Roll dice and with the higher die winning. In terms of advantage, the possibilities are (equality), or . Nontransitive dice have the property , and . "Go First 3" and "Go First 4" dice have the property of equality (no advantage) with no shared numbers. When picking the first player in a game, each player can roll a die and have an equal chance of getting the highest roll. In the graphs, hover over a letter to see the die values. Arrows indicate which die has an advantage.
Oskar van Deventer developed the set {{2,14,17},{7,10,16},{5,13,15},{3,9,21},{4,11,18},{6,8,19},{1,12,20}}. Eric Harshbarger developed the "Go First 4" dice. Whether there is a "Go First 5" set on 60sided dice is unsolved. Bradley Efron developed the set {{4,4,4,4,0,0},{3,3,3,3,3,3},{6,6,2,2,2,2},{5,5,5,1,1,1}}. James Grime developed the set {{2,2,7,7,7},{1,6,6,6,6},{4,4,4,4,9},{3,3,3,8,8},{5,5,5,5,5}}. [3] M. Gardner, "Nontransitive Paradoxes," Time Travel and Other Mathematical Bewilderments, New York: W. H. Freeman, 1988. [4] M. Gardner, "Nontransitive Dice and Other Probability Paradoxes," Wheels, Life, and Other Mathematical Amusements, New York: W. H. Freeman, 1983.
