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In 1977, Richard A. Epstein published his "Theory of Gambling and Statistical Logic", which summarized all the theoretical and statistical work done on games of chance in the last 400 years, and applied it to today's games. Additional, somewhat more specific, information was also provided by Allan N. Wilson's "Casino Gambler's Guide", published in 1965. Thus, for quite a few years there has been no reason for gamblers to depend on guesswork or intuitive logic. The following fantasies, however, identified in Epstein's book, are as widely held now as they were a hundred years ago.
"A bet with a low probability of high gain is superior to one with a high probability of small gain". Thus, a 30-to-1 proposition bet on the craps table is better than an even-money wager on the Don't Pass Line, and, in roulette, a bet straight up on a number at 35 to 1 is preferable to wagering on red or black, regardless of the odds.
"The probability of consecutive independent events is additive rather than multiplicative". Hence the chance of throwing a seven on the craps table is twice as great with two throws as with one. If the chances for successive wins in a fair game are 1 out of 2, and 2 out of 4, then the chances are 3 out 6, 4 out of 8, and 5 out of 10. In reality, the chances are 3 out of 8, 4 out 16, and 5 out of 32.
"Everything will even out. After a streak of wins, the chances of losing increase". If a craps 12 has not shown for a certain number of throws, it becomes a good bet. If, in roulette, red has not come up for a specific number of spins, black becomes a bad bet.
"The probabilities of favorable events occurring are greater than unfavorable events of equal probability". A person with one chance in a hundred of winning a pool, and a 1% chance of dying from cancer, feels that the former is much more likely to happen. Similarly, a gambler feels that his chances of winning a 20-to-1 bet are greater than his chances of losing his money in a proposition with 5% risk-of-ruin factor.
"The expectations for present events are based on past events, despite mathematical independence". Thus, in blackjack, if you have broken every time you have hit sixteen that day, you should quit hitting sixteen, regardless of what the dealer holds. If you have drawn poor cards in a number of double-down situations, stop doubling.
"One large bet in a game is preferred to a series of small wagers totaling the same amount in the same game, but a series of small bets in different games is better than a single large wager in any of them". Therefore, a $100 bet in craps is better than four $25 wagers, but four $25 wagers, one each on blackjack, baccarat, roulette, and craps, are considered preferable to one $100 wager on any of them.
"A group of additive bets is not very interesting, but a multiplicative bet is often worthwhile". Three $5 bets on the favorites in three consecutive races are not considered very good, but a $15 three-horse parlay (if the first horse wins, all the payoff is bet on the second; if that horse wins, the total payoff is bet on the third) is considered an excellent bet.
"Winning streaks extend long enough and happen frequently enough to counteract both losing streaks and intermittent losses". If you progress your bets in a winning series, but make minimum bets in a losing series, you will win enough to offset both losing series, and the short cycle losses.
"A successful gambling session is the result of your superior skill, but a losing session is the result of bad luck". When your spouse wins, however, it's because she was very lucky, and when she loses it's because she played badly.
"Seeing is believing, so what you observe at a gambling game is better basis for a playing strategy than what some mathematician writes in some book". Maybe he has never even played the game. If betting all the hard ways at craps, and never splitting at blackjack, has been winning for you, that must be the way to go.
"Everybody has only so much luck, so be prepared to recognize it and use it to your advantage". If you have been practicing with the dice at home and have thrown ten passes in a row, stay away from the casino; obviously you have used up your share of luck for the day.
"There is no reason to be concerned about a proposition where you have only one chance in five hundred to get hurt". As it is highly improbable that a blackjack dealer will not break once in nine hands, doubling up after each loss at a $2 table with a $500 maximum bet will surely make you a winner before the house limit wipes you out.
"The power of positive thinking applies to gambling". You can't make your point at craps, or draw good cards in blackjack, if you expect to lose.
"Not only are some players inherently luckier than others, but this also extends to dealers and inanimate objects". In blackjack, locate and avoid lucky dealers, and in craps, search out hot tables, and players with hot dice. Identify and refuse to bet on unlucky craps shooters.