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Page last modified: 7-09-95
[Note: this question is obsolete now that rec.gambling.blackjack is a separate group. This question will eventually be deleted from the rec.gambling.blackjack FAQ]
Answer: Simulations performed by rec.gamblers show different amounts of potential player advantage in theory in BJ, depending on strategies, exact rules, and playing conditions. These numbers typically approach 1% (an average penny gain for every dollar bet) though in certain particular, ideal circumstances this can get somewhat higher. There is disagreement on the net about how much advantage this translates into in "real-world" casinos, but it's generally believed that players can play with a small, long-run advantage in BJ. The variance is very high in this game, however, which makes the slight advantage in BJ far from a sure thing.
+-- Player's hand | | dealer dealer | |-might bust-||-might stand-| V 2 3 4 5 6 7 8 9 X A <------- dealer's upcard ---+------------------------------- XX | S S S S S S S S S S never, ever, ever split 99 | PS PS PS PS PS S PS ps s s split if (d <= 9), except 7 88 | Ps Ps Ps Ps Ps Ph ph ph ph ph always split 77 | ps ps Ps Ps Ps ph h h s h split if (d <= 7), stand against 10 66 | ph ps ps Ps ps h h h h h split if (d <= 6) 55 | DH DH DH DH DH DH DH DH H H never split, treat like hard 10 44 | h H H DH DH H h h h h never split, double against 5, 6 33 | h h Ph PH PH ph h h h h split if (d >= 4) and (d <= 7) 22 | h ph Ph PH PH ph h h h h split if (d >= 3) and (d <= 7) AA | PH PH PH PD PD PH PH Ph Ph Ph always split ---+------------------------------- A9 | S S S S S S S S S S always stand A8 | S S S S *DS S S S S S double against a 6 A7 | S DS DS DS DS S S h h h* double 3-6, hit against 9, 10, A A6 | DH DH DH DH DH H h h h h double low, hit high A5 | h h DH DH DH h h h h h \ A4 | h H DH DH DH H h h h h \ double against 4,5,6 A3 | H H DH DH DH H H h h h / A2 | H H DH DH DH H H h h h / ---+------------------------------- 21 | S S S S S S S S S S always stand 20 | S S S S S S S S S S always stand 19 | S S S S S S S S S S always stand 18 | S S S S S S S s s s always stand 17 | s s s s s s s s s s always stand on HARD 17 or above 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 > hit if dealer might stand, 13 | s s s s s h h h h h / stand if dealer might bust 12 | h h s s s h h h h h / (special case against 2, 3) 11 | D D D D D D D D D D always double 10 | D D D D D D D D H H double if (d < 10) 9 | DH DH DH DH DH H H h h h double if dealer might bust 8 | h H H DH DH H h h h h double only against 5, 6 7 | h h h H H h h h h h 6 | h h h H H h h h h h (4-2) 5 | h h h H H h h h h h (3-2) 4 | h h h H H h h h h h (2-2 pair if no more splitting allowed) ---+------------------------------- S=stand H=hit D=double P=pair(split) DH= double if allowed, otherwise hit DS= double if allowed, otherwise stand [uppercase] = "strong" hand, favorable to player [lowercase] = "weak" hand, favorable to house (*) notes: Playing A7 against dealer's ace: hitting gains 4.08% if dealer must hit on soft 17 standing gains 0.74% if dealer must stand on soft 17 Playing A8 against dealer's 6: doubling gains 1.96% if dealer must hit on soft 17 doubling gains 0.03% if dealer must stand on soft 17 (this rule may be ignored to simplify the strategy)
HOUSE RULES: Cards are dealt from 6 decks. Dealer must stand on any 17. Double-down allowed on soft hands. Pairs may be split only once. Player may double-down after splitting pairs. Surrender is not allowed. Strategy Table |---might bust---| |---might stand---| <---- dealer possibility ---+---------------------------------------- 2 3 4 5 6 7 8 9 X A <---- dealer's up card ---+---------------------------------------- Pairs XX | S S S S S S S S S S 99 | PS PS PS PS PS S PS ps s s 88 | Ps Ps Ps Ps Ps Ph ph ph ph ph 77 | ps ps Ps Ps Ps ph h h h h 66 | ph ph ps Ps Ps h h h h h 55 | DH DH DH DH DH DH DH DH H H 44 | h H H PH PH H h h h h 33 | ph ph Ph Ph Ph ph h h h h 22 | ph ph Ph Ph PH ph h h h h AA | PH PH PH PH PDH PH PH Ph Ph Ph ---+---------------------------------------- Soft Hands AX | S S S S S S S S S S A9 | S S S S S S S S S S A8 | S S S S S S S S S S A7 | S DS DS DS DS S S h h h A6 | H DH DH DH DH H h h h h A5 | h H DH DH DH h h h h h A4 | h H DH DH DH H h h h h A3 | H H H DH DH H H h h h A2 | H H H DH DH H H h h h AA | H H H H DH H H h h h ---+---------------------------------------- Hard Hands 21 | S S S S S S S S S S 20 | S S S S S S S S S S 19 | S S S S S S S S S S 18 | S S S S S S S s s s 17 | s s s s S s s s s s 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 11 | DH DH DH DH DH DH DH DH DH H 10 | DH DH DH DH DH DH DH DH H H 9 | H DH DH DH DH H H h h h 8 | h H H H H H h h h h 7 | h h h H H h h h h h 6 | h h h h h h h h h h 5 | h h h h H h h h h h 4 | h h h h H h h h h h ---+---------------------------------------- S=stand H=hit D=double P=split Q=surrender NOTES: 1) If more than one option is listed, options to the left are preferred over options to the right. Options less favorable than STAND or HIT are not shown. 2) Use the "Hard Hands" table only when the other tables do not apply. 3) If splitting Aces is not allowed, use the "Soft Hands" table. 4) Uppercase options favor the player, lowercase options favor the house.
<-- number of decks --> | 1 | 2 | 4 | 6 | 20 | 100 | ----------------+-------+-------+-------+-------+-------+-------+ AC | .1541 -.2228 -.3991 -.4569 -.5368 -.5638 | AC + LSR | .1761 -.1717 -.3323 -.3843 -.4552 -.4790 | AC + ESR | .7694 .3952 .2265 .1721 .0968 .0714 | ----------------+-------+-------+-------+-------+-------+-------+ strip | .0409 -.3214 -.4889 -.5437 -.6245 -.6447 | strip + LSR | .0707 -.2685 -.4239 -.4744 -.5429 -.5659 | strip + DAS | .1809 -.1795 -.3472 -.4021 -.4779 -.5034 | strip + ESR | .6511 .2927 .1320 .0801 .0084 -.0157 | ----------------+-------+-------+-------+-------+-------+-------+ vegas |-.1527 -.5257 -.7015 -.7590 -.8445 -.8663 | vegas + LSR |-.1095 -.4594 -.6221 -.6747 -.7469 -.7713 | vegas + DAS |-.0103 -.3813 -.5570 -.6146 -.6951 -.7223 | vegas + ESR | .5403 .1720 .0046 -.0493 -.1245 -.1500 | ----------------+-------+-------+-------+-------+-------+-------+ reno |-.4291 -.7400 -.8906 -.9404 -1.0154 -1.0337 | reno + LSR |-.3858 -.6737 -.8113 -.8560 -.9178 -.9387 | reno + DAS |-.3121 -.6176 -.7658 -.8151 -.8840 -.9073 | reno + ESR | .2639 -.0423 -.1846 -.2307 -.2307 -.3174 | ----------------+-------+-------+-------+-------+-------+-------+ "AC" rules: (typical of Atlantic City) dealer stands on soft 17 double down on any two cards double after splits no resplitting "strip" rules: (typical of Vegas Strip) dealer stands on soft 17 double down on any two cards (but not after splits) "vegas" rules: (typical of Vegas Downtown) dealer hits soft 17 double down on any two cards (but not after splits) "reno" rules: (typical of Reno, northern Nevada) dealer hits soft 17 double down allowed on two card total of 10 or 11 only DAS = Double After Splitting LSR = Late Surrender ESR = Early Surrender (no longer available)
Single deck blackjack is usually better than multiple deck blackjack for card counters, basic strategists, and the clueless. Additional decks make busts less likely, since one can draw to hands like 2,2,2,2,2,2,2,2,2 (for 18) which are improbable/impossible in single deck. Busting less often helps the dealer's hand more than yours, since the dealer is forced by the rigid rules to hit more often than you. Blackjacks are also less frequent, which is bad since you get paid 3 to 2 for those. All in all, multiple decks will cost a basic strategist nearly 0.5% in advantage, which is more than all but the very best package of favorable extra rules will give you. This was an intuitive explanation; a complete mathematically sound (albeit huge) proof can be generated by a combinatorial analysis program.
Card counters face the additional problem that the count is less volatile with multiple decks and hence offers less frequent opportunities for large favorable bets. Consider the difference between an urn with 1 black and 1 white marble versus an urn with 100 black and 100 white marbles. Draw half the marbles: what is the probability that all the remaining marbles are white? In the 1 and 1 case, there is a 1 in 2 chance. In the 100 and 100 case, there is only a 1 in 100,891,344,545,564,193,334,812,497,256 chance!
Counting is best done by counting several cards at once. It is easy to practice this counting method in the following way:
The first approach is to evaluate different systems by simulation. This approach obscures the particular advantages of each system, but it's easy to see how a system will perform in one particular realistic casino playing situation, and not hard to judge the tradeoff between performance and ease of use (see Q/A B18 for more details).
The second approach estimates several performance parameters of each system that collectively approximate the system's inherent potential. This allows the strengths of different BJ systems to be studied in detail, which should allow better, more precise comparison of different systems and aid efforts to improve a particular system. This approach gives results which may be used to determine which counting system is theoretically most profitable, but does not address the issue of how easy it is to use the counting system under actual playing conditions (see Q/A B19 for more details).
It's not yet clear how these two studies relate, and no rec.gambling.blackjack consensus has emerged as to how the more sophisticated performance parameters actually translate to advantage at the tables as in the simulations.
Answer: You pick 'em. A rec.gambling.blackjack study was accomplished that compared different systems, and here a summary of what came out:
Complexity is a subjective measure with guidelines described in the results paper. Power is the integer closest to p/0.05%, where p is the % advantage of the strategy one-on-one in a single deck, dealer hits on soft 17, no DDAS, resplitting-allowed game that's dealt down to 20 cards and using a 1-4 betting spread. 15,000,000 hands guarantee correctness to within 1 point 99% of the time.
name complex power card weights reference A 2 3 4 5 6 7 8 9 X -------------------------------------------------------------------------- BASIC 0 -5 Steve Jacobs UNBALANCED 10 2 13 1 1 1 1 1 1 1 1 1 -2 Steve Jacobs SUPER-SIMPLE OPT-I 2.5 16 1 1 1 1 -1 WGBJB (1) REVERE PM 3.5 16 -1 1 1 1 1 1 -1 PBaaB RED SEVEN 3.5 19 -1 1 1 1 1 1 R:1 -1 BiB OPT1-6+6 5 18 1 1 1 1 -1 WGBJB WONG HIGH-LOW 5 19 -1 1 1 1 1 1 -1 PB ZEN 5 19 -1 1 1 2 2 2 1 -2 BiB HORSESHOE 6 14 1 2 2 3 2 2 1 -1 -3 MDB (2) REVERE POINT COUNT 6 17 -2 1 2 2 2 2 1 -2 PBaaB OPT1-6+6 W/ ACE 7 23 1 1 1 1 -1 WGBJB ANDERSEN 9.5 16 -2 1 1 1 2 1 1 -1 -1 TtToLV USTON APC 10 22 1 2 2 3 2 2 1 -1 -3 MDB WGBJB: "World's Greatest BlackJack Book" by Humble and Cooper PBaaB: "Playing Blackjack as a Business" by Lawrence Revere BiB: "Blackbelt in Blackjack" by Arnold Snyder PB: "Professional Blackjack" by Stanford Wong TtToLV: "Turning the Tables on Las Vegas" by Ian Andersen MDB: "Million Dollar Blackjack" by Ken Uston (1) with modifications by 'thunk' (2) with modifications by Paul C. Kim
See answer B3 for definitions of "betting correlation", "playing efficiency", and "insurance correlation".
EXPLANATION OF COUNTING SYSTEMS =========================================================================== COUNTING COUNTING VALUES "BEST" EFFICIENCY CORRELATION SYSTEMS 2 3 4 5 6 7 8 9 X A SOURCE PLAY+ace BET+ace INSURE -------- ---------------------------- ------ -------- -------- ------ Griffin 0 0 1 1 1 1 0 0 -1 0 Griffin 64-64+ .85-.95 .85 Hi-Opt I 0 1 1 1 1 0 0 0 -1 0 Humble 61-63 .88-.97 .85 Hi-Opt II 1 1 2 2 1 1 0 0 -2 0 Humble 67-67+ .91-.99 .91 High-Low 1 1 1 1 1 0 0 0 -1 -1 Wong 51-63 .97 .76-.85 Ita 1 1 1 1 1 1 0 -1 -1 -1 Sys.Res. 53-63+ .96 .69-.76 Red 7's 1 1 1 1 1 ** 0 0 -1 -1 Snyder 54-64+ .98 .78-.87 Unbal 10's 1 1 1 1 1 1 1 1 -2 1 Roberts 61-61+ .73-.94 1.00 Uston +- 0 1 1 1 1 1 0 0 -1 -1 Uston 55-64+ .95 .76-.85 Uston APC 1 2 2 3 2 2 1 -1 -3 0 Uston 69-69+ .91-.99 .90 Wong Halves 1 2 2 3 2 1 0 -1 -2 -2 Wong 57-67+ .99 .72-.85 Zen 1 1 2 2 2 1 0 0 -2 -1 Snyder 63-67+ .97 .85-.91 ** red 7's +1, black 7's 0 Note: Playing efficiencies have a practical maximum of about 0.7. "Unbal 10's" is short for "Unbalanced 10 Count"
When playing Over/Under blackjack with this counting scheme, virtually all of the player's profit comes from the over-13 and under-13 side bets. This counting scheme is very poor for playing the blackjack portion of the bet, and will only allow the player to play about even with the house on the blackjack bets. However, the over/under bets can be very profitable if the game has good penetration. A 6-deck over/under game with good penetration can give the player an advantage of 1.5% or more. Single deck over/under games with good penetration (very rare) can give the player an edge of over 4% when using the over/under count.
Snyder's "Over/Under Report" discusses the over/under game in detail, and is available from RGE at an outrageous price.
There are undoubtedly many good books that are not listed here, as well as many terrible books that are not listed here. These reviews are only the opinions of the reviewers, and your mileage may vary.
Review by Michael Dalton (as reported by Adbul Jalib M'hall)
Dalton, Michael. Blackjack: A Professional Reference. Spur of the Moment Publishing, PO BOX 541967, Merritt Island, FL; 1991. (1964 pages)Reviews by Edmund Hack:Written by a NASA computer systems engineer, this book is a comprehensive reference to the game of blackjack. Over 1000 entries listing books, magazines, publications, newsletters, articles, reports, videos, software and other products available for serious players of the game twenty-one. Also included is the most comprehensive blackjack dictionary ever compiled explaining blackjack terminology, system and strategy descriptions, rules, and miscellaneous blackjack trivia. Complete basic strategy charts that cover most blackjack games in the world are also presented. Fully cross-referenced with recommendations.
Blackjack Video: Winning at Blackjack with Bobby Singer, JCI Video, 1987, 103 minutes. This video is a tape of a sales pitch/introduction to card counting seminar hosted by Bobby Singer, billed as the "World's biggest winner at the game of Blackjack" on the back cover. The tape covers 5 areas: Basic Strategy, Card Counting, Money Management, Team Play and Casino Awareness. Unfortunately, the information is incomplete. For example, the basic strategy section only covers hard and soft hands and the card counting section only covers the card values for the Hi-Lo count, but no bet sizing or strategy adjustments. The rest of the information is available for $149.00. For this price, you get a set of notebooks with lessons and audio tapes covering the Hi-Lo count and an 800 number you can call to find out where the best games are in the city you plan to play. I rented the tape for $1.50 and maybe got my money's worth.Reviews by Adbul Jalib M'hall:One interesting point covered in moderate detail is team play. Singer advocates playing 4 deck or up shoes with the "Big Player" approach pioneered by Uston and others. He advised using a counter at one or more tables who flat bets and uses hand signals (i.e. scratching the head) to call in a big money player. The current count is signaled to the Big Player by the stacking of chips in front of the counter in a particular way. The Big Player can then play out the rest of the shoe, presumably free of heat. If the count goes bad, the big player leaves, proclaiming a trip to the restroom is needed. The home study course is said to have info on bet sizing related/risk of ruin for teams and individuals.
The Winner's Guide to Casino Gambling, Edwin Silberstang, Plume, 1980 and 1989. This is a general overview of casino gambling with chapters on casino operations, comps, junkets, credit and the games offered. Detailed sections on craps, baccarat, roulette, keno, slots, video poker (89 edition only) and blackjack give the staff, rules, and procedures of each game, the house advantage, a glossary, and the best plays for each. In addition, there are anecdotes about playing the games. As the author has separate books on poker and sports betting, there is little information on them here and Red Dog and Pai Gow poker are not covered. The blackjack section has correct basic strategy information for 1,2, and 4+ deck games with and without DAS, and a discussion of Strip, Reno and Downtown rules variations. He presents the Hi-Opt I count (not by that name) and how to use it for bet sizing and insurance bets, but no strategy adjustments. There is a section written by a professional blackjack player on how to hide the fact that you are counting and life as a pro. If you want a single book as an introduction to casino gambling, this is it. [Note: there are 2 versions of the book out - a small green paperback from 1980 and a black trade paperback from 1989 that has been updated.]
Fundamentals of Blackjack by Chambliss and Roginski - this book is pretty much a standard blackjack book, but it has exceptionally good tables of information. I advise buying this book as a supplement to whatever book you use for your counting system (probably either Professional Blackjack, The World's Greatest Blackjack Book, Blackbelt in Blackjack or Million Dollar Blackjack.) The counting system discussed in "Fundamentals..." is not one that you would actually want to use, but the tables don't assume this system is used. Unfortunately, many of the tables were generated using Snyder's Blackjack Formula, and so the accuracy is not as good as would be the case with computer simulations.Reviews by Steve Jacobs:Card Counting for the Casino Executive by Bill Zender - this book is written for casino executives, as you might suspect, which makes it insightful reading for card counters. The book goes into detail about how pit critters should go about identifying and discouraging card counters. It also lists all kinds of ways the players can win, both honestly and by cheating. The author is fairly counter-tolerant, which is refreshing. Alas, the book is spiral bound, only 138 pages long, and *full* of white space.
Million Dollar Blackjack by Ken Uston. This is a good all-around blackjack book, although the advanced counting scheme is much more difficult than most. Ken gives a balanced view of blackjack, without the exaggerated claims that many BJ authors are fond of.World's Greatest Blackjack Book by Humble & Cooper. This is a good book with a pretty reasonable counting scheme. The authors are _way_ too paranoid about cheating, to the extent that they attribute virtually all of their losses to cheating. Otherwise, it is a good book. These guys have absolutely nothing nice to say about Lawrence Revere, so if you've read Playing Blackjack as a Business and would like to read an opposing viewpoint, this is the book for you.
Blackbelt in Blackjack by Arnold Snyder. The Red Seven count in this book is simple, and quite effective against single deck games. The Zen count is more difficult, but more powerful. Snyder includes some interesting ideas that aren't found in other books, such as "depth charging". This book is probably not as good for beginners as are the previous two books, but is a good book for more advanced readers.
Theory of Blackjack by Peter Griffin. This is one of the few good books that cover the mathematical considerations of the game. This book is either a complete must or a complete waste of time, depending on how you feel about mathematics.
Beat the Dealer by Edward Thorp. This book is a classic, and is still worth reading. The card counting schemes are now somewhat dated, but it is still a good book for card counters.
Professional Blackjack by Stanford Wong. Some people really like this book, but I didn't find it all that exciting. It is considered a classic, and has a lot of good material.
Playing Blackjack as a Business by Lawrence Revere. This is one of the most accurate books for basic strategy, and the color charts are very nice. The numbers in the tables were provided by Julian Braun, and are about as accurate as any available, but don't believe the numbers that Revere gives for player's expected gain. Revere's counting scheme isn't widely used today, and Revere's "I'm right and everyone else is a dope" attitude is very annoying, although partially justified if you account for the date of first publication and the scarcity of good books at that time. Revere also makes many inflated claims about player's expectation, which Humble & Cooper would attribute to character flaw.
Scarne on Cards by John Scarne. This book is simply wrong when it comes to blackjack, and Scarne was too arrogant to even consider the possibility that he might have been wrong. He spends a lot of time trying to discredit Thorp. This book has _negative_ value for serious blackjack players, and should probably be avoided completely.
Turning the Tables on Las Vegas by Ian Andersen. This is an entertaining book that describes techniques for disguising your play to avoid detection by pit critters.
Casino Tournament Strategy by Stanford Wong. This book combines previous Tournament Blackjack and Tournament Craps book together at a reasonable price. Covers many of the unique situations that come up in tournament play. Worth reading if you plan to play in tournaments.
Current Blackjack News, by Stanford Wong. $95/year (12 issues). Available through RGE.
Blackjack Confidential Magazine, 513 Salsbury Road, Cherry Hill, NJ 08034 $99/year (10 issues).
Win Magazine, 16760 Stagg St. #213, Van Nuys, CA 91406, (818) 781-9355 Formerly Gambling Times. $36/year (12 issues). Covers all gambling and gaming topics. [Some reports of irregular publishing schedule]
The Experts Blackjack Newsletter, Gambling Times Incorporated, 16760 Stagg St. #213, Van Nuys, CA 91406, (818) 781-9355 New, advertised in WIN Magazine. $30/year (6 issues)
The International Gamblers' Club Newsletter, P.O. Box 73, Thornhill, Ontario, Canada L3T 3N1 $24/year (4 issues). Founded by Lance Humble. They'll send you a free but dated sample if you write. Mainly BJ but contains some sports betting information. (I wasn't impressed with my sample).
Gambler's Book Club, 630 South 11th Street, Box 4115, Las Vegas, NV 89127, (800) 634-6243. Not a newsletter but call for their awesome, awesome, awesome catalog containing not only just about every blackjack book ever written but practically every book ever written on any gambling topic. They also operate a book store at the above address in Las Vegas. [And they have gambling experts (including card counters) working at the store most of the time, willing to answer questions -- Adbul Jalib M'hall]
Las Vegas Advisor, Huntington Press, PO Box 28041, Las Vegas, Nevada 89126, (702) 597-1884. $45/year (12 issues) (add $5 for first class delivery). Produced by Anthony Curtis. Lots of information on deals and freebies available in Las Vegas. Sometimes includes valuable coupons or arranges special deals for subscribers. (I have personally more than recouped the cost in actual cash back from coupons for about half year's worth of the subscription. -Hall)
Casino Player, 2424 Arctic Ave., Atlantic City, NJ 08401, 609-344-9000. $24/yr, (12 issues). It covers most gambling jurisdictions, with particular attention paid to AC and LV. Articles on all games, by Wong, Caro, Frome, Malmuth, Snyder, and others. It's a full color, slick, well produced magazine, about 60 pages.
That article is the only printed mention that I have seen on Uston's death. Maybe someone else has the citation for the Card Player article?