A counter-intuitive mathematical fact is the existence of Intransitive Dice. A set of 3 dice (A,B,C) is intransitive if A normally beats B, B normally beats C, but A does not normally beat C.
Here's an example:
- Die A has sides 2, 2, 4, 4, 9, 9.
- Die B has sides 1, 1, 6, 6, 8, 8.
- Die C has sides 3, 3, 5, 5, 7, 7.
The probability that A rolls a higher number than B, the probability that B rolls higher than C, and the probability that C rolls higher than A are all 5/9, so this set of dice is intransitive.