Knock out blackjack, p.1
Knock-Out Blackjack, page 1
Other Huntington Press titles:
The Art of Gambling Through the Ages
by Arthur Flowers and Anthony Curtis
Blackjack Autumn—A True Tale of Life, Death, and Splitting Tens in Winnemucca
by Barry Meadow
Burning the Tables in Las Vegas
by Ian Andersen
More Frugal Gambling
by Jean Scott
The Man With the $100,000 Breasts and Other Gambling Stories
by Michael Konik
No Limit—The Rise and Fall of Bob Stupak and Las Vegas Stratosphere Tower
by John L. Smith
The Theory of Blackjack—The Compleat Card Counter’s Guide to the Casino Game of 21, 6th Edition
by Peter Griffin
* * *
The Easiest Card-Counting
System Ever Devised
* * *
Olaf Vancura, Ph.D.
&
Ken Fuchs
Knock-Out Blackjack
Published by
Huntington Press
3665 Procyon Street
Las Vegas, Nevada 89103
(702) 252-0655 Phone
(702) 252-0675 Fax
e-mail: books©huntingtonpress.com
Copyright © 1998, Olaf Vancura, Ph.D.
ISBN: 978-1-935396-07-9
Cover Design: Maile Austraw Interior Design: Jason Cox
All rights reserved. No part of this publication may be translated, reproduced, or transmitted in any form or by any means, electronic or mechanical, including photocopying and recording, or by any information storage and retrieval system, without express written permission of the copyright owner.
To all who have been knocked out by the casinos ...
Acknowledgments
The authors are indebted to Andy Block, Anthony Curtis, Michael Dalton, Peter Griffin, J. P. Massar, Donald Schlesinger, Ralph Stricker, Edward O. Thorp, Zeb Vancura, and Dick Vannelli for reading, commenting on, and contributing to preliminary versions of this manuscript.
We also thank Paul Bauer, Geoff Talvola, and John Spaulding for assistance in the confirmation of K-O simulation results and for valuable feedback in initial field-trial applications of the K-O technique.
We are grateful to our wives Kathy and Tracy for putting up with grown men who behave like kids when discussing blackjack. You are real “Knock-Outs” to us.
Table of Contents
Round 1 A Historical Perspective of Card Counting
Round 2 The Basic Strategy
Round 3 An Introduction to Card Counting
Round 4 The Unbalanced Knock-Out System
Round 5 The Knock-Out System—Rookie
Round 6 The Knock-Out System—Preferred Strategy
Round 7 The Knock-Out System—Preferred Betting
Round 8 Enhancing Profits
Appendices
Appendix I: Rules of Blackjack
Appendix II: Blackjack Jargon
Appendix III: A Comparison of the K-O System to Other Sytems
Appendix IV: The Full Knock-Out System
Appendix V: The Effects of Varying Penetration on K-O
Appendix VI: Benchmark Risks of Ruin
Appendix VII: The K-O for 4 Decks
Appendix VIII: Customizing the Knock-Out Count
Appendix IX: Suggested Reading
Index
Preface
There is the notion, often put forth by the casinos, that card counting requires a mind like Albert Einstein’s, together with a memory tantamount to that of a Pentium computer. Nonsense! And yet, the vast majority of blackjack players do not presently count cards.
We have invented a new, simple, scientific technique of beating casino blackjack, which we call the Knock-Out (K-O) system. You don’t need a math degree to be able to participate; virtually anyone who has ever applied the principles of the basic strategy (and can count up and down by ones) will be able to put K-O to good use.
But don’t let the simplicity of the Knock-Out system fool you. K-O’s power compares favorably with all the proven card-counting systems. This has been verified not only through simulations of billions of computer-generated hands, but also by the actual play of card-counting teams throughout the United States.
After reading this book, you too will have the knowledge necessary to successfully “Knock-Out” the casinos in the game of blackjack.
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 blackjack. 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 corresponds 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 almost $2 billion from blackjack, with a typical blackjack table 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 attempts 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 surpassed roulette as the second most popular game behind craps.
To be sure, though, at this time almost all blackjack players 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, often 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 began working on a study of the game. After three years of painstaking 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 unlike the common wisdom of the day. In their paper the group noted that, “The ‘optimum strategy’ differs substantially 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 important 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 calculated 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 expectation 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 notion 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 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 demonstrated the percentage difference in expectation for appropriate hitting, standing, splitting, and doubling 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 encoded a computer to calculate the basic strategy. He obtained a
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 dollars” (the good old days) in order to try out the system.
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 meager 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 earnest. He recognized that although the Baldwin group had made great strides in the understanding of blackjack, they apparently had overlooked an important facet of the game. Baldwin and his colleagues wrote that their strategy was “developed under the assumption that the player does not have the time or inclination to utilize the information available in the hands of the players preceding him.” They further surmised, “There are tremendous difficulties in using this information except in an intuitive, non-scientific manner.”
Thorp took exception to these statements. He became convinced that, with proper play, a skilled player would be able to beat the game. That is, the tables would be turned, and the player would have a positive expectation. Hence, over time, the lowly player would be expected to beat the mighty house.
As is true of many inventors, Thorp had the wisdom to appreciate the importance of what many took for granted. For unlike the Declaration of Independence, which states that “all men are created equal,” the fact is that all cards (in blackjack) are not.
Thorp realized that certain cards were favorable to the player and others to the dealer. The Baldwin group had shown that this was true for the present cards in play (those the dealer or player were now holding). But Thorp took the concept a giant leap forward. He reasoned that, in general, among the remaining cards (those as yet still unplayed), an excess of certain card denominations would be beneficial to the player, while an excess of others would help the dealer.
And thus the modern system of card counting was conceived. Sequential hands are dependent events. Information on cards already played yields information about the cards still remaining. If the relative abundance of these remaining good and bad cards could be identified, then the player’s advantage or disadvantage could be estimated.
Thorp made good use of his access to computers, and several intense years of study and simulation ensued. At last, in 1961 he presented the exciting results at an American Mathematical Society meeting. In 1962 he published the first card-counting treatise on blackjack, the best-selling Beat the Dealer. In it were the words that would send the casino industry reeling: “In the modern casino game of blackjack, the player can gain a consistent advantage over the house by using the strategy that is presented in this book.”
Thorp’s book eventually created a sensation, riding a wave of popularity to the New York Times bestseller list. And why not? For, as Bryce Carlson wrote in Blackjack for Blood,5 “Here was a book, written by a respected mathematician from a prominent university, that contained the secret formula for making free money—or so some thought.”
Blackjack’s popularity soared. Major magazines ran articles describing how the game could be beaten. Consider the accolades in the following excerpt from Life: “Thorp does not cheat. But Thorp cannot lose. Humans have been betting on games of chance since the dawn of history, but Thorp must be considered the greatest system player of all time.”
Not surprisingly, casinos first reacted with anxiety. Commented Carlson, “If the man in the street was overreacting a bit, it was nothing compared to the hysteria that seized the casino industry. Suddenly, they had nightmares of thousands of trained counters swooping down on them like swarms of merciless locusts, devouring every hundred dollar bill in sight.” This frame of mind led many casinos to change the rules of the game to make it harder for players to win.
That situation didn’t last long, as Lance Humble and Carl Cooper wrote in The World’ s Greatest Blackjack Book,6 “Too many players refused to play blackjack with these unfavorable rules, and the win volumes dropped off dramatically.”
To bring players back, casinos were soon forced to capitulate and reinstate the old rules. After some tense days, the casinos began to relax when they realized that though many people thought they could beat the game, few actually could. Remarked Humble and Cooper, “The casinos soon realized that they had nothing to fear. The publicity that Thorp’s book provided turned out to be a boon.” Why? “The players kept losing at exactly the same rate as before, only now there were more of them.”
Blackjack’s popularity continues in high stride today. Apparently the lure of playing a game that is potentially beatable is sufficient for most people, who somehow believe that Dame Fortune will smile on them despite their inadequacies in play.
But these people miss the point. It’s not enough to merely show up to a game that can be beaten. One also needs to play properly. It’s similar to a college midterm exam on which you want to get an A grade. It’s a given that you’ll show up to take the exam, but you must show up prepared to earn the A.
But putting in work, practice, and patience to learn to play well, Carlson argued, “is not what the people were looking for. They preferred instead to continue in their old, uninformed ways.” Humble and Cooper have said that most people who bought Thorp’s book simply did not take the time to master card counting.
Of course, it didn’t help when supposed experts muddied the waters with misinformation. As soon as the diligent work of an esteemed scientist became public, self-proclaimed card-counting experts came out of the woodwork claiming supreme knowledge of the subject. (It’s amazing how that seems to work. It’s reminiscent of the developments in the first part of the 20th century shortly after Albert Einstein published his general theory of relativity. The great scientist Arthur Eddington was in West Africa observing an eclipse in an attempt to perform a test of Einstein’s ideas. A reporter interviewing Eddington commented, “It is said that the general theory is so complicated that there are but three men in the world who can understand it.” To which Eddington replied, “Who’s the third?” John Scarne, for example, labeled card counting “chicanery,” and argued that it required unusual natural ability. “You can’t remember all the exposed cards dealt to a full table of players,” Scarne wrote. While the statement is certainly true for most people, it is irrelevant and misleading. The Thorp system didn’t require the memorization of all the exposed cards. Quite the contrary; Thorp recognized that this was beyond the means of mere mortals and designed a system that could be implemented by everyday folks.
