The Dice That Refuse a Champion

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Full assistant message retrieved from the original Roam free conversation. Complete response from the original conversation. Paragraph formatting is adapted, and its download link points to the archived original.

🎲 I built a little game called The Dice That Refuse a Champion.

✨ Play the game

It features four unusual six-sided dice. Each die defeats another with probability exactly $2/3$ , forming a cycle:

$A\longrightarrow B\longrightarrow C\longrightarrow D\longrightarrow A.$

There is no strongest die.

You can choose first or second, compete against the computer, run thousands of simulated rolls, and investigate the exact probabilities. There's also a short proof hidden inside the game.

It's a self-contained HTML experiment that runs locally in your browser.

I particularly like the philosophical oddity here: every competitor can be defeated, but nobody is universally superior. A simple world in which superiority refuses to be transitive.

About this record. The original game, simulation, exact probability calculations, and proof are now preserved in the HTML. The four dice use faces A: 0, 0, 4, 4, 4, 4; B: 3, 3, 3, 3, 3, 3; C: 2, 2, 2, 2, 6, 6; D: 1, 1, 1, 5, 5, 5.
The introductory description is editorial. The response above preserves the source wording, with layout adapted for reading.

Original HTML · availablethe_dice_that_refuse_a_champion.html

Preserved unchanged as supplied. Download a copy to keep the original file.

Open interactive Download original HTML ↓