynn and Seri simulations that were written up asking, How True is Your True Count? I quickly discovered a version of what is now known as the Yamashita equation or the number of hands needed to break even against a known level of standard deviation units of downward fluctuations. I came to this by trying every possible way to do away with advantage as a measure of game earnings and only using standard deviation and expected value, here labeled G. VERY important was that I strictly followed all of the rules for such ingredients in that I strictly treated every outcome as a combination of expected value and deviation, and that the number of trials involved had to be closed and set to a definite number. By closed I mean that each trial had to be analysed from the view that you had to have no knowledge of the paths of outcomes in each trial, just the results.

First of all the bankroll had to be:  B >=X*sd*SQR(T) where X is the number of standard deviation units you were interested in and T is the number of trials. The only real revision, from 1982, of this is that today, with knowledge of barrier ruin instead of bankroll you might change the term to total funds potentially used in surviving T trials. As will be seen later however barrier ruin is a special and not general case. This relates to another rule in such analysis in that statistics is not a prediction of outcomes, but is a prediction of “future histories” or analysis of looking backward at the way you arrived at different results.

Every level of fluctuation had a breakeven point where:


The simple reserve calculations for how much reserves would have been used if I survived a number of hands to a given degree of probability is related to the number of standard deviation units of survival I wanted to examine. Classic Calculations of ruin that followed the recommendations of J. L. Kelly indicated that optimized betting would involve a long term ruin of 12% probability which is approximated by fluctuations of 1.2 standard deviation units (acctually 1 sd unit would be more correct except I am choosing to still use 1.2 Recently there have been some studies on chaotic approximations to the bell curve that call for curve broadening. We will briefly mention this in chapter 10 after a review in chapter 4A).

The maximum reserves used could be found by solving the combination of equations for the number of trials involved:

(1.2*sd/G)^2=T and B=T*G or B=(1.2*sd)^2/G;

Personally I decided to use the label HD or hands to double instead of T.

It would approximate the characteristics of long term optimized betting, even though here I was studying a double or nothing model based on a fixed betting strategy in that it could be demonstrated that long term, after this survival, 88% of all paths could be shown to result in infinite growth and 12% in ruin.

Put in simple terms anytime you breakeven, after playing a given number of hands there is a standard deviation measure for the fluctuations you have survived and that sd measure will allow you to extract a measure of the maximum use within those bounds of your reserves. The more you play, the less likely it is that you will fall to any breakeven point. Your playing safety tends to increase as the SQR of the number of hands that you play.

A simple thought experiment can easily show how boundary ruin vanishes, long term and how the above expression long term is a practical optimization of the number of units required for your playing bankroll.

Everytime you at least breakeven, you have both decreasing probabilities of being behind and an increase in the maximum reserve usage, over the number of hands you have played (and keep in mind that strange future history statement above). If you consider the entire history of your play and bankroll, the maximum reserve usage grows without any new moneys being put into your bankroll, unless you meet ruin.

Clearly the more you play, the more your bankroll safety increases not from the original money put in play, but from the total expected value being more and more being able to offset your fluctuations.

This is a simple fact that people who commonly advocate drastic underbetting fail to realize. Bankroll safety arises not from initial safety of your betting but from having the optimal combination of expected value PULLING your fluctuations.

My worst nemesis on this point has had to have been Don Schlesinger. Speaking against his Blackjack Attack is difficult due to his reputation, but usually when I have posted on the internet on these topics he has posted to claim, Clarke Cant is selling snake oil and directed everyone to ignore Cant and read Chapter 10 of his Blackjack Attack, Playing the Pro’s Way.

Well the Charts in Chapter 10 are indeed acurate and correct, in inclusion of this barrier element of ruin factor, which, as I say above, does tend to approximately double the element of ruin when you follow a fixed betting strategy. It happens because the closed box I mentioned above doesn’t let us know about the initial distribution of our losses until the hands have been actually played. Concerns about barrier ruin are overstated to begin, in his estimates, (which he later had quoted in several papers on bjmathcom) in that the box is opened, and the ways in which ruin is increased by early fluctuations is then recalculated and added to the initial calculations of long term ruin. So at best his famous charts are a bit exagerated.

What makes them totally useless for estimating your bankroll requirements for the best long term growth of your bankroll however is that barrier ruin is not a permanent problem. Several times in chapters 9 and 10 Schlesinger admits that barrier ruin exists only where you cannot or will not lower your betting unit size.

The fact is that barrier ruin vanishes once you have enough head room in your bankroll to lower your betting sizes by a factor of 3 to 1 and still meet minimum appropriate table game requirements. The fact is that any one of the advanced playing techniques  in this book (so far only optimized couponomy has been given and it itself is enough to aleaviate the risk of barrier ruin for most $5 chip players). To keep on adjusting bankroll requirements, once barrier ruin is gone, as everyone (unless possibly personally tutored by Don) would be lead to by being directed just to Blackjack Attack, is about like insisting your child keep on using training wheels on his bicycle—forever?

I first mentioned that I was using HD or hands to double, to rate games and conditions, instead of advantage in a published letter to Blackjack Forum, that I believe “hit the stands,” in 1983. I incorporated this math in my 1985 Atari program package. Copies of the stack of letters from Snyder had to be sent along to the Library of Congress because of the derivative nature of that package. This work also derives its expected value estimates from Snyder’s work and would be covered in the same permissions for derivative use that were then given. Nothing more needs to be said.

The earlier tables for couponomy were calculated with the following formulas for expected value and standard deviation:

For roulette even money bets wins were calculated as 18/38 probable, and losses as 20/38 probable, with an sd of 1. For craps I used wins .493 probable and losses .507 probable, with an sd of 1. For Blackjack I used a different approach from Theory of Blackjack, which has a section on couponomy, and an sd of 1.1  Some rounding was used for coupons where the HD was less than 30 hands/trials, to match more accurate T-test values for standard deviation. For initial playing barrier ruin is negligable with the suggestions to continue playing lesser coupons for at least a time as your mini bankroll grows. The subsidy factor involved of providing $140 per week to a couponomist is based on using the major coupons listed at the date of writing in Charles W. Lund’s mini board on lasvegasadvisor.com Only the coupons with easy availability to myself were included, and considered to be played within the restrictions printed on them. After approximately 12 days even the homeless person in chapter 1 would be able to approach this level of earnings (given enough bathing etc. too). After 1 week playing at the level of mini bankroll needed to play the least favorable 5-7 roulette coupons, the couponomist would have an element of ruin that is less than .003%. Applying the level of earnings above $140, each week to commonly available $5 single deck games, in the Las Vegas area, is more than enough, even limiting play to less than 4 hours per day, to have that same player betting black chips optimally in any of several single deck games within two months, even if couponomy is ceased after 3 weeks. More about this will be added in the Chapter on how to safely move on up.

Generally games of less than 10,000 hands to double will be the investment games that will build your bankroll. Lesser games are best saved in that they often will be the games, that are tough to grow your bankroll, but may have high limits that can give you a high, though fluctuating income, from playing, and profitable recreation as you move to larger investments.


Chapter 5, Psi blackjack is limited.


There is a big difference between the justified bashing of hunch players and those who use all sorts of bizzare divination schemes and voodoo to try to win at blackjack and the rationalizing of the so-called skeptic who in reality is only a conventionalizer. In truth the misslabeled skeptic is just as out of touch as the voodooer often; it is just that one is more politically correct than the other.

It is hard to justify the claims that there are no such things as magic and ESP. Let me begin by describing one who tried to apply ESP to blackjack and failed but was one of the developers and early remote viewers, in the military application of Remote Viewing back at SRI in Palo Alto California, and one who succeeded but found that he was paying a terrible price in emotional damage and disapointments, but where both are well documented to absolutely have such abilities (one hidden in his ability and still in part classified and one very well known). They are Danyon Brinkley, author of 3 books on the subjects of ESP and near death experiences, and (to use the penname he told me in 1988 he used when writing in the old Atari magazine, A.N.A.L.O.G.), Dr. Lee S. Brilliant.

I wrote to respond to a classified ad that ran in Blackjack Forum, in 1988 asking for teammates for playing in Northern Nevada. He identified himself, in the course of our 2 or 3 phone calls, as a California neurosurgeon (which I verified) and went over my qualifications. When I mentioned instances of trying to spot side damage from the effects in Wong type warps in cards (from the action of the dealer peeking under 10s and Aces to determine if they have a blackjack) I mentioned using the techniques Margret Corbett wrote about in, Help Yourself to Better Sight, and the tactics Peter Giles developed from that book, that Wong first disclosed in one of his early newsletters and included in his, Blackjack Secrets, book ---

As an aside, Giles recommended that you take a shuffled deck of cards and remove one card with your eyes closed, and place it faceup, but unseen, into the deck at random. Now riffle through the deck as fast as possible, only slowing down enough to barely perceive the value of the card. The drill is designed to build vision speed and visual acuity by forcing the software that regulates our eyesight to engage while we are riffling though too fast for our concious mind to slow down that process. The goal is to also relieve eyestrain.

---he mentioned that he had been involved in a program that sought to do the same thing with ESP and wondered, since I was well versed in the Corbett methods if I wished to try to develop a way to apply this same method to blackjack play. That was a little too weird for me. He did mention however that the program did involve classified research where the consciousness labs, the industrial design center, and the cybernetics labs were all involved. Through the books by Courtney Brown (not too creditable I thought), and David Moorhouse (very good and honest, his book was Psychic Warrior), and Ed Dames (who I felt was very open about his work though a bit irritating in using Scientology type descriptions such as calling methods technologies, and giving possible disinformation in some of his predictions), you had revelations about one project that used these labs together: Remote Viewing.

Exactly like the Corbett methods for eyesight, RV tries to relax the viewer, with the assistance of a guide and stop the conscious parts of our mind from censoring and distorting some of the hunches and feelings that we all have from time to time that cannot be explained by conventional views. To avoid selective observation and tendencies to explain away perceptions various forms of relaxation are used. To extract the information that may be contained in those moments of perception, the subject still has to be conscious however.

The Remote Viewing proticals are designed to provide double blind target selection and have the remote viewer only describe to his guide, the aspects of his perceptions that first only relate to sensations of touch, feel, smell, taste and sight, and then finish with an attempt to see if all perceptions can be engaged without reawakening those parts of our conscious mind that tend to distort our perceptions (as mentioned above). A database of information is assembled from several remote viewers and the data is prepared and tested against known information about the target. In application there is a continuous cycle through such data to further refine targeting goals.

That is not too practical for casino use, in that there is a need to quickly change consciousness states, that while the remote viewer is going to be fairly fast at it, is not fast enough to apply live in any casino. When data is gained offsite it will be totally out of context. There should be applications however, assuming of course the validity of remote viewing, to possibly noting changes in casino policies and rules in the future.

The man who actually has been able to demonstrate being able to win using such methods in casinos, was Danyon Brinkley. He survived 3 near death experiences and developed medically verified (One medical handbook of Disabilities even has a listing of Brinkley’s syndrome, as developing an ability, often uncontroled and disrupting, to engage in ESP abilities due to high electricity exposure)abilities to perceive things like hole cards and developed an extensive track record of sports wins that enabled him to take care of expenses while recovering from his initial injuries in a lightening strike. In his book, Living in the Light, Danyon (he would prefer his first name be used and through personal experience has one hell of  a sense of humor, I just wish I had known who he was when I met him), describes, reading hole cards in 53 straight times, in live casino play. He wasn’t catching views of the hole cards due to vision damage from the original lightning strike.

The major problems for him were the emotional grief he faced after trying to get players and bettors he would aid to follow through on promises to donate to various charities and the shear emotional pain he would feel from detecting the manner which average casino patrons would be actually trying to lose, where gambling was actually a bizzare cleansing ritual.

What this means for the open minded blackjack player is that it is necessary to admit the possibility that our hunches may hold some useful information, but to realize that there is nothing free easy or automatic. Lee gained his abilities through rigorous training and a hard nuts and bolts approach to life almost as demanding as the skeptic’s in analysing new data from perceptions. Danyon gained his abilities through terrible injuries to himself. Almost obvious, but somehow never said much before is that we need to test, analyze and practice using information from ESP with the same rigor that we would test our ability to detect flashes of hole cards. Nothing is going to be true or accurate just because it came from some psi related source anymore than information coming from Snyder, Wong, Thorp or Schlesinger, or me, is true, just because it came from someone having some standing.

The ability for psychokinesis to actually alter outcomes appears to be limited as well, despite the humorous claims from the webmaster of the bjrnet.com voodoo board, Zombie (who has been a great help to me several times). The most that any practitioner can do, it appears is alter outcomes from their means, by standard deviation measures proportional to their abilities. In simpler terms even the best practitioner of voodoo or magic, say someone able to perform the feats done by the characters in the movie, The Craft, is only able to disturb short run and not long run outcomes. They can bend the curve of results but not “hang it.”

What that means is that it is best even for the best Rver, literal frybaby, or a board certified witch doctor to stick to known or more conventionaly verifiable strategies.


Chapter 6, Bangers and other tasty tricks to do to a casino.


The peeking devices are designed to limit the damage done to cards when the dealer would conventionaly look under aces and tens to determine if they had a blackjack and avoid the inevitable tells they would exhibit as they reacted to the hole card and their chances of winning or losing versus the players. They come in various forms but the most typical ones now in use involve a window and mark on the face side of the corners of the cards designed to limit the information available to the dealer to only the fact that an ace is not in the hole when a ten is up and a ten is not in the hole when an ace is up.

The machine I will describe as my typical device is the type that has the dealer turn the cards 90 degrees away from the customers when the card is an ace up and pointing toward the customers when the card is a ten up. The corner of the card that typcally doesn’t have the index at the corner is the corner that is inserted when the ten is up, while the corner that typically has a small ace is the corner inserted when the ace is the faceup card. Dealers are trained to more than anything else, when they first deliver their cards to themselves, don’t accidently flip the bottom card up and expose it.


                      ---!  Guide


!  J                    !

!                        !

!                        !

!                        !

!                        !

!                        !

!                        !

! __________ J!   This would be the view of having a jack as the top card



                                        ------!   Guide                                      


/!                                        A !

 !                                           !

 !                                           !

 !                                           !

 !                                           !

 !A____________________!           This would be the view of having an ace as the top card


(and I am sorry about the graphics folks)

The pressure is at the edges of the cards as they are slid into the guides, but is lighter in the middle of the card. In normal procedure the pressure, being directly on the top card, and not the bottom one, bends the top card deeper and differently over time. The diagrams below show the typical bends for the backs of aces, tens and low cards that results.

( down bend symbol

) upbend symbol


Ten card (back view)       Ace card (back view)     Cards 2 thru 9 (back view)


___________                   ___________                  ___________

!                    !                 !  (                  !                !  )                )!

!                  ( !                 !     (               !                !     )          )   !

!                (   !                 !        (            !                !       )     )      !

!             (      !                 !          (          !                !           )        !

!        (           !                 !             (       !                !        )    )      !

!   (                !                 !                (    !                !    )           )   ! 

!(_________!                   !________(_!                 !)_________)!   


A slight clumping effect can be found too that will be covered in the chapter on shuffle machines.

Insurance gains are 20% greater in these games due to being able to distinquish between aces and tens as hole cards. Typical reading accuracys are in the 90% range if they are found at all. The level of the bending is slight however and compares with the bending found in normal hole card  peeking by only being about 1/3. Wong’s, Basic Blackjack, has the proper playing strategies for bent cards in general.

The first series of countermeasures for this playing was found in the Safejack systems. They use a small bar code section to have the table read the hole card directly, and are the only system to use no guides. The need however to have the hole card reader do a wide scan however is highly error prone. Cards other than the dealers tend to be picked up. The system is subject to crashes whenever the number of hands being played changes. You can also build a simple device that will crash the system by causing false readings.

Simply take any bar code reader and couple the signal directly to any digital recorder device, such as the chips in Birthday Cards that let you record an audio message to the recipient. Once recorded, instead of feeding this signal to a speaker, feed it to any high power led that has both visual and infra-red light output. Place your device in the back of a blinking badge, such as those that circulate every Comdex show in Las Vegas, or any large ham radio convention (thanks Wayne Green, the publisher of 73 magazine, and Knightmare, the hacker, between articles by both of you I thought this up). The device will keep outputting the signal that is in the same band as the scanning laser system, except that it will now register the card you select. Haven’t you ever wanted the fun of playing a game with several thousand aces?

The next countermeasure was suggested by the Griffin Agency reportedly and I got another report that it originated with a dealing school owner in  Reno. Both were related to me by sources at the Cal-Neva in Reno. That countermeasure is to have the dealer only push the bottom card into the reader. In that procedure all cards are bent in the way  the diagram above shows for low cards, but the downbends are now upbends. Profits for the player however are still found due to 2 causes:

the procedure is clumsy where the dealer has to pull the hole card in, and tends to cause the dealer to flash the hole card.

the dealer has to run the top card along the surface, smoothing it along.

The result is that in this procedure there are still distinquishing bends between high and low cards, though we lose being able to distinquish aces and tens, because the high cards are flatened out. The game becomes the same as you would find with conventional peeking and warp play.

The last group of countermeasures is readers that use guides still but move both aces and tens for checking the same way. These use infrared bar code markings or dot patterns. They tend to play the same as in the diagrams except there is no turning to distinquish between aces and tens and the low cards do not endup with 1 or 2 diagonals. Part of the phenomenal accuracy of bangers is that only low cards can endup with normal procedures with both diagonals bent. The direction of the bends is not affected by this countermeasure.

Cut Control lite is a strategy for when a dealer flashes a card during the last riffle of a shuffle, in typical 1 deck, or highly favorable rules 2 deck, games. The following table shows recommendations for jumping your bets high or low on the first round of play based on these observations. Best of all, you don’t even have to be the person cutting to take advantage of this. You gain cover: not always betting low on the first round, without the loss in expected value that random betting off the top would bring.


Card exposed         position in deck exposed       position of cut                  Bet

High                        High                                       High                             Low

High                        High                                       Low                              High

High                        Low                                        High                             High

Low                         High                                       High                             High

Low                         Low                                        High                             Low


The chart continues but is easiest to remember by memorizing just one line and remembering this simple rule: whenever you change one entry from a valid line you must change one more entry to get a valid line.

Full cutcontrol is something covered in Dustin D. Marks books, Cheating at Blackjack (and the same title except with squared added), though this is certainly information that is freely available to all players and thus not cheating.

Banger play, since the stress is at a diagonal of the cards, creates other oportunities in handheld games. The bends are not necessarily fully corner to corner. When the bends are off corner a wear point is created that marks the cards so that they can be viewed from the side of the pack when held by the dealer. A player can gain much of the profits that techniques known as ace keying (not covered in this book; this book is not complete so much as what the title implies: Therapy for your game) are able to gain in shoe games, in handheld games.

All of these tactics are profitable or can greatly extend your playing time in the casinos, but can compromise some attempts at optimal spreads in your betting strategies. For this reason Chapter 4 was split to have this material inserted, but still labeling the next chapter 4 (4A) because of its completion of chapter 4.


Chapter 4A, the rest of Chapter 4.


Lets return to this equation (Xsd/G)^2=HD.

The results are that for a given number of standard deviation units we have a number of hands where we pull ahead and stay ahead, at that level of fluctuation. By staying ahead we reach infinite growth (in the ultimate long run, pit boss tolerance willing). All of the Classic Optimal bankroll examples of even money payoff games show an 88% chance of such success, and 12% chance of failure, when a fixed betting strategy is used. By approaching the same results with fixed betting I will show the same outcomes with a blackjack bankroll, as a test of that bankroll being equally optimized for growth in the same long term.

The level of breakeven success that corresponds to 12% ruin is 1.2 sd units. By itself then (1.2sd/G)^2 only shows the number of hands where such breakthrough is achieved in the long term future history of our bankroll, or our playing.

We can explain both barrier ruin and optimal bankroll requirements for this long term growth by examining all the outcome pathways that would/do take an infinite number of hands to either reach double or nothing outcomes, by looking at those paths every HD hands. With the smallest amount of upward drift from that set of paths, which we are looking at as a flat string of HD number of hand sections, we reach, “infinity and beyond,” in our results. With the smallest amount of downward drift we wipeout. That pathway is the dividing line between ALL the infinite possible paths that wipeout and ALL the infinite possible paths that achieve success (the initial HD length of hands is finite; infinity divided by any finite number is still infinity).

Bankroll requirements are thus (1.2sd)^2/G for all the infinity of outcomes that survive the first HD number of hands without ruin. Thus I consider the optimal number of bankroll units we should divide our bankroll into to achieve optimal growth over infinity to be given by this equation, in that the outcomes of this type of fixed betting match the outcomes of fixed betting in more classic examples.

Within every HD hands win/loss order can be distributed in every way . Initial, or early losses only have the initial bankroll amount to offset your bankroll level from going toward ruin, while later fluctuations are offset both by your initial bankroll amount and the accumulated expected value of your hands.

Before HD hands are finished that total offset to possible fluctuations is less than it is for the optimal infinite growth of your bankroll. The average chance of ruin is thus about double what the long term chance of ruin is, in the first HD number of hands. The barrier ruin effect rapidly decreases thereafter.

In chapter 6 we covered techniques that either add camoflage without costing expected value, or that add tremendous expected value, but would make hash of any precisely optimized betting spread. It is far more important to optimize the application of a less than optimal betting scheme than it is to depend on a scheme that is compromised by such tactics.

Once a well known poster on bj21.com and bjmath.com, claimed that I was wrong to claim that you could have an optimal bankroll requirement calculated with a less than optimal spread, and the example he gave was a schedule that was much like a typical one an opposition bettor would use (as covered in Snyder’s, Blackbelt in Blackjack). The point I tried to make then and make here is yes. Yes the ability of such a player to determine what his optimal unit size should be should not depend on whether or not he uses a precisely optimal spread.

The best methods for finding the optimal spreads are those written by Brett Harris and archived on bjmath.com I contend that my formula from 1982 –which has other labels now – gives bankroll requirements for any positive expectation spread. It does not give an optimal spread however.

But just like Brett Harris I consider hands to offset to be a better way to rate games than advantage, DI or SCORE. HD, other than being based on offsetting 1.2 sd units, rather than just 1, is the same as his H0. Since HD here also gives the hands to double a bankroll it would take on average I think it has intuitive merits as well.


Chapter 7, Shuffletracking to the Limits, how to use the blackjack formula for ST too.


Imagine if you will going in your favorite casino where you find a 4 deck shoe game and the dealer is shuffling an orange deck and has a red, blue and green decks stacked already to load into the shoe. She tells you, “hold on a second while I finish this deck. The pitboss is not in a good mood so I will have to shuffle on the last round where a card appears from the green deck. Otherwise I would deal them all out.”

You quickly salivate and try to come up with all of the ways you could borrow money if you needed to in that you are playing 3 single decks stacked together, but with a shuffle point, C=1, all the cards of each deck are dealt out and even part of the green deck. The estimate of your edge using this book, or BJF, is sky high.

As the chips go back and forth and your pile of chips eventually rises higher and higher (and turns ever more disgusting colors, but higher denominations) the pit boss suddenly appears with 4 red back decks and says, “enough of this crap.”

The shoe is now loaded once again but now the dealer shuffles each new deck and you notice that she is grabbing precisely 26 cards for each riffle. She deals. You notice that she has just gone through 51 cards, and of course the burn card, when on the next round she turns the discards 90 degrees and lo and behold, the discard rack is wide enough to fit the cards edgewise. She keeps all of the decks still separate.

You are every bit as good as she is, in eyeballing the cards, and are still able to tell when you are going from one deck to another during a round. Suddenly the pitboss appears and growls, “hey let me show you how I want you to shuffle these damn cards.” With that he takes the cards, it was time to shuffle anyway, and washes (moving the cards about face down as if shuffling a dominoes set) all 4 decks. He picks up precisely 52 cards and counts them out, saying, “just checking to make sure there are 52. Hey what count are you using there buddy?”

You meekly respond, “hi-lo,” as you try to reach your cell phone in case you have to face another rough session with the guards and want to have your lawyer on the line.

“Well bud, I usually use hi-lo myself. I am not as good at the Uston +/- or the Zen these days. Everybody seems to be using hi-lo.” With that he counts the 52 cards and keeps tossing and adding cards until he shows you the deck and asks, “could you count them sir? Hey I want you to wash all the cards and deal them,” he says to the dealer.

She responds, “oh he is not in a very good mood,” but she keeps on making sure each deck totals to 0 hi-lo points.

You don’t know what the hell to do now. But you go ahead and play as the dealer still grabs 26 cards in each hand, while doing each riffle, and still stacks the discards into separate deck size piles…..

The estimate is now your BJFT=BJF*CFS; using the BJF for C=1, still dealing each subdeck, here with a size of 1 deck, to the last card, and CFS=BE^2. For counts that don’t equate the ace value and tens value, you have to adjust the count for aces.

You adjust a count for aces the same way that you would adjust count values from an unbalanced count to obtain an equivalent balanced count.


The K-O count uses the hi-lo numbers plus counts the 7 as +1, or:


A         2         3         4         5         6          7         8         9         X


-1       +1      +1      +1       +1        +1        +1        0         0         -1


To evaluate the BE and PE, using the Blackjack Formula we must adjust out the imbalance, which we do by subtracting 1/13 from each of the above. The K-O count becomes:

-14/13 +12/13………._                                    to counting the 8s and 9s as –1/13, and the tens as –14/13.

(since Ken Fuchs said such nasty things about me and a prior draft of this book I am going to act childish, pout and leave it to the reader to figure out the PE and BE for the K-O system)

If you use the K-O in true count mode you have the full power for your BA and PA calculations. If you use the running count mode your effective PE is cut in half. For the K-O system Ken Fuchs has good betting tables (good for this count…) that let you use the full BE figure. For some systems this should be cut down as well.

When you adjust an ace zero count for the aces you do the same calculations except the count initially now has a minus imbalance. If you were ace adjusting the Hi Opt I count, used in chapter 3, you would have a minus 1 imbalance. Zen counts would initially use –2 for the ace. You would add +1/13 to the count values (or tags if you spend a lot of time on bjmath.com) and evaluate the same way.

In both converting unbalanced counts to equivalent balanced counts, and ace adjusting a count that has aces counted at a lower value integer than the tens, you adjust during play by keeping count of the number of ¼ decks seen,  the aces as a side count. For typical unbalanced count adjustments you substract one point for each ¼ deck seen, from your running count; for typical ace adjustments you add the difference between counting ¼ decks as +1, and aces, as –1, to your running count. The true count is found by dividing by the number of decks in the initial pack unseen. Ace adjustment of this sort goes back to the first edition of Beat the Dealer, by Edward Oakely Thorp. Converting  unbalanced counts occurred to many, many people, but the first to publish, and the first to write a formal proof of the validity of this, was Brett Harris. Brett Harris has also comeup with an unusual series of counts that use the additional information that subtracting that –1/13 gives, to have a count only have one or two levels of integers involved in its card values (tags), but give the same playing information as a much more complex count.  Now back to our strange casino….

On every shuffle she checks each deck to make sure each subdeck totals 0 hi-lo points. But pretty soon the pitboss shows up and again and yells, “we are going to show him we know countermeasures. Shuffle them and deal them out just like the joint next door does.”

Magically as you play a screen flashes in your head, and reads, “the next subdeck has +3 points more than zero. The next subdeck has –2 points than normal. The last subdeck in play has –2 points more than normal,  the discard subdeck has +1 more point then normal.” But you keep on playing and play the first subdeck as if the running count through it were 3 less than your actual count. You play the next as if the running count were +2 higher than normal.

If you were to magically know that a deck had additional points in it than zero, you should play as if the running count differed by the negative of that addition. For the first subdeck we have SD1=+3; play through as if the running count were 3 lower. SD2=-2, play as though the running count was 2 higher. SD3=-2; play as if the running count were higher. You still play as if  each subdeck was separate, but your win rate goes up.

The reason is that each deck now has volatility within it – which is how profits from counting come about, and an added measure of volatility from being mixed in with the other subdecks. Your overall edge is: BJFS (your total edge playing this shoe game with this magic). BJFS=SQR (BJFT^2+BJFO^2).. BJFO is the BJF for the game if your were playing without this magic.

You win even more money than ever. The dealer starts hinting at romance, and the pitboss suddenly reapears and says, “don’t grab so many cards each time.”

Your profits skyrocket as she grabs only 13 cards in each hand. Your subdeck size is ½ deck now. This is why the V tables were left in interpolation form and didn’t have entries for the hundreds of possible subdeck sizes. This imaginary casino uses a one pass shuffle, leading to the following relationship:

Subdeck size (which you use for the BJFT) =Grab size (the fraction of a deck that the dealer uses for each riffle)*2 (since there are two grabs in each riffle) *passes (the number of times the entire pack of decks is broken down and shuffled)

This is how you estimate the BJFS for when you use the magic of shuffle tracking.

I appologize to people like George C. and others who may have covered this territory before and would like to give credit to him, and Arnold Snyder for some of the information that follows, but mostly I am going to use the above terms, as opposed to others like slugs, plugs etc., and follow the general description of shuffle tracking given by Michael R. Hall, who posted early on about shuffle tracking (ST hereafter). What we will add are my own labels , some tips on using the built-in error checksums that I believe are left out in most works to date, and some opinions (of course).

Approaching a fresh table you should first of all observed the shuffle used and the mapping of the shuffle. Cards as they are used are placed in the discard rack such that you should look at the rack as having sections you label, having counted them:










G1 is the first group of cards of G size number of cards. Most casinos deal using lay and pay these days, mainly for survelience reasons. The dealer may pickup the cards that complete the first grab size as she picks up the cards from the player, 2 spots to your right. You must keep that count in one register, whether it is in your head, using some memory trick (as in, The Memory Book, by Jerry Lucas and Harry Lorayne) or with some device (rotating your chips is suggested almost to death, but it works). You must then start the count for G2 on the hand one spot to your right. Unlike handheld games it is not recommended that you adjust your count too often during play unless the game is faceup or you can keep another spare register available in your head. You should count each card for each G section as it goes into the discard rack.

When the dealer reaches the shuffle card she will take out the remaining cards – called plugs, or sometimes the procedure of handling them is called plugging – and will either stack the discards on top or place them on top of the discards. It is slightly better that the dealer stacks the remainder, on top of the discards, than the other way around. If the last round is not finished on a G boundary, some of the remainders can be associated with the last incomplete G, or Gn, using the labels given here.

There are a variety of tactics to use to map the shuffle, that other works can cover, and where Arnold Snyder has developed mapping labels,  where shuffle maps can be read too by paid users of his rge21.com, and where similar can be found to paid users of bj21.com and to registered shuffle tracking project workers on bjmath.com (I tend to avoid these paid or registered sites simply because I know how personal information could be hacked by the misfortune of teaching an otherwise dense ex-wife how to hack). For one pass shuffles the finished pack of cards should now be viewable as a stack of subdecks:




Take careful note of two or more of those SDs, and, well all of them of course. The highest value of SD of course, which for shuffle tracking, see above, is the SD with the most MINUS count total, and at least one or more of the SDs that are drawn from the discards ONLY, and not the remainders (or plugs if you still insist).

Now comes the cutting ritual. Long term your profits are enhanced if the cuts are made as close to the SD borders as possible. About everyone, except Bob Fisher (who I respect on everything else it seems except one prank that I still laugh at), recomends that you try to cut the most profitable subdeck to immediate play first, if you are cutting. I agree, in that you can then possibly be requested to cut by the other players—they feel you are a “lucky cutter,” as everyone will have a better chance with the best subdeck played first. You don’t really need the best subdeck to be played first, and knowledgeable pitbosses will often see this and suspect you are shuffle tracking from it, but your goal is to simply try to see that the cut is on a SD boundary (by the way SD is also a usual abreviation for single deck and this label should help keep in mind what ST can do). Whether or not the cut is, you begin counting for your playing decisions and G counting immediately (at least the SD you saw split up is now at the back of the pack and won’t “bother” you anymore, and you still have approximate information, that at least is good enough to raise or lower your betting on, about that fraction of SD section you are starting on—maybe it wasn’t ruined.

The last step is your error checksums. This involves the count in your selected SD, coming to the predicted count from your tracking information. Once again it helps if the cut fell on a SD boundary.

I know that this is a lot of work: counting G sections at minimum, and keeping separate registers, while counting as well through each already mapped SD section. The best way to handle it is to concentrate on the new G sections. Begin keeping a second count, called the temp, but thankfully with the same cards as you count them for the new G sections, everytime you are definitely in a new SD. Play that SD as its own subdeck, and with the negative of the offset from previously tracking and assembling G sections for that SD,  added to your temp. You can even bet and play by the true count of  the temp count, but be prepared to have to switch if completion of your hand takes you into another SD. If that happens, start the temp over, but keep on with the counting for the new Gs. Think of  say seeing a hand bust that has a 4,X and X. For level one counts this hand is –1. Think of one minus thrown in the G and one in the temp.

Finally we are near the end—but you are correct ST is very hard work. It is at least 3 times as hard as regular counting. But few other books and posting have ever dared to put down what it takes to take ST to the absolute limits.

The last step to discuss is your checksum SD, when you come to it.  These guidelines tend to match several trials runs on one of the popular tracking practice programs.

If your checksum SDs match predictions, you are ready and are likely getting the full advantage that this section predicts.

If you are off by +/-1 you should depend on getting 80% of the BJFT added to your edge and move your fraction of bankroll down accordingly.

Off by +/- 2 lower the BJFT for betting estimates to 60%

Off by +/-3 lower the BJFT to 40%

Off by +/-4 drop the BJFT.

You are not expected to have to work out these levels during play, but each session should have unit sizes already worked out to drop down to. Suppose you are betting in a game that has a fully mapable 2 pass shuffle, where the grab sizes are about 18 cards. Your suddeck size is about 1.4, (go ahead and round to 1.5) and 6 decks are in the pack. You might still have a huge edge overall but your unit size might go from $100, down to $15, depending upon the other variables. If your error is at the final level your betting should drop down to a normal betting spread for the game overall.

That is all the steps to take ST to the absolute limits but there are several pointers as well. Your mapping gets detailed, not having to estimate G sections averaged through the remainders, faster with deeper shuffle points. You don’t just gain from a higher BJFO component. Don’t be afraid to leave if a new dealer changes the shuffle (map-wise) or has different grab sizes. Grab sizes, and errors, can be compensated by adjusting your SD size upward by playing 2 SD sizes together, but you still should base your tracking on the grab size. Have as many estimates prefigured as possible after your initial scouting. You can use the BJF in a coffee shop, but believe me, this book is not going to be welcome in any casino, which you should be able to see after reading the prior chapters (maybe after casinos settle down and realize few people – as usual – are not going to apply themselves?, but only the future knows.). Many people may decide that the other tactics, such as bangers, are more than enough to add to their shoe playing. I don’t recommend that ANYONE (except maybe….naw too cheap a shot) use ANY unbalanced count for ST. You may or not want to take ST to these limits but I have yet to find any valid way to handle the numerous pivot adjustment that would be necessary to these limits, or any way whatsoever you could adjust your pivots to any unusual SD sizes. If you cannot take a system all out, why bother?


Chapter 8, Amazing health tips and test of your attitudes to health. Yes too, plans to build and muscle relaxer and blood cleanser.


By now the intricacies of what it would take to drive every ounce of profit out of ST have taken their toll. You want to relax and unwind and let the tension out of your muscles. This chapter is for you. It is also going to provide a lot of cheap shots, but what the hell you bought the book and are entitled I guess. I am writing this damn thing and still playing because I still have symptoms of a conective tissue disease called fibromeleosis, a serious form of fibromyalgia, and occasionally some symptoms of Chronic Fatigue Syndrome will surface as well. I will suddenly feel tired and some serious autoimmune problems will develop if I don’t rest right away. At the same time I have to stay in shape and exercise or face scarring around muscles and joints. Any 9 to 5 job is ladden with pitfalls. Not even with the Disabled Americans Act is it possible for most employers to accommodate this problem. Casinos and playing blackjack gives me the freedom to live life to the full. But rest assured it has not been easy and there have been several alternative remedies that have helped along the way.

But what is your attitude about seeking alternatives? Believe it or not people do in fact die from literally hundreds of diseases that have remedies that are unusual. Examples abound from unusual cancer claims to heart resection surgeries that once were out of favor, but are now are standard for cardiac insuficiency.

But don’t take my word for it. Dr. Richard Sullivan was the US Surgeon General under president George Bush, and a former director of the American Cancer Society, and had some very unusual views on alternative therapies, despite his position, in his fairwell speech to the ACS on medical research ethics.

He talked about Alternative Cancer Therapies being ignored that often, freely admitting it, everyone knew worked, but were supressed or ignored, simply because they could not be used with normal definitions of medical ethics. He singled out the Gerson Diet therapies for cancer, saying that all research confirmed every detail in the claims, Gerson made, in his book, Results of 50 Cases, but that together no doctor could feel comfortable using them, in that taken as a whole the Gerson methods would preclude conventional treatments, that might be also needed in various emergency situations. He also talked about treatments that were well known to have good results, but which could not be tested in any double blind studies.

The death of actor Steve McQueen is a perfect example of this. McQueen did not actually die of cancer, despite claims of his widow later on. His previous wife, Ali McGraw stood by his decision to seek laetrile therapy and a diet much like the Gerson therapies in Tijuanna Mexico. The preponderence of evidence is that his lung cancer had died and that he was nearly free of cancer, his tumors dead, before he died. The actual cause of death was allergy to anesthesia during emergency surgery to remove DEAD tumor tissues that had floated around his chest cavity, and were interupting heart beat. Even the most successful alternatives in medicine are going to have interactive risks.

Are you really ready to take responsibility for your health and the possible results of your decisions? Is your family going to second guess your decisions in an emergency? The reason I bring all of this up in a blackjack book is that your attitudes about health are going to say a lot about your attitudes toward success and whether or not you should even be playing in a casino. They are about as good a test as any of some of your possible hidden agendas. Along the way, in this chapter that point is going to be raised again and again as we look at simple methods and devices that can relieve your casino stress, and enhance your wellbeing, and some say save your life from certain conditions and diseases.

I used to hate  Radio Shack (tm) for their convienience and  the fact that their prices were always 40% higher than mail order. I grew up making it a holy crusade to shop lift from them as much as possible. But if you needed that part now they were always there and their tech support used to be the finest anywhere. The parts given can be found there and at outlets such as JDR Microdevices, Digikey and Electronics Surplus, among others. Some parts can even be dumpster dived. The text description of the circuitry of the first device you will probably want to draw out, and some soldering is required in both. One is a pulsing device that helped me relieve muscle pain and scarring. The other is a deep tissue magnetic device that has the same results. Both are designed to mildly electroporate (ionize or electrify if you will but not that much) your body, so that pain signals are blocked and various toxins are more easily removed.

Parts list:

2 100 ohm resistors

1 1 meg variable linear resistor

1 100 mfd electrolytic capacitor

1 500 mfd electrolytic capacitor

1 small LED virtually any type will do

1 small signal general purpose PNP transistor

1 small signal general purpose NPN transistor

1 9 volt battery and clip (clip can come from an old 9 volt battery)

1 8 ohm to 1 Kilo ohm audio transformer

1 500 Kilo ohm resistor

2 aligator clips

misc. wire and etc.

the resistors can be any small signal type.

The connections are base of the NPN transistor to the negative lead of the 100 mfd capacitor and one side of the variable resistor, and one side of the 500 K ohm resistor. The emitter of the NPN transistor is to ground. The other end of the 100 mfd capacitor and the center terminal of the variable resistor are connected to the collector of the PNP transistor and one side of one of the 100 ohm resistors. The collector of the NPN transistor is connected to the other 100 ohm resistor. The other lead of this resistor is connected to the cathode (negative side) lead of the LED. The other lead of the LED goes to the base of the PNP transistor. The unconnected lead of the 500K resistor, the emitter of the PNP transistor and the positive lead of the 500 mfd capacitor are connected to the positive connector of the 9V clip (the is the female connector for the clip and the male connector of a 9 V battery). The remaining lead of the remaining 100 ohm resistor is connected to one of the 8 ohm imp. leads of the audio transformer. The other lead of the transformer is connected to ground as is the other battery clip terminal. Two light gauge multistrand wires are connected to the two 1K ohm imp. leads of the transformer and to the gator clips (and I solemnly swear that any print version will have nicely illustrated diagrams). I generally use 2 of my watches as electrodes and place them over a sore muscle. In about 2 or 3 minutes the barely perceptable pulses, which can be adjusted, just watch the LED to verify the device is pulsing, will cut pain and inflamation without the muscle jerking of higher voltage devices of similar design have. Please use this device only with battery power.

The other device takes any camera strobe flasher. A coil has to be made or converted somehow, but the 2 best solutions I found are the coils of old larger woofer speakers, or taking a spool of magnet wire and rewinding it onto a same size spool. It is recommended that you use lots of  shoe “goo", goop", or the clear version of “liquid nails" around the soldering you do for this device. After the coil is wound, with that option, or the voice coil is extracted from the woofer, wrap the coil liberally with electricians black tape, every way you can. Now take the flash apart and find one of the leads going to the small strobe unit. Cut one and solder speaker size wire, or small diameter lamp cord to the two parts of the cut. You should then use the original batteries or solder new power leads to the old battery leads. Even the small flash units in disposable cameras will have enough power. Place the coil in a small plastic sandwich bag and over the painful area. Use the original flash leads or traces and wire in a small switch. There will be a thump when the flash is triggered (also fun for shooting small bolts across the room and bulk erasing video tapes).

Now for another attitude review (in a sneaky way you are testing yourself as you read this in a near subliminal fashion). Just like Dr. Sullivan mentioned in his speech this type of device has other well known and researched properties that both work and there is no way in hell the FDA will ever approve (but might wink at).

Charles Ostman is perhaps the world’s leading authority on nanotechnology, or the science of very small machines. This field runs from small robotic devices, now used by the US customs service (he designed them reportedly, but this is a grey area, not classified but still highly compartmentalized), to motors that can be etched onto microchips, to having viruses modified to produce tiny screws and other microparts. He stated on a recent Art Bell program, “all viruses depend on one or more of the outer protein sections acting as a spring and thrusting the body of the virus through the cell membrane.” (check the audio archives on artbell.com)

Dr. Kaali has done research at the Einstein School of Medicine in the area of virus destruction using small microcurrents, in the test tube and body, that are able to cause the spring section of individual virons to jam open and cause the virus to not be able to enter cells. Unless the FDA has somehow blocked the site, despite everything checking out, bio-electrifier.com has most of the papers alleging that such devices also do the same thing with the AIDS virus. Most of the material is prepared by a gentleman named Beck. He writes similar snide remarks, but well researched, as is my style, about the hidden agendas even AIDS patients have about life and death, that speak of hidden suicides by patients even after they have remissions from such treatments from such devices. The AIDS virus has a site, labeled Lp5, that is its spring.

That is why I have included this discussion. If an AIDS patient, literally watching their body rot away from opportunistic infections that would in most of us only cause an itch or skin rash, can have such powerful hidden self destructive agendas, are you sure about yourself?? Can you really walk the knife edge of playing blackjack, where results really don’t mean a damn thing until 100s of hours of play and yet where you have to be totally engaged to keep the count (this is why too I put this section after the section on ST)? Can you really say you are ready to play until you are able to accept the consequences of your actions and are not going to blame others or break away from any authorities?

Now the test! If your thoughts were that somehow you would not use such a device in the face of AIDS, until it was absolutely proven you are not ready. Equally so, if you were not ready to accept the dangers etc. But without the distraction of this presentation those thoughts would have remained buried, if this were just another examine yourself presentation.

Well the devices do work well getting rid of those aching muscles from being in those stools too long. Try to set time aside to also practice whatever form of meditation that your religion (or lack there-off) allows you. This can be as simple as simply sitting up, (upright positions usually are best) and closing your eyes. In no system of meditation do you try to force yourself to relax though in some you may use a chant-like thought, to divert your normal thoughts. Don’t fight those thoughts. Instead let them flow freely until they fade and allow your mind to get quiet. Now enjoy the quiet. Some may even become interested in Remote Viewing from this. I really think it is useless for blackjack, but the training tapes by Ed Dames are accurate but all of the scientology type terms he uses put me off. Any search engine will take you to his online texts I think. The best instruction is probably Joseph Moneagle’s. Try it if you wish. Good luck!!


Chapter 9, how to beat those feared shuffle machines (and why they are probably illegal too).


Perhaps the best information on the internet so far about shufflers in the “Grimore” of Green Baize Vampire’s (that is his penname and he is a hell of a nice guy too) website (perhaps easiest to reach through the links page of bj21.com). He gives a detailed reading on the first generation of continuous shuffle machines that is simply great. Most of the details concern how to determine the latency, or the delay time, in rounds, until cards reappear. These early CS machines would place a round’s discards to the rear of the pack and shuffle them in, and quickly be ready to play another round. The clocking of the latency is important in that, even though the early machines would place the discards “to the rear,” the number of cards shuffled in would vary. For example: if an early CS used 6 decks altogether,  this had to be tested too by clocking (it might actually be 5 or 7 decks), mainly by keying cards in a way but in the reverse of keying cards to spot aces. Instead 3 cards are memorized that are in the discard pile next to each other and the number of rounds for the same cards to appear together would be tested. With enough samples to have statistical significance, that would be used as the average delay. Once the average delay was established, the playing strategy was to count that number of rounds and play, using as your true count divisor the remaining cards left. The running count you played by is ONLY the number of rounds that corresponds to that delay. If you had a delay of 8 rounds, corresponding to just under 4 full decks at a full table (amazing that people did play them and play newer versions now),  in a 6 deck game, you would ALWAYS divide the running count for ONLY the last 8 rounds, by 2.

The tedium here was the need for the clocking etc. People, GBV reports one team was lead by Stanford Wong, beat these machines in spectacular fashion. The detection teams at the casino would have their hands full having to keep an expiring count  and would and will today having to reprogram tracking surveilence software, for such plays.

The newer King  (shuffle master gaming ) and the Quick 5 " (licensed to 3 makers I believe) machines are supposed to end the possibilities of such counting by having the possibility of  the hands just discarded appearing on the same round. Well whoever sold the casinos on this idea didn’t do their math too well, because this machine is beatable still, and doesn’t require the clocking to determine “average latency,” that the other previous CS machines did.

Both are sold with literature that states they use a random number generator that moves the discards quickly (I am paraphrased from both so that the similar language doesn’t have to be duplicated) in a normal distribution into the cards being readied for play, but ends the dangers of card counting in that cards may reappear in 100 rounds or on the same round. The King uses 4 decks, while the Quick 5 uses 5. The King is taller and moves the stack up of cards up and down to a fixed shuffle mechanism. The Quick 5 uses a moving shuffle mechanism. For both there is one quick riffle of the discards into the main pack, so that your players will not have to wait or be led to walkaway during even the quickest delays while other machines have to be loaded and unloaded. That insertion is similar and has a normal distribution. Both sellers talk about improvements to the random number generators used being improved, to end the danger they can be shuffle tracked.

That normal distribution for insertions still causes a delay in the reapearence of the cards. The fact is, that you can select the latency you wish to play to. If you select rounds corresponding to 1 deck, you will adjust your true count always by counting the last one deck’s worth of cards, dividing the running count by 3 and multiplying the count again by ¾, or simply dividing by 4. If you select 2 decks worth or rounds,  you would divide by 2, and then multiply by ½ or again divide by 4. Strange you say…damn right! But just because the equivalent true count divisor turns out to be invariant does NOT in any way mean that there is not any exploitable latency. Chapter 10 will take a whimsical trip through physics and philosophy to show how invariance is nothing to be feared and not reason to jump to conclusions—except for bad mathematicians.

In this instance the shallower penetration is going to be better to play. The reason that you multiply by ¾ or by ½ is that the probability of having early reinsertion lower your count and profits goes up as you count more rounds.

Suppose you chose to count 3 rounds at a full table with 7 spots. That is close to .3 or 30% of the pack. You have a 70% chance that those cards will take at least 30% of the pack to reappear. You are facing 70% of the count; with 30% chance of the cards reappearing.

It is all reciprocal; as you choose to count more cards the significance of your count goes down. 

Approximately the best profitability would be in counting 2 and ½ decks (about 2/3rds of the pack is the actual maximum)  before you let the count “expire,” but for me the approximate 30% solution is best.

The BJF is: EC=effective depth or C; BJF=SA+3*(BA+PA+RA), using EC instead of C.

In both examples it would seem to be very shallow penetration, but from a careful reading of  Theory of Blackjack (all editions would have this information) by Peter Griffin, all the hands played are at that depth. It is if you were allowed to play thousands of shoes by first seeing  75 cards + burned, played the round (and included the players cards now on the layout, which helps too –so never let the top counted round “expire,” in your running count until the end of each round). The edge is not spectacular but it is still an edge and few casinos will believe it is there; just look at the odd fact the true count divisor is always the total number of decks in the pack again! It is too strange, but the income player, with a black chip and higher bankroll, would do well to play these games, raise their bets ferociously (at least for now) and milk that casino for every possible comp. Even after it is proven this edge exists the surveilence  staff is going to find it hard to prove that the player is counting (thankfully there have been enough outside -- and even a few inside quiet stockholder -- lawsuits where some degree of proof is needed to throw out possible counters –the Coast Casinos group excluded).

There are still some of the original non-continuous shuffle machines problems that need to be discussed. The biggest problem relates to bangers and the more tradition problems of warps, where normal peeking under tens and aces would bend cards (perhaps reread chapter 6). I had 2 opportunities to gain inside access to information on this. One was the casino manager at the Verdi Nevada Boomtown casino telling me about the original trials of the shufflemaster machines. The other was a suveilence worker from the video room at the Atlantis, in Reno, telling me about early trials of tracking software there (management is now much more tolerant of counters and has come to realize that allowing some skilled players a narrow edge is necessary to their own profits as well, to keep others playing –we are supershills at best, to the casinos).

First I was told that it was at Boomtown that the first regulations were written up by the Nevada authorities (gaming is such a misleading term I won’t use it even though it is part of their proper title) banning  having normal peeking under tens and aces, when shuffle machines were used. Even during the first tests, the uniform shuffle action, on cards with even the slightest bends, was enough to jamup the shufflers and cause massive clumping of cards. The most recent public comment on these closed regulations was reported in the Reno- Gazette Journal, when the Alamo casino, in Sparks Nevada, was approved to first add table games, on the condition that shuffle machines and peek readers be used on all tables to avoid (para.): the losses due to hole card play and malfunctions of shufflers that happened when regulations were violated at other properties….owned by the owners of the Alamo etc. That there is such a regulation is hard to verify openly in Nevada, but it is specific that procedures not be allowed that put bent damaged cards through any shuffle machines.

Yet from the chapter on bangers it is obvious that cards are still bent by the necessary guides used in the various practical peek reading systems in use. A careful reading of  the open regulations on changing cards however admits  that peek readers damage cards too. Just point your browsers to Gannet news service links or the state of Nevada sites.

This don’t-do-it-but-we-admit-that-this-happens-in-normal-use admission has been used by myself and others to argue that Nevada, and other gambling regulators, have not fully upheld their own regulations, including in recent class action lawsuits alleging deceptive video slot machine displays. Normally gambling (until the Federal Government comes in to, no doubt, eventually make things worse) is a state issue but this contradiction was used to reopen discovery in those cases. There is massive overlap between the peeking and shuffle device makers and the video slot and video poker machine makers. Normally there would be no case in that these “makers had been approved by competent state authorities: thus the US Federal Courts have no jurisdiction…”..That didn’t happen. As long as these dern things are used with peek readers they are probably illegal.

And even if the legal mess is untangled (read quietly settled with lots of “hush money”), there is no real danger that any shuffle machine not having at least normal distribution will ever be licensed. Already these makers have created a device that actually makes it likely for deck compositions to possibly remain in play longer. By not always taking discards deep (to the end of the pack) there is a delay in the time that the pack is “turned over,” and cards at the end are on average available for play. Not every discard packet is sent deep; when a riffle is done deep the cards at the back still have to wait to come forward, even though the wait becomes less and less. For the average player, in rare but noticeable circumstances, streaks would have some validity, due to this changing deck compositions, for the subset in play. What would take 8 rounds of full table play, to push forward rear cards into play would take, under the same circumstances (I am assuming a 4 deck shoe and half deck size inserts;  these parameters vary in the new CS machines) would take 64 rounds, with the Quick 5 or King machines. Taking out the normal distribution of where the riffles are inserted. “To finally beat those damn card counters,” would be suicidal. Players playing all manner of otherwise, in normal games, bogus progressions and parley systems, would have, indeed already have, some real possible edges.

The clumping effects are present when banger bends are combined with shuffle machines. My Atlantis source quit when he was told to ignore an older couple he was checking out for possible card switching (a cheating move you can read more about in the books by Dustin D. Marks I already mentioned), and count down, both mentally and with the tracking software they were reportedly testing, a suspect counter. When I told him about what I was told at Boomtown, he begged his job back and gained access to files having records of about 10 million hands of checked play. He setup a script to filter out and examine basic strategy players and their results. I didn’t take proper notes but I would estimate that to be cut to about 1.5 million hands (I missed a golden opportunity). He was able to combine with files from several other beta test casinos, to get this number. He reported that basic strategy players did .2% better with the shufflers used with peek readers etc. This is comparable with the no-shuffle simulations Wong included in the latest edition of his,  Profesional Blackjack, but still within normal ranges for fluctuations.

Anecdotally the boss at Boomtown stated that in trials they tended to beat counters (those trying to count, but who are losers in the long run) about as normally, while those who stuck to basic and flat bet slightly won. It is quite possible that both are just fluctuations and selective observation too, but it would make sense for the clinging of like bends to like bends to be amplified by this combination (shufflers and peek guides).

Im a sure however that the CS machines have more of a problem with this: that they damage cards more and have more clumping. Whenever the riffles are preformed deep, there is more pressure that can keep cards together. If you go back over the banger diagrams you can see where the typical bends are more unique too: aces have unique bends, tens have unique bends—more unique than the regular warps that were found to cause problems in the initial shufflemaster trials. There is also more likelyhood that low cards are going to be placed deep than high cards. Even with the small sizes used before shuffle of the discards, a hand with more cards before busting is more likely to be madeup of small cards than large cards. The bust card is placed lowest on the discard pile, but the rest are more likely to be little cards. When sent deep the discard pack with lower cards is going to have a slight tendency to push the rest forward. These machines tend to do over time what “cut control lite” does.

All in all the casinos themselves have made a terrible mistake in listening to the idiotic consultants who helped develop these devices.


Chapter 10, Why I believe in Anarchy, Chaos, and human progress.


Part one, why real Gods don’t give a damn about your little 16 versus 10 problem.

Consider if you will all of the attitudes people have, not against gamblers who lose, but gamblers who win. One exwife was a strict southern baptist (who I still wonder why I married), who would rant and rave about how terrible the casinos were, and would claim to approve of me beating them, but harped against me for disrespecting God for doing so, and seemed more upset I beat-em than she claimed to be over the way they beat others.

The roots of this go back to ideas of predestination and God knowing all and how gambling was letting God decide where the money should go (even today it is alleged that the LDS church –the Mormons—are opposed to gambling not on strictly moral grounds but that their priesthood system still uses “the office of the urim and thurim,” to find out God’s will, and that gambling is opposed more, in colloquial terms, to prevent bad ripples in the force…). Anything else using gambling methods was to mock God. It was Cardano that pointed out that where the ball on the roulette wheel fell was decided more by the opportunities for it to fall that any selection by God.

God deciding EVERYTHING made a big comeback in the time of the protestant reformation when Calvin came along. Freewill was just a dellusion of sinners trying to deny the grace of God…..to more or less decide arbitrarily who goes to hell, even if you accepted him. A more live and let live view of God slowly developed over time.

Then came quantum mechanics with all of its strange twists of logic and common sense---but the math cameup right and the equations predicted the outcomes of experiments well. The universe wasn’t built like a perfect watch like Newton thought afterall. Randomness and not being able to really findout where an electron was, developed in the full rules by Feynman eventually, came about by looking and relooking at the fact that the frequency of a photon was always in proportion to its energy. It turned out that the orbits of the electron were determined to stay only because the inability to find its precise location behaved like a wave, and the wave had to have a pattern that didn’t put more than one set, of all things PROBABILITY numbers on finding the little sucker. It was shear dern randomness that kept the universe going in the little things and there weren’t any clockwork laws.

After Planc got it, Einstein wrote a paper on how the best explanation was that light was only emitted in discrete packets he called quanta. After starting the field he decided he didn’t like it and went into relativity. DeBroglie figured out that the old e=mc^2 stuff if applied to an electron’s mass and orbital momentum energy, meant that it might have a wavelength by applying the Planc stuff to the total energy state. The orbit would get screwed-up if this wavelength didn’t form a standing wave. Shrondenger and Heinsenberg argued politics and physics for 15 years before they decided to leave it at Shrondenger’s Wave Equation that every real particle had to have a stable energy state and a stable energy state required that every possible pathway through time and space had to have integer DeBroglie wavelengths over that interval.

Dirac made things complicated by adding relativity to quantum mechanics, discovering things like anti-matter and making it necessary for Richard Feynman to have to discover new principles in statistics to explain virtual particles and having to make equations work  forward and backwards because of that darn Dirac.

Relativity began with a Scot named Maxwell, who developed the first equations to explain electromagnetism. It was all thought at the time that he used tensor (exact differential) equations to save on paper and ink costs. Another bad explanation of Maxwell was that his electromagnetism required something called the aether for electromagnetic waves to vibrate in. An american, Michelson ruined that idea by showing no results for trying to detect the aether by examining the interference patterns in a huge concrete table floating on mercury with mirrors along 2 perpendicular paths (he must have also been trying to pickup cable for free too?).

An Irishman named Fitz-Gerald simply decided that aether must have somehow had properties where it got dented by differences in motion, so he wrote an equation to correct assumptions and went back to the nearest Dublin pub to chase women and raise hell but smart hell so as to be tolerated. Einstein was of a similar bent (he liked to please the women so much they sometimes said “ouch Albert.” His first wife divorced him for “physical incompatability” while his second wife insisted on spending their honeymoon in a pushchair around the gardens of their hotel. Albert, after his first trip to the USA developed a fasination for chearleaders and American Football, and even talked DePathe films into doing a few films about it, which were bizzare, due to being filmed in Germany. He died a New York Giants fan, with several Princeton cheerleaders giving birth to smart children with bad hair.) but had an excuse for being lazy about math that came from reading Ernst Mach.

Mach stated that there could be no such thing as any previledged observers in Physics and that all math did for physics was insist there was. Einstein used this excuse to write about the stuff with the mirrors, by saying maybe the aether wasn’t dented, but maybe the way you can measure things is. By denting time and space any observer is just as good as any other if the laws of physics really are fair and for everyone (good hair or bad). A Polish guy named Minkowsky really upset Einstein when he proved that while each observer would have different views of events they were viewing, compared to other observers, their measurements were linked by an equation that was more or less the 4 dimensional hypotenuse of their measurements. The problem for Einstein was that there was a link but no way to show how their observations would change if they tried to visit each other. Special Relativity told you how they were linked if they were already on the way toward each other, but it had problems with how they accelerated to get going.

Einstein kept trying to do the math but all he got was tired….and writing up Newton’s law of gravitation in tensor form…and kept hating it. At one point 1912, he decided, what the hell I’ll publish anyway and everyone said so what. At this point a young lad named Swartzchild (actually blond and German) told Albert that there was a type of math that made it possible to use the same equations to describe acceleration the same way for both linear acceleration and spinning a weight about the room on a string, since you really wanted to preserve that Mach stuff, but you would have to learn more math. It was Reinman spherical geometery, where every line had to be set on an n-dimensional spherical surface, and the diameter of the surface was given by a differential equation that was most easily solved by putting it in a matrix form called a Ricci tensor.

Now Einstein knew about that e=mc^2 (he developed it as an approximation for the apparent rise in mass for objects going near the speed of light, and others, like those irritating quantum guys were using it saying, “if it’s good for the delta, it’s good for the whole damn mass”) but also saw that if accelerations were equal in their local effects and the result of increased speed is apparent increased mass,  who is to say that the bending of space is not equivalent if viewed as a consequence of acceleration, or as a consequence of the mass increase, and that if we believe those quantum guys, maybe all gravity is, is the bending of space, by mass in general, forcing a change in Minkowsky invarient solutions where bent space-time means that as you expand the time interval you contract the space interval.

That is what special and general relativity are. Invariance is just invariance the way a problem solves and doesn’t mean you are spinning your wheels the way those CS machine guys thought.

But Dirac added relativity to quantum mechanics…..but let’s just see what happens when you add quantum mechanics to general relativity that way another skirt chaser, this one in a wheelchair, Stephen Hawking did (yey Steve; way to go. Losing a divorce suit badly  by having all your conquests brag about you despite MS in court—what a guy.).

Hawking simply was willing to admit both Relativity and Quantum mechanics were true, in his famous paper (written for the Gravity Research Foundation prize competition) called, Blackholes are Fuzzy but have no hair. The strange probability things quantum stuff does created a loop-hole in the solutions for General Relativity, where something Swartzchild used to chide Einstein about, blackholes (before getting killed in WWI), turned out to be not totally black; they actually would fade out over time. The solution had to acknowledge the time effects caused by a black hole, meant that this fade-away, now called Hawking radiation, had to be spread over the lifetime of the blackhole. Hawking was a little scarred of that result and tried to gloss it over by stating that there was no information content in this artifact and the radiation would not be detectable until the background radiation from the big bang faded enough to allow real observations of Hawking radiation to be made.

Hawking goofed.

Two more papers, in 1989, entered into the same competition (it is a tradition to give such papers goofy names and use weird aliases) were, Einstein is Smiling; Feynman is laughing, by Charles Kelley (name allegedly drawn from a Minneapolis Phonebook – the paper was entered on a postcard with, “guess what this is a stolen identity,” written on it), and, All Interactions are Virtually Relative, by Odo Kubiyashy (mailed from a Star Trek convention in Lakeland Florida.) established this goof.  My original source on these papers was the shopper paper for the Dinkeytown neighborhood of Minneapolis  Minnesota that a nurse had with her, while I was being prepped for a Positron Emission Tomogrphy scan, at Hennepin County Medical Center. A poor guy got a call from the Gravity Research Foundation asking if he were Dr. Kelley.  It was so funny I had to research it further…

The “postcard paper” just stated that background radiation doesn’t really rule out detection of Hawking radiation that has information about the future size and lifecycle of a blackhole and that this timelooping must result in a new parallel universe, and that the process must include all blackholes, even those that arise out of vacuum fluctuations, and where the entropy flow is not visible (entropy increasing from a future to past flow of information, decreasing in the root universe etc…beyond  the scope of this book) due to cosmic censorship imposed by blackhole thermodynamics. The Kobiyashy paper said that all interactions that appear to be only virtual particle interactions, to observers far from a blackhole, will appear to be real particles and excede background radiation near a blackhole, providing a window for the time reversed information to flow from the ultimate fate of a blackhole, or at least the version in the observer’s universe. This proved that universes have to be branching off at all times: The Kelley-Kobiyashy conjecture. It is the accepted explanation of the arrow of time problem (why does time always seem to flow in the direction of increased entropy?) too.

Well parallel universes do damage to the idea of the Christian God who is so loving and powerful and already has everything worked out such that you either go to heaven if you accept his solutions which are perfect, or go to hell if you don’t. Such an all knowing God can only be all knowing of one of those parallel universes (not?). A real God (worthy of the capital G) is probably one who creates by allowing interesting Chaotic things to happen, and doesn’t really need to run your life or have already laid out what is going to happen when you hit your 16. Good Luck and Embrace the Chances that creates.

We really prove that bankroll equation: why infinite ruin is really lower than finite boundary ruin (and doesn’t require any new ruin formula either ).

The really total correct way to figure out ruin chances would be to use Feyman’s methods and totally exhaust all of the possible bankroll outcomes and solve them as a sum over histories. The bell curve is an infinite approximation of what an interim solution to the limits of a probable histogram would be. The formula given here is almost the same as taking infinite solutions for ruin, and solving the bankroll requirements over what Brett Harris calls his similar h0 (the long run index) as being the required bankroll to survive enough hands at a given probability to break into the long run.

That is used to approximate the optimal bet to bank ratios.

But ruin over a finite number of trials IS ALWAYS twice the Classic element of ruin, calculated over an infinite number of hands and infinite spread of outcomes. Having double ruin over a finite domain, DOES NOT change the fact that the bet to bank ratio is optimized. Otherwise the classic coin flip examples would not show optimal growth even with (diminishing) barrier ruin.

Finite ranges have to have discrete win/loss states. In the Classic formulas, expected value always exists, independent of wins or losses and is just offset by fluctuations. In the Classic formulas expected value is there just hidden at some times, while in real world, with finite states with discrete win/loss states, EXPECTED VALUE adds to our bankrolls ONLY AS COUNTABLE MONEY after a win. With a win equated to ½ probability, ruin increases by 2 to 1 within any finite range, even while expected value still rises as given in the Classic Formulas. Once outside of the initial long run number of trials, expected value more approaches the Classic approximation where expected value is not discrete. The length of the long run index, in sd terms, equates to long run element of ruin, as given Classically, even while, in the initial range, the short term element of ruin is double etc.

Having established the term discrete state expected value we must still broaden our estimates for optimal bet to bank ratios. Blackjack falls into the discrete win state only about 47.5% of the time, and not 50%. The number of discrete win states is decreased, and the impact of losses is increased. The ratio of sd/ev that has been used by Brett Harris and Patrick Sileo to develop their similar bankroll formulas is not optimum, in my opinion. To reflect the discrete state reduction in ev you must multiply by (.475/.525)^2 or use the approximate ratio 1.2sd/ev and expand from there, WHICH IS EXACTLY MY BANKROLL FORMULA AND HAS BEEN SINCE 1982! Chapter 4 was my understanding in 1982. Chapter 4A was to good deeper into why you can have extra ruin and not have it effect your bankroll. The conjecture I give here is that all initial finite ranges tend to have twice the short term ruin as their long term ruin, without effecting estimates of optimal bankroll required, with the other half of this being the well known decrease in edge,  as measured by total bets over the history of your bankroll, that Stanford Wong wrote about in his paper, What Proportional Betting Does to Your Win Rate. The same way the Wong result does not effect the growth of your bankroll, just the total money return over history, this effect ends too, with growth of about 2.5 to 3 times of your bankroll. The 1.2 adjustment is based on the newest claims made concerning the possible behavior of normal curves when examined by Chaos Theories. Generally those claims are that the effects of discrete wins and loses are such that normal curve estimates have to be further broadened by the square of the actual loss/win probability, in addition to the standard measure of standard deviation per hand, in approximately the same range of initial outcomes as the range where the Wong effect, in terms of bankroll growth, is overcome—even while it remains for the history of how much money was bet etc. While there is almost as much evidence that this becomes as unnecessary as other attempts to account for this initially higher ruin,  practical unit size rounding for the chips used in most casinos appears to extend such effects.  Neither the initially higher ruin, when you first play, or the edge over history, ever mean that you need more money for an optimal bankroll. (On further analysis double discrete ruin appears to be permanent even at infinity as your bankroll goal. Even then bankroll requirements are not doubled.)


Chapter 11, the Uston+/-, Zen, and Victor APC count indexes.

All indexes reflect my opinions on index selection and a personal preference to drop indexes of less than 50% correlation with effects of removal. I have not recalculated numbers for late surrender in the Zen and Victor APC counts as I have for the Uston +/-.

I have not attempted any i18 condensation either. This is best done individually for each count using the tables in Theory of Blackjack, by Peter Griffin (newer editions preffered for this), and following these rules:

Select an index with the highest product of correlation and importance. Keep multiple indexes that have the same value or can be rounded to the same values. Most tries at more accuaracy yield little more gain. Gain for true count point is best found by dividing the sum of squares of your point count by the inner product, as found in the third chapter. True edge indexes, in my opinion, lead one to understate this gain per true count point, and lead to drastic underbetting of some spreads. Infrequent indexes have an element of cover, in situations where playing just basic strategy makes it more noticeable that you may be a counter. All charts assume the dealer stands on all 17s initially, then give indexes if there is a change when the dealer hits soft 17s. * Indicates consulting a detailed basic strategy might be recomended. DA$ indexes are omitted. Indexes are single deck with some compromise for multideck.

The Uston +/- count performs nearly exactly as well as the hi-lo count. Difference can be good, if the pit boss uses hi-lo….


                               2         3         4         5         6         7         8         9         X         A

count values            0         1         1         1         1         1         0         0        -1         -1


your cards               dealer upcards

s18                                                                                                       h         h          .*

 17                                                                                                                              -8

 16                         -11     -11       -13     -17        s           h        h         h         0           7

 15                          -7        -7         -9     -12     -13          h       14         9         3           8

 14                          -4       -4          -6       -8       -8         14      15        12        6          

 13                          -1       -1          -3       -5       -5                                                      14

 12                           3         3           1       -1        0                                                      20

 11                       -16      -16        -17       d        d         -12      -8        -6        -4          -1

 10                        -11      -11        -12     -16    -17          -7       -5       -2          3           2

   9                          0          0         -3       -6      -7            4        9

   8                         11         9          6         3       3           13

   7                          h        17        13       12     14

A9                         8          8          6          5       5

A8                         6          3          2          0       0

A7                         1         -1         -6        -8    -10

A6                         *         -3         -7       -16   -16

A5                         h          h        -2         -8       d

A4                         h          h        -2        -10      d

A3                         h          5        -2         d        d

A2                         7          3        -1         d        d

AA                       $           $          $         $        $        -13     -12       -12     -11        -9

XX                     10          9          6          5        6

99                       -2         -1         -3         -5      -3           5       -7        -7         s          2

88                        $          $           $          $        $          $        $         $       

77                    -15        -12          $          $        $          $

66                       0          -1         -4         $         $

33                     15           4         -3        -7         $          $

22                      h           *          -3        -6         $          $

Insurance 1 deck 1.5; 2 decks 2.5; all shoe games 3


dealer hits soft 17s

your cards               upcards

                              6               A                           late surrender

s18                                          7                               9          X         A       h17     A

 17                                         -7                 17                               

16                      -17                2                 16          0          -4         -4                -7

15                      -15                4                 88                       1                              *

14                      -10                6                 15          3           0          0                 -2

13                       -7               10                14           6           2          4                  2

12                       -3               16          1-deck 77      4           0          2                  0

A9                        4

A8                      -1

A7                     -12

A6                     -12

AA                                      -10

XX                       5

99                        -5               0

88                       -4


The Zen count here gives the original values and the original indexes. Anyone using the values from Blackbelt in Blackjack has been using these (I did them for myself, and then sent an error sheet to Snyder that had those I felt were wrong in his initial printing.) indexes for some time probably. You might get a kick out of knowing, that they were done using a Timex/Sinclair 1000 computer and the Algebraic Approximation paper written by Snyder, originally.

                              2         3         4         5         6         7         8         9        X         A


                              1         1         2         2         2         1         0         0       -2         -1

s18                                                                                                                          -4

  17                                                                                                                        -13

  16                      -16     -18      -21      -25     -21         h          h        h        -1        12

  15                       -9     -12      -14      -17      -17        23       20       13        5         14

  14                       -5       -7        -9      -12    -12         24       27       20       12        18

  13                       -1       -3        -5       -8       -7                                                      25

  12                        6         4         1       -2        0                                                     37

  11                      -24      -26     -28      -32    -35        -17     -12        -9       -7         -2

  10                      -18      -20     -22      -26    -28        -12       -8        -3        5          5

    9                         1        -1       -4        -9     -11           7       15

    8                       20        14      11         6        5          29

    7                         h        28      22        19      21

  A9                      16       14      12          9        9

  A8                      13         6        4          2        1

  A7                        2        -2     -11       -13    -13

  A6                        *        -5       -9       -23    -24

  A5                        h         6       -2       -11    -26

  A4                        h         6       -2       -12        d

  A3                      16         6       -2       -11        d

  A2                      13         6         1        -6        d

 AA                                                                            -20    -18     -18      -18       -13

 XX                      17        14       11        8        9

  99                       -2        -3        -5       -7       -5        11    -14     -13          s          4


  77                     -26     -23        $          $        $           $

  66                        2       -1       -6          $        $

  33                      23        5        -5       -11     -13         $

  22                        h        *       -4         -7     -12         $


Insurance 1 deck 3; 2 deck 4; shoes 5

dealer hits soft 17s                                            late surrender


                                     6                A                                9           X          A

    S18                                           12                  16           1          -4          -1

      17                                          -11                  15           5          -1            3

      16                        -15                4                  14                        5

      15                        -21                7

      14                        -15              11                 I didn’t revise the Zen surrenders for h17,

      13                        -11              19                 from an original program run after getting

      12                          -4              30                 surrender effects of removal.

      11                                           –4

      10                                             3

        7                         19

      A9                          8

      A8                         -1

      A7                        -17

      A6                        -23

      A5                        -25

      AA                                         -15

      XX                          8

      99                          -8                0

      88                                            -6


The Victor APC first appeared in public, in an article in Blackjack Forum. While it is a level 3 count it is a bit easier than it appears, at first glance to count. All the low cards are either 2 (2 thru 7)or 3 (the 5s), while the high cards are either –3 (X), or –1 (the 9s). It is best for single decks only. In power it is the top of virtually any multilevel count, in most single deck games. A player building their bankroll, and trying for the lowest HD possible, might try it, if they can handle the difficulty. Some unusual plays have fairly high correlation indexes in this count, making it deceptive too.


                            2         3         4          5         6         7         8         9         X         A

                            2         2         2          3         2         2         0        -1        -3         0

s18                                                                                                     h         h         -1

  17                   -57     -55       -60      -58     -63       -47        s          s          s       -16

  16                   -19     -23       -27      -31     -25          h         h        10        -1        19

  15                   -12     -16       -20      -23     -22         31      31        19         8        23

  14                     -6       -9       -13      -15     -18         32      38        28        15       27

  13                      0       -2         -6        -9       -8         52       49         h         30       37

  12                     10       6           2        -1        0                                                       59

  11                    -31    -33       -36      -41     -41       -20      -15       -11       -9        -1

  10                    -27    -27       -30      -31     -39       -15      -10         -4        8           7

    9                       2      -1         -6      -12     -14           9       20

    8                     29      20        14         9        5          38

    7                       h      39        30        28      27

 A9                     24      21        16        14      12

 A8                     22      11          6          4        2

 A7                       *        0       -14       -18    -18

 A6                       *       -6      -16        -31    -30        20

 A5                       h        9         -1       -12    -27

 A4                     24        9        -2       -13     -19

 A3                     22       11       -1       -11     -15

 A2                     20       11         3        -5       -5

 AA                      $         $         $          $        $          $         $          $          $       -10

 XX                    24        19       14        11      12

 99                      -4        -5        -9       -12      -9          5      -22       -23          s          5


 77                       $        -31       $          $        $         $

 66                       1          -2      -9          $        $

 33                      36          9      -6        -14     -16       $

 22                        h          *      -4          -7     -14       $


Insurance 1 deck 6; 2 decks 6.5; shoes 7


                                                      The late surrender Uston APC indexes closely match (why are the others so off in that similar count?).


Dealer hits soft 17s                                       late surrender

                  6                A                                     9             X              A

s18                              17                      16          1             -2             -1

  17         -62              -13                      15          4             -1              2

  16         -30                 7                      14          6              4               6

  15         -27                12                     77          3              0               2

  14         -19                17                     88         10             3

  13         -13                27

  12           -5                47

  11         -37                -4

  10                                7   ..

    9          -5   …

    8           6   ..

    7          26     …

 A9           11

 A8             0

 A7          -24

 AA                            -12

  99                            -14

  88                              -8

That completes the inclussion of these neglected counts.


But a word about risk adverse indexes.

Most methods of  modifying indexes for only adding more money for double-downs and pair-splits when it is optimal for the long run growth of your bankroll are still compromises, which need not be. You can find out how much each true count point improves your return on ANY double or split by simply finding the inner product between your point count and the Griffin effects of removal for that decision, from the tables in his, Theory of Blackjack, and dividing by the sum of squares of your point count values. Instead of facing the possibility of numerous tables, for various starting edges, use this added number,  to find out if you are beyond the usual index, to have the same edge improvement, that you had when deciding what fraction of your bankroll to put down for your initial bet.

It is an easy calculation, that you would use by thinking of each true count past the index number providing so much improvement, in percent. Then you would double or split if the improvement in making the play matched the edge you estimated, when you sized your bet, for your initial bet.

That should be your final exam!


Chapter 12, Moving on up, how high is the blackjack sky and how to safely climb on up.


T-hop (a well known and liked poster on bjrnet.com) one time posted his views on this subject. Here are mine.

I recommended that everyone, except the high roller etc., should start with a couponomy mini bankroll, just to experience the feel of the roller coaster ride that even the best players and estimates of optimal bankroll are subject to. The jumps in the ratio between your bankroll and daily wins or loses in a coupon run are about what you will experience with about 4 hours of play at single deck games, played with normal estimates. I also recommend the once the coupon bankroll is up to about $150 or so that you begin to go ahead and play $5 minimum single deck games, and quit when you lose more than your weekly couponomy expectation; or, in other words, play with the money above $150, since your element of ruin, for coupons, will remain low, and quit when loses hit this barrier.

There are of course $3 minimum tables, but the spread of 1 to 2 or 1 to 3, that I would recommend, is clumsy and looks like more or a spread to the eye, at a distance, than betting with $5 chips does. If you can find, OF COURSE, good $1, or $2, single deck games, by all means start with those instead (they are just too rare these days, but who knows, the Gold Spike and Western may turn into good games—their customers will toughen you up regardless, be careful),  if you find any. Once your total bankroll approaches the normal optimal levels, you may or may not continue your coupon playing.

If you can keep your appearance up – for the homeless, or near homeless category—you should by all means continue coupon playing. Please stick to the HD measures for game quality and your required bankrolls.

Look for the climb through $1 or $2 units to $25 units to flow smoothly. A $10 to $30 spread is going from 2 red chips to a red and a green chip after all. Rounding upward will not have any real impact on your long term bankroll growth if you have at least 60% of the money required to move up. A real difficulty is going from $25 units to $100 units.

At that level, in any casino (see Max Rubin’s, Comp City), you are moving up the comp level even without any suspicions of your play. You must have explanations for having the money that are just smart enough to have gotten it, and too dumb to be regarded as a threat. You might also consider a strategy of holding out on moving your betting units and playing in the style of a so-called “money management” player. Playing directly $50 units is a mistake, in my opinion. The move from 2 green to adding a black chip looks too suspicious.  You wakeup the pit once the black chips come out. Mix in other colors of chips; at the end of winning sessions, try to remove about half the black chips you have, try to bet green, and play back if you will by going ahead and betting $100 units for a few hands, and appear to chicken out ASAP. Going from 2 green chips to 6 green chips, doesn’t bring the same heat that going ahead and betting in a black chip does.

This book doesn’t cover the calculations for how variance and covariance effect your betting. During the mid to late growth stages of your bankroll this is seldom optimum anyway. But it is possible to spread more than 1 to 3, in single decks if you always bet two hands. You would then use the variance and covariance formulas to estimate your overall sd, based on one bet and earnings, and add the gains, but use the special formulas for the higher sd (but below 2). Telling the pit that you are trying to capture an ace, or the like, works usually  (and the last parts of banger strategy may allow you to do just that).

Another tip is to always set your unit bet size based on the normal counting of that single deck game, while letting the added gains, from the tactics in this book be “gravy.” The money will come.

Once you are at the $100 unit level,  for single decks, taper off and top off your betting levels and take it easy. Three hours a day, $100 units, spread over Las Vegas, Reno, or even Laughlin or Tahoe, is not a lot of exposure and is still $300K per year (unless you have exwives like mine disrupting things). That level of average daily wins can be sustained, you don’t want to just play single decks, by looking upon other games, such as the CS machines, as income games--to add to your investments let’s say.  Then you can look forward to taking the plunge with things like ST.

Have a top-off goal and be quiet about it. There is such a thing as a compulsive gambling WINNER you know. I never forget the first time my bankroll went into the blackchips and I walked by a DeLorian I had the cash to buy—this was just before the factory closed and a stainless-steel car sure would have been handy when I moved to Minnesota later too. I didn’t buy it. I was so wrapped up in taking my bankroll to the next level (there was no IRS transaction reporting then either) that I didn’t buy it. There are other opportunities you know. If you cannot find other ways of making money, when you have 300K per year coming in, you don’t deserve it! (That experience ended badly when I started having problems with a former girlfriend who was in the music business, and was harrased, by her from playing. I went back to dealing craps and laying low, except to make a few tries, but by that time I was too known as a local and dealer and the tip hussles—“you deal too so tip—“ were almost as bad as getting Griffinized. The girlfriend I won’t name, except to say she was the cousin Patty Smythe always complained about in several interviews, about how she would probably drive her out of the music business if she screws up the publishing of one more song. Then came 6 years of being in and out of wheelchairs….)

The IRS is beatable as are some of the reporting requirements. Example: sometimes having markers at 2 different locations, owned by the same casino company. You can sometimes have transfers between the locations written down as happening at only one of the two casinos, or even more. Sometimes you can arrange for the same to be done to accounts that are overseas that appear to be creditors of yours, where the transfer can be regarded as being totally overseas. A few cards or statements that show a numbered account and direct billing and payment being available to that account can have the casino pay the wire fees too. Be creative.

The same is true regarding the IRS itself. Whether you take the approach of the Audit Defense Network, that everything that can be related to attempts to earn income is deductable, and seeking every tax credit, or the opinions of people like Irwin Shiff (The Federal Mafia is good), that the IRS is full of it, the IRS tax code is 20% the government equivalent of a Seinfeld script (about nothing), nothing, 30% if nothing applies to you, another 30% special interest deductions, 5% actual taxes, and 15% attempts to have civil rules (best case wins) apply to criminal prosecutions (which should be presumed innocent). US laws are a worldwide joke. The US has perhaps the world’s fairest jury system and criminal rights, but the US constantly fails in trying to pass new laws in screwed-up ways that are known to be null and void, if properly challenged from the time that a congress critter’s aide first types up a proposed language file.

The biggest power that the IRS has is claiming (successfully—judges know who gets the money that results in their paychecks) that defeats are injuris rulings (that is bad latin for only applying in this case and means that quotable precident is NOT set by that decision). The second biggest is the failure of juries to know that they are allowed to judge both the case at issue and the law as well, AND CAN IGNORE INSTRUCTIONS, and aquit for any damn reason they want. What do you expect however from a public that doesn’t know pleaded is a double modifier and that plead (as in rhyming with head) is the original and proper past tense verb form of plea. The first means that you can beat-em but your neighbor next door has to totally reconstruct his case to do the same, by not being able to cite your case and decision. The last is ignorance of the law.

Treat all of these as further games to master, or games you graduate to playing and maybe you can become wealthy enough to start changing things. But if you do, don’t fall for whatever it is that keeps us trapped on this planet. Raise hell and try to get us into a real space program. Example: there is a $110 billion backlog in bids for launch vehicles to orbit comsats. Every month a NASA funded publication, Ad Astra, shows the total going up. Yet the total costs of funding “a cheap not dirty proposal for a space plane,” that would use a 747 as the first stage of an otherwise direct to orbit mini shuttle could be funded for $2 billion. That is quite a multiplier for an investment, that people like Bill Gates virtually walk around with. Until we reach out, and the gov’ment won’t do it or will screw it up, into space all of our troubles in “all living together on this one planet,” will keep us STUCK on this one planet, until we become Nebishes (the term comes from T. J. Bassinger’s books, Half past Human, and, The Godwhale—he shortened his name to Bass, for these two scfi classics. Nebish also is found in Yiddish as a term for a “nobody.”), or with all of our computers and neat toys, nothing more than that we might as well be chipmakers for a “grey alien” version of the Star Trek Borg!

It must take great efforts to keep us stuck while the money is to be made getting up off or butts and going to the stars. Maybe by this book some candles can be lit or relit, where people of true faith and goodwill will have sources of high income not subject to us staying krazy glued to our cubicles like the Dilbert strip pictures by whatever wants the earth to just plain SUCK and keep us here, and can be sources of getting us going. The entire personal computer industry was made by hacker misfits and the like. Who says that maybe it isn’t time for an independent venture capital movement that has thousands of sources….You get the idea…..CC out!

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