Optimal Yatzy Strategy

Abstract: Yatzy is a famous dice game that is played with a scorecard and five dice. By rolling the dice the player’s goal is to achieve a combination of dice and place the score in one of 15 categories. At the end of the game when all categories are filled the points for every category are summarized. We have developed an algorithm that makes up the optimal strategy of the game by calculating the expected value for each state of the game, recursing backwards from the last roll of the game to the first. The implementation was unsuccessful, as the algorithm was too inefficient to run in an acceptable amount of time. Instead, a part of the algorithm was run, starting the game with 10 randomly chosen categories filled with 0 points and collecting the average scores for the remaining categories using 1 million simulations. The result was 167.60 points, which sets a lower boundary to the expected value for the complete game.