Non-transitive dice
A beats B, B beats C… can D beat A?
Playback is compressed; model values are shown separately.
Make a prediction
Which die is more likely to win this pairing?
Ready. Adjust the settings or press Run.
How it works & assumptions
Enumerate all 36 ordered face pairs. 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].
Fair, independent six-faced dice. Ties are counted separately. Replay uses the same random sequence.
References: CS109: Sampling, Bootstrap, and P-Hacking, Lisa Yan (2020), slide 69
Random runs are reproducible from their setup links. Replay keeps the same seed; New random run changes it. A sample run need not equal the theoretical average.