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Blackjack TherapyBy Clarke Cant BJRNET EDITOR
NOTE: 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: BA=BE*(LH+H)*(H-1)/[10*(H+1)] 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: PA=4.3*(C^2)*PE/[N+SQR(N)] 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. RA=(C^2)*H*V/[5*SQR(N)] 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. DA=(.69/N)-.65 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: V=[(V1-Vi)/N]+Vi 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 th |
