On Medians Of Lattice Distributions And A Game With Two Dice

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Combinatorics, Probability, And Computing


Let D₁ and D₂ be two dice with k and l integer faces, respectively, where k and l are two positive integers. The game G_n consists of tossing each die n times and summing the resulting faces. The die with the higher total wins the game. We examine the question of which die wins game G_n more often, for large values of n. We also give an example of a set of three dice which is non-transitive in game G_n for infinitely many values of n.