Pigtail: A Pig Addendum

The object of the jeopardy dice game Pig is to be the first player to reach 100 points. Each turn, a player repeatedly rolls a die until either a 1 is rolled or the player holds and scores the sum of the rolls (i.e., the turn total). At any time during a player’s turn, the player is faced with two choices: roll or hold. If the player rolls a 1, the player scores nothing and it becomes the opponent’s turn. If the player rolls a number other than 1, the number is added to the player’s turn total and the player’s turn continues. If the player instead chooses to hold, the turn total is added to the player’s score and it becomes the opponent’s turn. In our original article [Neller and Presser 2004], we described a means to compute optimal play for Pig. Since that time, we have also solved a number of Pig variants. In this addendum, we review the optimality equations for Pig, show how these equations change for several Pig variants, and show how the resulting optimal policies change accordingly. [excerpt]