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Department 1

Computer Science


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.

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