Note that not all entries are filled in in the table. However, if I had 500 points rolling 3, banking the 500 points is the best play because the risk of Farkling is too high to wager the 500 points. This information has enough information to derive the optimal strategy.įor example, lets say I have 250 points and I am rolling 3 dice, it can be seen that the best option for me is to roll again (yielding an expected value of 293.4 which is better than 250). By optimal play, I mean the player always takes actions to maximize her expected score. Each entry of the table contains the expected value of the state, which is how many points we can expect to make from that state on average, assuming optimal play. I make this intuition precise in the table below. On the other hand if the current score is low and there are at least four dice to roll, it is best to make the small gamble and keep rolling. Intuitively, if the current score is high and there is only one or two dice to roll, it is too risky of a gamble to roll.
At any games state, the player has multiple options: she can end her turn, accepting her current score, or she can gamble her current score by rolling the remaining dice for a chance to score more points. The "game state" of Farkle roll can roughly be characterized by 2 values: the current score accumulated, and the number of dice left to roll. There are many variants to Farkle, but I like to play by this set of rules. Before I begin, let me first state the value of different dice rolls I assumed while developing the strategy.Įverything else is considered to be a Farkle (0 points).
All of my findings are based on sound mathematical methods and a computer program was used to determine the optimal strategy. If you are unfamiliar with the game, I encourage you to skim the linked article so that you can better understand this blog post. In this post, I will discuss my findings in terms of an optimal strategy for Farkle, which is a dice game of chance.
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