Towards Optimal Play in Multi-Player Yahtzee1

Article type: Research Article

Authors: Pawlewicz, Jakub²

Affiliations: Warsaw, Poland

Note: [1] This article is an expanded version (fully revised and thoroughly refereed by ICGA Journal referees) of a contribution to the CG2010 Conference in Kanazawa, Japan, under the title “Nearly Optimal Computer Play in Multi-Player Yahtzee” by the same author.

Note: [2] Institute of Informatics, Warsaw University, Warsaw, Poland. Email: pan@mimuw.edu.pl

Abstract: Yahtzee is the most popular commercial dice game in the world. It can be played either by one or many players. In case of the single-player version, optimal computer strategies both for maximizing the expected average score and for maximizing the probability of beating a particular score are already known. However, when it comes to the multi-player version, those approaches are far too resource intensive and thus are not able to develop an optimal strategy given the current hardware. This article presents the first in-depth analysis of the multi-player version of Yahtzee. The proposed implementation of an optimal strategy for the single-player version significantly speeds up the calculations. Resources necessary to memorize the optimal strategy for a two-player game are precisely estimated. It is shown that developing an optimal strategy for more than two players is not possible with the use of the current technology. For this case, a heuristic strategy is suggested. By means of experiments created especially for this purpose, it is proven that, in practice, this strategy is indistinguishable from the optimal one. An experimental analysis of the actual advantage of the optimal strategy over suboptimal opponents like humans has also been conducted. Our results show that (1) Yahtzee is “highly” a game of chance and (2) the advantage of the optimal strategy is insignificant.

DOI: 10.3233/ICG-2011-34103

Journal: ICGA Journal, vol. 34, no. 1, pp. 7-21, 2011