Optimum Strategies for the Game Super Six

TL;DR

This paper derives the optimal strategies for the game Super Six, analyzing how players should decide to roll or stop based on the current game state to maximize their chances of winning.

Contribution

It provides a detailed analysis of the optimal strategies in Super Six, considering different game states and player situations, which was not previously established.

Findings

Optimal strategies depend on the number of sticks on the lid.

Players should always continue if 1 or 2 sticks are on the lid.

Players should stop if 5 sticks are on the lid.

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.