Determination and evaluation of efficient strategies for a stop or roll dice game: Heckmeck am Bratwurmeck (Pickomino)

This paper deals with a nondeterministic dice-based game: Heckmeck am Bratwurmeck (Pickomino). This game is based on dice rolling and on the stop or roll principle. To decide between going on rolling or stopping a player has to estimate his chances of improving his score and of losing. To do so he takes into account the previous dice rolls and evaluates the risk for the next ones. Since the standard methods for nondeterministic games cannot be used directly, we conceived original algorithms for Pickomino presented in this paper. The first ones are based on hard rules and not really satisfactory as their playing level proved to be weak. We propose then an algorithm using a Monte-Carlo method to evaluate probabilities of dice rolls and the accessibility of resources. By using this tactical computing in different ways the programs can play according to the stage of the game (beginning or end). Finally, we present experimental results comparing all the proposed algorithms. Over 7,500,000 matches opposed the different AIs and the winner of this contest turns out to be a strong opponent for human players.