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
Liar's dice a die (or dice) is the winner. The loser of the last round starts the bidding on the next round. If the loser of the last round was eliminated, the next player starts the new round. As with any game of chance, probability is highly important. The key element is the "expected quantity": the quantity of any face value that has the highest probability of being present. For six-sided dice, the expected quantity is one-sixth the number of dice in play, rounded down. When wilds are used, the expected quantity is doubled as players can expect as many aces, on