From a site selling the dice: "With these dice all players will have an equal chance of ranking first, second, third and fourth. And only one roll is required."

Wikipedia distinguishes between "go first fair" and "permutation fair". I believe Harshbarger wanted to find permutation fair dice.

Pretty sure he means this: - assume heads beats tails - if both players get opposite results (HT, TH) then the winner is obvious - if both players get heads, player A is the winner - if both players get tails, player B is the winner.