  Each of two players, by turns, rolls a dice several times accumulating the
successive scores until he decides to stop, or he rolls an ace. When stopping,
the accumulated turn score is added to the player account and the dice is given
to his opponent. If he rolls an ace, the dice is given to the opponent without
adding any point. In this paper we formulate this game in the framework of
competitive Markov decision processes (also known as stochastic games), show
that the game has a value, provide an algorithm to compute the optimal minimax
strategy, and present results of this algorithm in three different variants of
the game.
