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Arnold Snyder's articles in Blackjack Forum magazine were the first to bring Shuffle Tracking to the general public. The Theory of Blackjack, Peter Griffin, 1996 (1979), ISBN 0929712129 If the 'Banker' has an initial total of 0, 1 or 2, the 'Banker' draws another card. The gambler's fallacy exposed Consider a flipping coin game with two players where each player having 50% chance of winning each flip. After a flip the loser transfers one penny to the winner. The game ends when one player has all the pennies. If the number of flips is infinite, the probability that the game will eventually end is 100%. If player one has n1 pennies and player two n2 pennies , the chances P1 and P2 that players one and two, respectively, will end penniless are: A couple already has two daughters. What is the probability that the next child is a son? (Answer: 0.5) [if we assume the gender of a child is completely random, and that a male or female child is equally likely, either or both of which may be incorrect.] Calculates interactively the probabilities and expectations for each possible card-distribution in the shoe Their Flash games work right in Safari, either free-play or for real money. Bingo The game of poker (or at least most of the variants) is considered to be computationally intractable. However, methods are being developed to at least approximate perfect strategy from the game theory perspective in the heads-up (two player) game, and increasingly good systems are being created for the multi-player or ring game. Perfect strategy has multiple meanings in this context. From a game-theoretic optimal point of view, a perfect strategy is a minimax one that cannot expect to lose to any other player's strategy; however, optimal strategy can vary in the presence of sub-optimal players who have weaknesses that can be exploited. In this case, a perfect strategy would be one that correctly or closely models those weaknesses and takes advantage of them to make a profit. Some of these systems are based on Bayes theorem, Nash equilibrium, Monte Carlo simulation, and Neural networks. A large amount of the research is being done at the University of Alberta by the GAMES group led by Jonathan Schaeffer who developed Poki and PsOpt. Video poker Encyclopedia of Casino Twenty-One
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Roulette  Random number games Example: The player originally bets $10 and the dealer shows an Ace. The player takes Insurance by betting an additional amount of $5. Suppose the player's hand is 19. The dealer turns up his 'hole card' after the Insurance betting period is over -- and it's a 10-valued card. The player loses his $10 bet. But the Insurance bet wins, so the player gets 2:1 on his $5 Insurance wager and receives $10 (on top of the $5 which are returned to him). Note that the player came out even (i.e. did not lose any money) on that round. The bank is at the outset put up to auction, i.e. belongs to the player who will undertake to risk the largest amount. In some circles, the person who has first set down his name on the list of players has the right to hold the first bank, risking such amount as he may think proper. It might be pointed out that where economic activity is concentrated in transfers of wealth rather than its creation, gambler's ruin results in most of the wealth being held by a very small number of participants. We see this in the stock market when speculative activity is the norm rather than long-term dividend producing investment   You call this one and it's all over, baby. - Scotty Nguyen, during the 1998 World Series of Poker. Down to him and one other player, he said this to his opponent who called, and it was all over. Roulette Following the settlement Providian National Bank announced that they would not let users of their Visa card gamble over the Internet. MasterCard will now require Internet casinos that use their cards to ask gamblers where they live and keep a record of the information. The company also requires the sites to post notices stating that Internet gambling is illegal in California and other States. Most of the publicity this case attracted had died down until Thursday December 7th when a new case was filed.
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