Optimal Solitaire Yahtzee Player: Disclaimers

In particular, take note of the following points:

• The Optimal Solitaire Yahtzee Player is designed to maximize its expected final score, while playing Solitaire Yahtzee with fair dice. The employed strategy is neither aimed at maximizing the likelihood of breaking a high-score, nor aimed at beating the final score of opponents. To optimize performance for such purposes requires a different strategy.

• When assessing a given game state, the Optimal Solitaire Yahtzee Player takes all legal future developments of the game into account. Because the dice rolls are not under control of the player, there is no guarantee that in any particular game the indicated expected final score will be obtained, or even approached. For instance, the final scores from one million simulated games by the Optimal Solitaire Yahtzee Player ranged from 73 to 845. Also see Backgrounds.

• The Law of Large Numbers does guarantee that, when games are played with fair dice, the actually obtained average final score taken over a large number of independent games will be close to the theoretically expected final score (i.e. 254.5896...) with great probability. However, the number of games to play for obtaining a predetermined accuracy of approximation with a predetermined confidence level can be enormous. For instance, two independent simulations of one million games yielded average final scores of approximately 254.51 and 254.65 respectively.

• The (conditional) expected final scores as given by the Optimal Solitaire Yahtzee Player are based on the assumption that all future choices in the game are made optimally. It is imaginable that there are situations where one choice is best under optimal play, but where another choice is safer if you do not know how to proceed optimally.