Pig (dice game)

Basic rules

The canonical rules used in most casual play are straightforward and easy to teach:

• Players take turns; on a player’s turn they may roll a single six-sided die as many times as they wish.
• If the die shows 2–6, that value is added to the turn total and the player decides whether to roll again or hold.
• If the die shows 1, the player scores nothing for that turn and the turn ends immediately.
• If the player holds, the turn total is added to their running score. Play passes to the next player.
• The objective is to reach or exceed a mutually agreed target score (commonly 100) before other players.

Strategy and mathematics

Though the rules are simple, Pig has nontrivial strategy. Players balance the incremental gains from additional rolls against the probability of rolling a 1 and losing the turn total. Computer analysis and dynamic programming have been used to compute optimal play for the standard single-die variant; these results show that optimal policies vary with the current scores and the remaining distance to the target. Simpler heuristic strategies—for example, “hold when the turn total reaches a fixed threshold”—are popular and perform well for casual play. Because of its clarity and well-posed decision structure, Pig is also used as an example problem in probability, expected value calculations, and reinforcement learning.

History and development

The game appears in collections of folk games and was described in popular game literature in the mid-20th century; John Scarne discussed Pig in 1945 as a common dice pastime. Since then, Pig has attracted attention from recreational-mathematics writers and computer scientists interested in optimal stopping problems. The simple rule set has led to many documented variants and to implementations as classroom exercises and programming assignments.

Variants and common adaptations

• Two-dice Pig or “Big Pig”: uses two dice and adds rules for doubles or combined rolls that change outcomes.
• Pass variants: allow a player to pass some or all of their turn total to another player under certain conditions.
• Scoring or target adjustments: lower or higher winning totals, or bonus rules for specific roll sequences, alter strategy and game length.

Uses and cultural notes

Pig is frequently used in classrooms to demonstrate probability, expected value, and risk assessment. It also serves as a simple benchmark problem for algorithmic research into dynamic programming and reinforcement learning. Physical play requires only a single die and paper for scores, and many digital versions exist for solo practice or statistical experimentation. For further general information on jeopardy dice games and recreational play, see related summaries at jeopardy dice games and general game collections at game references.