Craps principle and formula_29 ; in particular, the probability of a draw is irrelevant. If the game is played repeatedly until someone wins, then the conditional probability above is the probability that the player wins the game. This is illustrated below for the original game of craps, using an alternative proof. If the game being played is craps, then this principle can greatly simplify the computation of the probability of winning in a certain scenario. Specifically, if the first roll is a 4, 5, 6, 8, 9, or 10, then the dice are repeatedly re-rolled until one of two events occurs: Since
Craps does not stop gamblers from believing in them. One of the best known systems is the Martingale System. In this strategy, the gambler doubles his bet after every loss. After a win, the bet is reset to the original bet. The theory is that the first win would recover all previous losses plus win a profit equal to the original stake. The main article on martingale describes the flaws in this system. Other systems depend on the gambler's fallacy, which in craps terms is the belief that past dice rolls influence the probabilities of future dice rolls. For example, the