A mathematical approach to an optimal strategy for the dice game pig

It was the purpose of this study to investigate various pure strategies for the dice game Pig. Two basic approaches were considered for formulating an optimal strategy: the maximum number of rolls per turn that a player should take and the maximum number of points per turn that a player should attempt to accumulate. Basically, an optimal strategy for Pig will be one which allows a player to accumulate a maximum number of points in a minimum number of turns in order to achieve a goal of 100 or more points. Computer simulation of the game was used to verify the results and to attempt to distinguish subtle differences among the competing strategies which could not be determined through a purely theoretical formulation of the game. It was found that an optimal roll-per-turn strategy will be for a player to toss no less than two times per turn and no more than three times per turn. The optimal point-per-turn strategy from initial position of zero points is to attempt to accumulate at least 25 points. Through the computer simulation of the game, it was found that optimally a player should attempt to accumulate from 22 to 26 points on any turn if he is to attempt to accumulate the same number on each turn