Martingale system

No wagering system can consistently beat casino games of pure chance such as craps, but that does not stop hopeful gamblers believing in them. One of the best known systems is the Martingale System, in which the player starts by betting $1 and doubles his bet whenever he loses. Upon winning, he starts over at $1.

The idea is to realize a net win of $1 after every eventual win. This system fails because the player will either run out of money after having to double his bet several times in a row after a streak of losing bets, or he will be unable to bet the amount dictated by the system because it would exceed the maximum bet allowed by the casino.

Gambler's fallacy

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 gambler's fallacy indicates that a craps player should bet on eleven if an eleven has not appeared or has appeared too often in the last 20 rolls.

In reality, each roll of the dice is an independent event, so the probability of rolling an eleven is exactly 1/18 on every roll, even if eleven has not come up in the last 100 rolls, or if eleven has come up 5 times in the last 5 rolls. The common term to describe this is "dice have no memory".

Parity hedge system

The parity hedge system is a hoax promulgated by Quatloos. Despite the fact that no such system exists (indeed, it is a mathematical impossibility), several gambling-related web sites have retold the 'parity hedge' story without attribution.