Count face pairs
Die A has faces 2, 2, 4, 4, 9, 9. Die B has 1, 1, 6, 6, 8, 8. Their 36 ordered face pairs are equally likely. A wins 4 + 4 + 12 = 20 of them, so A beats B with probability 20/36 = 5/9.
Compare dice in pairs
Discover why a die can beat one rival and lose to another.
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What next?
- Nontransitive dice
Practice · Find dice that beat one another in a cycle, then test how rolling twice changes the best response.
- Probability
Book · Count outcomes, update chances with new information, and compare decisions through worked examples.
- Race patterns with a biased coin
Previous lesson · Track both patterns on one sequence and count unfinished races.
- Choose a die after two rolls
Next lesson · Build the distribution of sums before choosing a counter to an opponent.