Gambling Guide

Pig is a simple folk jeopardy dice game first described in print by John Scarne in 1945 (Scarne, John. 1945. Scarne on Dice. Harrisburg, PA: Military Service Publishing Co.). As with many games of folk origin, Pig is played with many rule variations. Commercial variants of Pig include Pass the Pigs™, Pig Dice™, and Skunk™. Pig is commonly used by mathematics teachers to teach probability concepts.

Contents 1 Basic Rules 1.1 Example Play 2 Teaching Mathematics and Computer Science 3 Optimal Play 4 Rule Variations 4.1 Two-Dice Pig 4.2 Big Pig 4.3 SKUNK 5 Jeopardy Dice Games

Basic Rules

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 decisions:

• roll - If the player rolls a
  • 1: the player scores nothing and it becomes the next player's turn.
  • 2 - 6: the number is added to the player's turn total and the player's turn continues.
• hold - The turn total is added to the player's score and it becomes the next player's turn.

The first player to score 100 or more points wins.

Example Play

For example, the first player, Ann, begins a turn with a roll of 5. Ann could hold and score 5 points, but chooses to roll again. Ann rolls a 2, and could hold with a turn total of 7 points, but chooses to roll again. Ann rolls a 1, and must end her turn without scoring. The next player, Bob, rolls the sequence 4-5-3-5-5, after which he chooses to hold, and adds his turn total of 22 points to his score.

Teaching Mathematics and Computer Science

Pig often serves as a simple, fun example for teaching probability concepts from the middle school level upwards. For example, the Interactive Mathematics Program uses The Game of Pig as the core example for its Year 1 probability curriculum, and offers a downloadable Pig simulation tool to test simple strategies for long term scoring. Similar curricular materials are available on the NZMaths Statistics Web-site. A more comprehensive list of online Pig teaching resources is also available.

Pig also provides many valuable exercises for teaching Computer Science in areas ranging from introductory courses to advanced machine learning material. See Computer Science Resources for the Game Pig and/or the following journal publication:

Todd W. Neller, Clifton G.M. Presser, Ingrid Russell, Zdravko Markov. Pedagogical Possibilities for the Dice Game Pig. Journal of Computing Sciences in Colleges, vol. 21, no. 6, pp. 149-161, June 2006.

A guide to computing optimal play for Pig and similar games is freely available as the NSF-sponsored project Solving the Dice Game Pig: an introduction to dynamic programming and value iteration.

Optimal Play

Optimal play for 2-player Pig

Optimal play for 2-player Pig was computed by Todd W. Neller and visualized by Clifton G. M. Presser in 2001. The figure to the right visualizes optimal play. At any time, the relevant decision information includes the player's score, the opponent's score, and the turn total. Such information corresponds to a 3D point in the graph's space. If this point is inside the gray solid, the player should roll. Otherwise, the player should hold.

Details of the analysis are available from the Game of Pig website, and:

• Todd W. Neller and Clifton G.M. Presser. Optimal Play of the Dice Game Pig, The UMAP Journal 25(1) (2004), pp. 25-47.

Analyses of many 2-dice variants are available in:

• Todd W. Neller and Clifton G.M. Presser. Pigtail: A Pig Addendum, The UMAP Journal 26(4) (2005), pp. 443-458.

A Pig applet with an optimal computer opponent is also available.

Rule Variations

Common rule variations include:

• Two dice: two dice are rolled instead of one.
  • Doubles 1s are bad: all points are lost.
  • All doubles are good: twice the amount added to the turn total, except double 1s add 25 points.
• Any number of dice ("Hog" variation): the player rolls only once per turn with an arbitrary number of dice.
• 6 is bad: a roll of 6 is treated as a roll of 1.

A more comprehensive list of Pig rule variations is also available. Below are a few variations in detail.

Two-Dice Pig

This variation is the same as Pig, except:

• Two standard dice are rolled. If neither shows a 1, their sum is added to the turn total.
• If a single 1 is rolled, the player scores nothing and the turn ends.
• If two 1s are rolled, the player’s entire score is lost, and the turn ends.

Big Pig

This variation is the same as Two-Dice Pig, except:

• If two 1s are rolled, the player adds 25 to the turn total.
• If other doubles are rolled, the player adds twice the value of the dice to the turn total.

SKUNK

Not to be confused with the commercial game Skunk, SKUNK (a.k.a. THINK) is a variation of Two-Dice Pig that is played with large groups. Rather than rolling in turn, all players begin the round standing. At any point in the round, a player may hold by sitting down. The round continues until a 1 is rolled, or all players have sat down.

Skunk is played in five rounds, and scoring is recorded in a 5-column table with columns labeled with the letters of the word "SKUNK". The first round score is entered in the "S"-column, the next in the first "K"-column, and so on. After five rounds, the highest-scoring player is the winner.

Jeopardy Dice Games

Pig is one of a family of dice games called jeopardy dice games (Reiner Knizia. Dice Games Properly Explained. Elliot Right-Way Books, Brighton Road, Lower Kingswood, Tadworth, Surrey, KT20 6TD U.K., 1999). For jeopardy dice games, the dominant type of decision is whether or not to jeopardize previous gains by rolling for potential greater gains. Most jeopardy dice games can be further subdivided into two categories: jeopardy race games and jeopardy approach games. In jeopardy race games, the object is to be the first to meet or exceed a goal score (e.g. Pig, Pass the Pigs™, Cosmic Wimpout, Can't Stop™). In jeopardy approach games, the object is most closely approach a goal score without exceeding it (e.g. Twenty-One (die variant of Blackjack), Macao (R. Knizia. Dice Games Properly Explained. 1999)).