Optimal Play of the Farkle Dice Game

Abstract

We present and solve optimality equations for the 2-player, jeopardy dice game Farkle (a.k.a. Dix Mille, Ten Thousand). For fairest play, we recommend 200 compensation points at the beginning of the game for the second player. We then compute the strategy that maximizes expected score, demonstrate a means for replicating such play with mental mathematics, and augment this method so as to enable human Farkle play against which complex optimal play maintains only a small win advantage of ~1.7754%