I have mentioned this book in a previous post. Fifty years ago I was getting books through a book club, and this book came as a set along with The Compleat Strategist by J.D. Williams. I have retained these books all this time, during my college days, living in Austin, Dallas, New York, Dallas again and now San Antonio. Looking back I see I have not kept wives as steadfastly as I have kept these books. That’s the way it is with books.
The Williams book deals with a subsection of game theory, particularly zero-sum games, and it concentrates on games involving two parties. Blackjack is a card game played in casinos, and it is, in its simplest form, a two-person, zero-sum game. However, blackjack, as played in casinos does not lend itself to game theory.
The reason you can’t apply game theory to blackjack (also known as twenty-one) is that the dealer is not allowed to play a strategy. For any given state of a hand of blackjack, the dealer is not allowed any options. For example and as explained in the book: When the dealer’s hand is 16 or below, the dealer must take another card. When the dealer’s hand is 17 or above, he may not take another card. There are exceptions to this rule, but in all cases the dealer never has any options.
The time was practically at the dawn of the computer age. People did not talk about my computer. They talked about the computer. Very few individuals owned a complete computer.
Baldwin, Roger; Cantey, Wilbert; Maisel, Herbert; and McDermott, James, “The Optimum Strategy in Blackjack,” Journal of the American Statistical Association, Vol. 51, 429-439 (1956)
The summary of the paper is that a person playing against a casino has a 0.62% edge when a certain strategy is employed. As the book recounts, the authors later found a mistake in their computations, and the players actually have only a 0.32% edge. The book is a bit unclear on this. On page 15 the author states the house edge is 0.62%, but in the footnote at the bottom of the page the house edge is referred to as -0.62%, which would mean a 0.62% edge for the player. Likewise, the footnote corrects the house edge to -0.32%.
To simplify the scheme, on average, when playing against the house, if a player bets the same all the time, the house is going to win. However, if the player keeps track of cards that have been played out of the deck, thereby obtaining knowledge of cards remaining in the deck, then the player can make small bets, and obtain small losses, when the situation is not favorable to him, and he can make large bets, and obtain large gains, when the situation is favorable. Implicit in this is that the player must play every hand to stay in the game. The dealer will reshuffle the deck or obtain a fresh deck anytime a player joins the game. A reshuffle erases any special knowledge the play may have had about the remaining cards to be played.
Beat the Dealer is the story of Thorp, who with the backing of some rich players, played $10,000 and beat the Las Vegas casinos. He also mentions what may be amusing to modern readers, his thanks to M.I.T. Computation Center for the use of an IBM 704 computer. This powerhouse of computation had 18,432 bytes of RAM and could execute up to 4000 instructions per second. How would you like to have one of these babies built into your microwave oven?
If you saw the 1988 movie Rain Man, you will recall the crucial episode is when Charlie Babbitt uses his autistic brother Raymond’s ability to count cards and to take home a sizable amount of cash from the casinos, thus saving his business and the plot. Also, you will recall that in the movie the casinos were less than enthusiastic about losing in a systematic way, and they not very politely disinvited the pair from ever playing in the town again.
Thorp’s was the first use of the strategy to beat the casinos, and they were less polite with them than with the fictional Babbitt brothers. Specifically, prior to forbidding Thorp to play, they brought in cheating dealers to dissuade his endeavors. This after employing frequent reshuffles and multiple decks to defeat card counting. These are, after all, for-profit business, not charities.
Since the late 1960s, Thorp has used his knowledge of probability and statistics in the stock market by discovering and exploiting a number of pricing anomalies in the securities markets, and he has made a significant fortune. Thorp’s first hedge fund was Princeton/Newport Partners. He is currently the President of Edward O. Thorp & Associates, based in Newport Beach, CA. In May 1998, Thorp reported that his personal investments yielded an annualized 20 percent rate of return averaged over 28.5 years.