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Three Nontransitive Dice

OVERVIEW
  • 3D printed in Polished Metallic Plastic: Grey nylon plastic with a subtle metallic sparkle and polished sheen (formerly Polished Alumide.)
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  • This product is intended for mature audiences.
$14.00
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Product Description

A set of three 6-sided dice that beat each other in a cyclic manner. Die A is labeled {1, 3, 8, 14, 15, 16}, Die B is labeled {4, 5, 6, 7, 17, 18}, and Die C is labeled {2, 9, 10, 11, 12, 13}. The numbers 1 through 18 are used once and on each die the sum of the faces is 57

If Dice A and B are rolled, B beats A 5/9 of the time. If Dice B and C are rolled, C beats B 5/9 of the time. And if Dice C and A are rolled, A beats C 5/9 of the time. There are no ties. The probabilities of one die beating another is not transitive among the three.

How to play with an opponent who does not know the secret of nontransitive dice: Let your opponent pick any one of the dice. Then you pick the corresponding die that beats it 5/9 of the time.

 

How to play a fair game with two players: First, each player blindly picks one of the three dice, leaving one die behind.  The players roll against each other, and the player who rolled the lower number switches to the die left behind.  Play continues in this way with the loser of each roll switching to the die left behind.  The first player to win four rolls in a row is the overall winner.

What's in the Box
INCM
Three Nontransitive Dice
Polished Metallic Plastic
Width
4.0 cm
Height
1.3 cm
Depth
3.3 cm

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