Pig (dice)
Encyclopedia
Pig is a simple folk jeopardy dice game
first described in print by John Scarne
in 1945. 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.
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 options:
The first player to score 100 or more points wins.
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:
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.
Recently, the CS 61A class at Berkeley using Python has decided to use Pig to explore function abstraction. See http://www-inst.eecs.berkeley.edu/~cs61a/fa11/projects/pig/pig.html
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:
Analyses of many 2-dice variants are available in:
Human-playable Pig strategies are compared to optimal play in:
A Pig applet with an optimal computer opponent is also available.
A more comprehensive list of Pig rule variations is also available. Below are a few variations in detail.
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.
. Dice Games Properly Explained. Elliot Right-Way Books, Brighton Road, Lower Kingswood, Tadworth, Surrey, KT20 6TD UK, 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 to 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)).
Dice game
Dice games are games that use or incorporate a die as their sole or central component, usually as a random device.-Collectible dice games:Patterned after the success of collectible card games, a number of collectible dice games have been published...
first described in print by John Scarne
John Scarne
John Scarne was an American magician and book author who was particularly adept at playing card manipulation. He became known as an expert on cards and other games, and authored a number of popular books on cards, gambling, and related topics.-Early life:...
in 1945. As with many games of folk origin, Pig is played with many rule variations. Commercial variants of Pig include Pass the Pigs
Pass the Pigs
Pass the Pigs is a commercial version of the dice game, Pig. Pass the Pigs was originally published under the name Pig Mania!- Rules :...
, Pig Dice, and Skunk. Pig is commonly used by mathematics
Mathematics
Mathematics is the study of quantity, space, structure, and change. Mathematicians seek out patterns and formulate new conjectures. Mathematicians resolve the truth or falsity of conjectures by mathematical proofs, which are arguments sufficient to convince other mathematicians of their validity...
teachers to teach probability
Probability
Probability is ordinarily used to describe an attitude of mind towards some proposition of whose truth we arenot certain. The proposition of interest is usually of the form "Will a specific event occur?" The attitude of mind is of the form "How certain are we that the event will occur?" The...
concepts.
Basic Rules
Each turn, a player repeatedly rolls a dieDice
A die is a small throwable object with multiple resting positions, used for generating random numbers...
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 options:
- 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 probabilityProbability
Probability is ordinarily used to describe an attitude of mind towards some proposition of whose truth we arenot certain. The proposition of interest is usually of the form "Will a specific event occur?" The attitude of mind is of the form "How certain are we that the event will occur?" The...
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
Computer science
Computer science or computing science is the study of the theoretical foundations of information and computation and of practical techniques for their implementation and application in computer systems...
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.
Recently, the CS 61A class at Berkeley using Python has decided to use Pig to explore function abstraction. See http://www-inst.eecs.berkeley.edu/~cs61a/fa11/projects/pig/pig.html
Optimal Play
OptimalStrategy (game theory)
In game theory, a player's strategy in a game is a complete plan of action for whatever situation might arise; this fully determines the player's behaviour...
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.
Human-playable Pig strategies are compared to optimal play in:
- Todd W. Neller and Clifton G.M. Presser. Practical Play of the Dice Game Pig, The UMAP Journal 31(1) (2010), pp. 5–19.
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.
- Double 1s are bad: all points are lost. (See "Two Dice Pig" below)
- All doubles are good: twice the amount added to the turn total, except double 1s add 25 points. (See "Big Pig" below)
- 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 KniziaReiner Knizia
Reiner Knizia is a prolific German-style board game designer. Born in Germany, he developed his first game at the age of eight. He has a PhD in mathematics, and has been a full-time game designer since 1997, when he quit his job from the board of a large international bank...
. Dice Games Properly Explained. Elliot Right-Way Books, Brighton Road, Lower Kingswood, Tadworth, Surrey, KT20 6TD UK, 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
Pass the Pigs
Pass the Pigs is a commercial version of the dice game, Pig. Pass the Pigs was originally published under the name Pig Mania!- Rules :...
, Cosmic Wimpout
Cosmic Wimpout
Cosmic Wimpout is a dice game produced by C3, Inc in 1976. The game is played with five custom dice, and may use a combination score board and rolling surface, in the form of a piece of cloth or felt available in various colors and designs...
, Can't Stop). In jeopardy approach games, the object is to most closely approach a goal score without exceeding it (e.g. Twenty-One (die variant of Blackjack
Blackjack
Blackjack, also known as Twenty-one or Vingt-et-un , is the most widely played casino banking game in the world...
), Macao (R. Knizia. Dice Games Properly Explained. 1999)).