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
Hazard (game) chance of 6, he could win £8 (4/5 × £10). For each main the probability of winning can be calculated: In some reports on the rules of the game, the main is determined randomly by tossing the dice until a valid main appears. In this case the overall player disadvantage is 1.84%. If the caster can choose a main, he should always choose 7 (resulting in the lowest disadvantage, with 1.41%). This is the origin of a similar dice game, craps, since if 7 is always chosen the game devolves into craps. The name "hazard" is borrowed from Old French.