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
Dice chess kings is to reduce the elements of chance in the game. Another form of dice chess is "Vegas Fun Chess", whose rules are described here. That site also indicates that "Pritchard's Encyclopedia of Chess Variants contains descriptions of seven versions of what he calls 'Dice Chess'." John Gollon, in his book "Chess Variations: Ancient, Regional, and Modern", notes three ways in which dice may be used in connection with a game of chess. The most common is similar to that described in the preceding sections. A second way to use dice is to have each player roll one die on