Pig (dice game)

Pig is a simple dice game first described in print by John Scarne in 1945.[1] As with many games of folk origin, Pig is played with many rule variations. Commercial variants of Pig include Pass the Pigs, Pig Dice,[2] and Skunk. Pig is commonly used by mathematics teachers to teach probability concepts.

Pig is one of a family of dice games described by Reiner Knizia as "jeopardy dice games". 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.[3]

Gameplay

Each turn, a player repeatedly rolls a die until either a 1 is rolled or the player decides to "hold":

The first player to score 100 or more points wins.

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.

Optimal play

A visualisation of optimal play in the game of 2-player Pig

Optimal play for 2-player Pig was computed by Todd W. Neller[4] and visualized by Clifton G. M. Presser in 2001.[5] 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.

Many 2-dice variants have been analysed,[6] and human-playable Pig strategies have been compared to optimal play.[7]

Variations

Common rule variations include:[8]

Two-Dice Pig

This variation is the same as Pig, except:

Big Pig

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

Skunk

Skunk (or 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.[9]

Teaching

Pig often serves as a simple example for teaching probability concepts from the middle school level upwards. The game also provides exercises for teaching Computer Science in areas ranging from introductory courses to advanced machine learning material.[10]

References

  1. Scarne, John (1945). Scarne on Dice. Harrisburg, Pennsylvania: Military Service Publishing Co.
  2. Pig at BoardGameGeek
  3. Reiner Knizia, Dice Games Properly Explained. Elliot Right-Way Books, 1999
  4. Todd W. Neller and Clifton G.M. Presser. Optimal Play of the Dice Game Pig, The UMAP Journal 25(1) (2004), pp. 2547.
  5. http://cs.gettysburg.edu/projects/pig/pigVis.html
  6. Todd W. Neller and Clifton G.M. Presser. Pigtail: A Pig Addendum, The UMAP Journal 26(4) (2005), pp. 443458.
  7. Todd W. Neller and Clifton G.M. Presser. Practical Play of the Dice Game Pig, The UMAP Journal 31(1) (2010), pp. 519.
  8. http://cs.gettysburg.edu/projects/pig/piglinks.html
  9. http://illuminations.nctm.org/index_d.aspx?id=248
  10. 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. 149161, June 2006.

External links

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