The Mathematics of Gambling

The Mathematics of Gambling, 9780897460194 (0897460197), Lyle Stuart, 1985

Casino card games such as baccarat and blackjack differ significantly from casino games such as craps, roulette, and slot machines in that they are not indepen- dent trial processes-that is, the cards that already have been played do affect the odds on subsequent hands. Consider for a moment the game of blackjack, where the cards used on a round are put aside and successive rounds are dealt from an increasingly depleted pack. The cards are reshuffled before a round if the remain- ing unused cards would be insufficient to complete a round or earlier, usually at the casino's discretion. What the early research on blackjack (contained in Beat the Dealer) showed and what has been confirmed repeated- ly in the intervening 23 years is that the end pack pro- vides favorable situations often enough to give the player an overall advantage.

While it is foolish to keep a record of past decisions at craps in order to determine which numbers are "hot" or "cold" (the dice have no memory), an ability to keep track of which cards have been played and knowledge of their relationship to the player's expectation can be beneficial, as long as the cards are not reshuffled after every hand.

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