Western Michigan University mathematician Allen J. Schwenk discovered this oddity in 2000: Consider three fair six-sided dice of different colors, marked with the following numbers:

• Red: 2, 2, 2, 11, 11, 14
• Blue: 0, 3, 3, 12, 12, 12
• Green: 1, 1, 1, 13, 13, 13

Now:

• The red die beats the green die 7/12 of the time.
• The blue die beats the red die 7/12 of the time.
• The green die beats the blue die 7/12 of the time.

We’ve seen that before. But look at this:

• A pair of green dice beats a pair of red dice 693/1296 of the time.
• A pair of red dice beats a pair of blue dice 675/1296 of the time.
• A pair of blue dice beats a pair of green dice 693/1296 of the time.

The favored color in each pairing has changed! Schwenk writes, “I call this a perverse reversal.”

(And a bonus: It turns out that a pair of Schwenk dice of any one color is an even match against a mixed pair of the other two colors.)

(Allen J. Schwenk, “Beware of Geeks Bearing Grifts,” Math Horizons 7:4 [April 2000], 10-13, via Jennifer Beineke and Lowell Beineke, “Some ABCs of Graphs and Games,” in Jennifer Beineke and Jason Rosenhouse, eds., The Mathematics of Various Entertaining Subjects, 2016.)