Seven Non-Transitive Dice

Seven Non-Transitive Dice, a.k.a. Oskar's Dice (designed in 1992) is a set of seven dice as follows, see also Wikipedia:

• A: 2, 2, 14, 14, 17, 17
• B: 7, 7, 10, 10, 16, 16
• C: 5, 5, 13, 13, 15, 15
• D: 3, 3, 9, 9, 21, 21
• E: 1, 1, 12, 12, 20, 20
• F: 6, 6, 8, 8, 19, 19
• G: 4, 4, 11, 11, 18, 18

Die A beats die C, as statistically when you throw both many times, die A will turn up a higher number than die B more than 50% of the throws. Similarly die C beats die G. So whien die A competes against die G, which will win? Surprisingly G beats A. This is why these dice are called "non-transitive".

This specific set of seven dice has the property that for arbitrarily chosen two dice there is always a third one that beats both of them. Namely,

• G beats A,B; F beats A,C; G beats A,D; D beats A,E; D beats A,F; F beats A,G;
• A beats B,C; G beats B,D; A beats B,E; E beats B,F; E beats B,G;
• B beats C,D; A beats C,E; B beats C,F; F beats C,G;
• C beats D,E; B beats D,F; C beats D,G;
• D beats E,F; C beats E,G;
• E beats F,G.

Whatever the two opponents choose, the third player will find one of the remaining dice that beats both opponents' dice.

Order the set of dice in a single color by buying this model. Order the set of dice in seven different colors by ordering each die separately as follows.

1. Die A
2. Die B
3. Die C
4. Die D
5. Die E
6. Die F
7. Die G

Watch the YouTube video.
Read at the Shapeways Forum.
Read more at the Non-Twisty Puzzles Forum.

Please contact Oskar for information about the stickers, or if you want to purchase a complete stickered set. See also Eric Harshbarger's production of Oskar Dice.