Practical Play of the Dice Game Pig

Introduction to Pig

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. However, optimal play is surprisingly complex and beyond human potential to memorize and apply. In this paper, we mathematically explore a more subjective question:

What is the simplest human-playable policy that most closely approximates optimal play?

While one cannot enumerate and search the space of all possible simple policies for Pig play, our exploration will present interesting insights and yield a surprisingly good policy that one can play by memorizing only three integers and using simple mental arithmetic. First, we review the criterion for optimality and discuss our means of comparing the relative performance of policies. Then we describe and evaluate several policies with respect to the optimal policy.