Pig (dice game)

Pig or Evil One is a simple dice game with one dice . The rules were first written down in 1945 by John Scarne . Variants of this game are Up One Hundred One and Bad Three .

In game collections , these games are regularly included in the relevant rulebooks.

regulate

Pig is played with a single dice and dice cup.

The first player to collect a total of 100 points wins. Within a turn, all dice are added together until either a ONE is rolled, then the turn is over and all points on this turn are lost, or the player passes the die on. Only in this case the number of points rolled are added up and credited to the player's account.

In the variant Up to One Hundred and One , the same rules apply as with Pig and Bad One , but the goal is to achieve 101 points.

In addition to the version in which the one ends the move, there is a variant with the game Evil Three in which the move is ended by throwing a THREE. The winner here is whoever has the most points after the round.

strategy

Optimal game strategy is surprisingly complicated, despite the simplicity of the game. A simple tactic is to consider at which number of points you should continue playing. If you already have points in a move , you will probably lose points on the next roll of the dice or gain another 2, 3, 4, 5 or 6 points with probability . You should therefore only continue to play if the expected profit exceeds the expected loss, that is, if ${\displaystyle a}$ ${\displaystyle \textstyle {\frac {1}{6}}}$ ${\displaystyle a}$ ${\displaystyle \textstyle {\frac {1}{6}}}$

${\displaystyle \textstyle 0\leq {\frac {1}{6}}\cdot 2+{\frac {1}{6}}\cdot 3+{\frac {1}{6}}\cdot 4+{\frac {1}{6}}\cdot 5+{\frac {1}{6}}\cdot 6+{\frac {1}{6}}\cdot (-a)={\frac {20}{6}}-{\frac {a}{6}}}$, that is, if . ${\displaystyle a\leq 20}$

But that's not the best strategy, because risking points is very different from risking losing the game. You will certainly have to behave differently if your opponent or you are already clearly in the lead. That makes an optimal strategy much more complicated.

supporting documents

1. ↑ ^{a b} The Big Game Collection - Premium Edition . Rules booklet for the game collection by Schmidt Spiele; P. 13.
2. ↑ ^{a b} "Naked Sparrow" In: Erhard Gorys : The book of games. Manfred Pawlak Verlagsgesellschaft, Herrsching o. J .; P. 403. (Note: Gorys exchanges the title of Bis One Hundred and One with the game Naked Sparrow in his presentation )
3. ↑ ^{a b} "Böse Drei" In: Robert E. Lembke : The large house and family book of games. Lingen Verlag, Cologne, no date; P. 244.
4. ↑ Todd W. Neller Clifton GM Presser: Optimal Play of the Dice Game Pig

literature

• Clifford A. Pickover: The Math Book: From Pythagoras to the 57th Dimension - 250 Milestones in the History of Mathematics , ISBN 978-90-8998-280-3

Web links

• The Game of Pig website