Atlantic City
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| Hilton Hotel and Casino Atlantic City |
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The advantage scientists bring into the game is less their mathematical or computational skills than their ability to think scientifically. They are less likely to accept an apparent winning strategy that might be a mere statistical fluke. -Jim Simons, President, Renaissance Technologies
Casino games provide models for application of the theory of probability. Casino gaming is a rapidly growing industry in the United States. About thirty years ago it was legalized in Atlantic City, New Jersey, as a way of revitalizing a declining resort city. More recently, casinos have been making inroads in the city of Philadelphia, Pa. despite heavy opposition. It is a trend that cannot be ignored.
With the exception of blackjack, casino games are mathematically engineered to provide a negative expectation for the player, that is to say, the house has the edge. The game of blackjack is not engineered at all because it was not until 1956 that the mathematics behind it was understood. It was found by experience that under a set of rules that are acceptable both to the player and to the house, the house had about a 5% edge.
The mathematical analysis of the game and the publishing of winning strategies led to the drawing of considerable sums from casinos in Nevada, where the rules are the most favorable to the player. The majority of these players were recognized and banned from the tables, but there remain a few devotees who have learned to disguise their play so as not to be recognized as "card counters" and who continue to walk away with profits. In these pages we discuss the mathematics of the "basic strategy" for blackjack, which is a break-even strategy. In time we may augment this with stragegies that give the player a positive expectation based on the cards remaining to be dealt, however there already is a considerable amount of literature on this subject.
We also discuss a few of the cases where the game of roulette was beaten and tell how it was done.
We also try to debunk some of the fraudulent schemes for beating these games. We know of no fraudulent schemes for beating blackjack - these are genuine. Most schemes for beating roulette and all schemes for beating slot machines, however, are fraudlent.