setup
You need: Two standard 6-
sided dice (numbered 1 to 6).
2 players
rules
Both players roll the dice at the same
time.
If the sum is 7 or 11, Player 1 wins.
If the sum is 2, 3, or 12, Player 2 wins.
Any other sum = tie and they roll again.
expected outcome
Total possible dice combos = 6 × 6 = 36
Winning outcomes for Player 1:
7 → (1,6), (2,5), (3,4), (4,3), (5,2), (6,1) = 6 ways
11 → (5,6), (6,5) = 2 ways
Total = 8/36 = 2/9 ≈ 22.2%
Player 2 wins:
2 → (1,1) = 1 way
3 → (1,2), (2,1) = 2 ways
12 → (6,6) = 1 way
Total = 4/36 = 1/9 ≈ 11.1%
Tie: 24/36 = 2/3 = 66.6%