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 pool the system goes into. They also provide players with a physical representation for the modifiers, as real, concrete dice are added to the pool (or taken away from it). Some people also find rolling a large handful of dice fun in its own right. The other thing dice pools allow is opening up a lot of design space for game designers; if something other than the number on the dice is important, the number itself can be used to add richness to the system. West End Games's "Ghostbusters" role-playing game by Greg Stafford, Lynn Willis, and Sandy Petersen featured a