Optimal Play of the Dice Game Pig

The object of the jeopardy dice game Pig is to be the first player to reach 100 points. Each player's turn consists of repeatedly rolling a die. After each roll, the player is faced with two choices: roll again, or hold (decline to roll again). • 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 holds, the turn total, the sum of the rolls during the turn, is added to the player's score, and it becomes the opponent's turn. For such a simple dice game, one might expect a simple optimal strategy, such as in Blackjack (e.g., "stand on 17" under certain circumstances, etc.). As we shall see, this simple dice game yields a much more complex and intriguing optimal policy, described here for the first time. The reader should be familiar with basic concepts and notation of probability and linear algebra. Required Publisher's Statement Original version available from the publisher at: http://www.comap.com/product/periodicals/ This article is available at The Cupola: Scholarship at Gettysburg College: http://cupola.gettysburg.edu/csfac/4 Optimal Play of the Dice Game Pig 25 Optimal Play of the Dice Game Pig Todd W. Neller Clifton G.M. Presser Department of Computer Science 300 N. Washington St. Campus Box 402 Gettysburg College Gettysburg, PA 17325–1486 [email protected]