KnocK- out Blackjack The Easiest Card-Counting System Ever Devised Olaf Vancura, Ph.D. & Ken Fuchs Huntington Press Las Vegas, Nevada Table of Contents Round 1 A Historical Perspective of Card Counting .............1 Round 2 The Basic Strategy .................................................18 Round 3 An Introduction to Card Counting .........................42 Round 4 The Unbalanced Knock-Out System .....................59 Round 5 The Knock-Out System—Rookie ..........................71 Round 6 The Knock-Out System—Preferred Strategy ........79 Round 7 The Knock-Out System—Preferred Betting..........92 Round 8 Enhancing Profits .................................................109 Appendix .................................................................................141 Appendix I: Rules of Blackjack ..............................................141 Appendix II: Blackjack Jargon ...............................................145 Appendix III: A Comparison of the K-O System to Other Sytems ..................................................148 Appendix IV: The Full Knock-Out System ............................157 Appendix V: The Effects of Varying Penetration on K-O .....162 Appendix VI: Benchmark Risks of Ruin ................................166 d • Knock-Out Blackjack Appendix VII: The K-O for 4 Decks ......................................167 Appendix VIII: Customizing the Knock-Out Count ..............168 Appendix IX: Suggested Reading ..........................................170 Index ........................................................................................172 Round 1 A Historical Perspective of Card Counting It isn’t so much the money. It never has been. The big part of winning is being able to feel the way David must have felt when he killed Goliath. —Edward O. Thorp, Beat the Dealer The popularity of gaming continues unabated. This year, gamblers will wager more than $400 billion in casinos and state lotteries in the United States.1 To place this in context, on a yearly basis, the average American wagers about $1,600! And in virtually each of the hundreds of casinos spread throughout the nation, the number-one table game is black- jack. From the Las Vegas Strip to the Atlantic City Boardwalk and every gambling jurisdiction in between, blackjack reigns supreme as the king of casino table games. Nearly $90 billion a year is wagered at blackjack tables. This corre sponds to an annual wagering level of some $350 per citizen on this one game alone. And how do we do against the mighty house? Not so well, it turns out. Annually, American casinos collectively win al- most $2 billion from blackjack, with a typical blackjack table 1 Statistics based on the Ernst & Young Compilation of the Gaming Industry. 2 • Knock-Out Blackjack realizing some $250,000 in profits. Given these substantial losses by the wagering public, it is perhaps all the more amazing to learn that a skillful blackjack player can beat the casinos at their own game. With proper play, blackjack can, in almost all situations, quite legally be beaten. This is accomplished by a technique called card counting. The idea behind card counting is simple: a player uses information about cards already played to determine the favorability of the remaining pack. Not too hard. To date, however, this concept has been difficult to implement. We’ll attempt to remedy this in the pages that follow. But first, let’s take a quick look back at some of the key milestones in the history of blackjack. In particular, we’ll focus on at- tempts to beat the game over the past half-century or so. THe Origins Of CArd COunTing As with many of life’s pleasures that are now taken for granted, the exact origin of the game of blackjack is unclear.2 Several countries have laid claim to (originating) the game of twenty-one. It may have been an offshoot of the Spanish “one and thirty,” in existence since at least the 16th century. In any event, twenty-one was introduced into American gaming halls shortly after the turn of the 20th century. After a few years, houses began to introduce a variation wherein a hand consisting of an ace of spades and a black jack garnered a bonus. This gave birth to the name blackjack. The game spread to Nevada in the 1930s, and by 1950 blackjack had sur passed roulette as the second most popular game behind craps. To be sure, though, at this time almost all blackjack play- 2 See, for example, Scarne’s New Complete Guide to Gambling by John Scarne, 1974, Simon & Schuster. 3 • Knock-Out Blackjack ers performed poorly and lost quickly. Though the game had been offered in casinos for decades, it was played crudely. Players typically employed very conservative strategies, of- ten refusing to hit stiff totals of 12 through 16, which could potentially bust with the draw of another card. However, in the second half of the century, things began to change. In 1953, a group of four Army mathematicians be gan working on a study of the game. After three years of pains- taking calculations (the computer age had not yet dawned), Baldwin, Cantey, Maisel, and McDermott published the first blackjack basic strategy in 1956. In “The Optimum Strategy in Blackjack,” published in the Journal of the American Statistical Association, Baldwin et al. described what they termed the “optimum strategy,” now commonly referred to as the basic strategy (see Chapter 2). The strategy they recommended was very un like the common wisdom of the day. In their paper the group noted that, “The ‘optimum strategy’ differs substan tially from the published strategies of card experts and the usual style of play in the casinos.” In addition to presenting an accurate basic strategy for the game of blackjack, the Baldwin group reported several other impor tant findings. First, they determined that with proper strategy, the player has a better expectation in blackjack than in any other casino game. Though the group originally calcu- lated an expectation of –0.6% (the player is expected to lose 0.6% of total initial wagers), they later revised this upward to –0.3% (the actual ex pectation for the single-deck game they analyzed was nearly 0.0%). Before that time, the prevailing “best” strategy (attributed to Culbertson et al.) yielded a rather dismal expectation of –3.6%. Another major find of the Baldwin group was the no- tion that certain dealer upcards are favorable to the player, while others are unfavorable. That is, the player’s chances of winning a hand are dependent on the dealer’s upcard. Of 4 • Knock-Out Blackjack this, the group wrote summarily, “The player’s conditional expectation, given the dealer’s upcard, shows considerable variability.” This is a very important concept and one we shall explain shortly. At about the same time, others began studying the game.3 In 1956, Richard Epstein created a “decision matrix” that The Wisdom of YesTerYear Today’s experienced players might be amused by the strategies employed by black- jack players of decades earlier. Below is a sampling of the Baldwin group’s overview of prevailing 1950s’ play. On hitting and standing: “Few experienced players rec ommend standing on a total of 13 under any circum stances, and standing on 12 would be completely out of the question.” On splitting: “Splitting 8s, for example, is seldom seen in the casinos, while splitting 10s and face cards is not uncommon.” On doubling down: “Doubling down is not recom mended by any writers. Doubling down is not com mon in the casinos and, in particular, the idea of dou bling down on soft hands prob- ably does not occur to most players. One may even go so far as to say that doubling down is the most neglected and underrated aspect of blackjack strategy.” 3 For a more detailed description, see for example Allan Wilson’s The Casino Gambler’s Guide, 1965, Harper & Row. 5 • Knock-Out Blackjack demonstrated the percentage differ ence in expectation for appropriate hitting, standing, splitting, and dou bling down. In conjunction with estimates of initial two-card hands, Epstein calculated the basic strategy expectation to be –0.14%. By 1959, Robert Lea had en coded a com puter to calculate the basic strategy. He obtained a more cor rect estimate of the expectation at –0.01%. To differing degrees, these bright investigators had begun unraveling the secrets of blackjack. They recognized that proper basic strategy made blackjack almost an even game. What’s more, some of them even had an inkling that the game could be beaten with additional information. Indeed, the understanding of the game was revolutionized once again when a young scientist named Edward O. Thorp— “a veritable supernova,” according to Wilson—burst onto the scene. Dr. Thorp came across the results of the Baldwin group shortly after their article was published. For an upcoming trip to Las Vegas, Thorp wrote the basic strategy rules on a small card. Upon arriving at a casino, he “purchased ten silver dol- lars” (the good old days) in order to try out the system. The CulberTson sTraTegY Below is a sampling of the strategy es- poused by the Culbertson team, as reported by the Baldwin group. Hitting and standing: Stand on 14 or more if the dealer’s upcard is 6 or less. Stand on 16 or more with a dealer upcard of 7 or more. Stand on all soft totals of 18 or more. Splitting: Only split aces. Doubling down: Never double down. 6 • Knock-Out Blackjack Thorp writes in Beat the Dealer,4 “In a few moments the slowness of my play and the little card in my palm amused and attracted bystanders. The dealer could not conceal his scorn.” He adds, “These sentiments were soon laced with pity when these people saw, further, the details of the way in which I played.” However, some twenty minutes (and a seven-card hand totaling 21) later when Thorp still had not exhausted his mea ger stake, he noted, “The amusement and patronizing attitude of some bystanders changed to respect [and] attentiveness.” After his trip, Thorp began studying the game in ear nest.