Optimum Strategies for the Game Super Six

Abstract

In the game "Super Six", after successfully getting rid of a stick by rolling with the die a number that is not occupied, the player has the choice to continue to roll the die or to stop and to hand over the die to their opponent. The probability to win depends on the situation and on the chosen strategy. In this paper, the optimum strategy to maximise the winning probability is derived. If there are 1 or 2 sticks on the lid, it is always best to continue to roll the die. If there are 5 sticks on the lid it is best to stop. If there are 4 sticks on the lid it is best to stop unless both players have one stick in their hands. If there are 3 sticks on the lid, the optimum strategy depends on the number of sticks in the hands of the two players.