Nontransitive Dice
Nontransitive dice break the intuition that "beats" should be a ranking. With Efron’s four dice each die beats the next in a cycle two times out of three, so whichever die your opponent picks, you can pick one that beats it. This tool shows the face values, lets you choose a die and pick the winning counter-die, and simulates thousands of head-to-head rolls to reveal the win percentages and the full round-robin matrix of who beats whom.
Runs 100% in your browser — simulations are computed locally on your device.
Read the full guide to this tool
Notes
- Efron’s dice form a cycle A→B→C→D→A where each die wins about 2/3 of rolls against the next.
- "Beats" is not transitive here: there is no best die, so the player who chooses second always has the advantage.
- Comparing dice by their average face value is misleading — what matters is the face-by-face win count.
- Runs 100% in your browser — simulations are computed locally on your device.
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