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Yahtzee is a popular dice game that involves a combination of chance and decision making. We implemented a brute-force algorithm to understand optimal play for a solitaire version of Yahtzee using Mathematica. The novelty in our approach is that we were able to compute probabilities and expectations of the optimal player’s score  exactly  as rational numbers. Previous work involved only numerical approximations. We give an overview of our approach and analyze some of the data generated by our implementation. The figures provided in the article should give an insight as to how a game under optimal play would typically unfold.

Let’s Get Rolling! Exact Optimal Solitaire Yahtzee