Efron's Dice are a set of four (non-standard) dice A, B, C, D such that A has a 2/3 probability of beating B when they are rolled together; B of C; C of D; and D has a 2/3 probability of beating A. The dice are thus non-transitive.
- A: 4/4/4/4/0/0
- B: 3/3/3/3/3/3
- C: 6/6/2/2/2/2
- D: 5/5/5/1/1/1
The probability of A beating B, and B of C; is clearly 2/3. For C over D the probability is
- 1/3+2/3×1/2 = 2/3;
for D over A it is
- 1/2 + 1/2×1/3 = 2/3.
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