Theoretical Probability of Rolling Certain Scores It seems very attractive to try and calculate the probability of completing various target scores (such as full. Yahtzee is a dice game involving a combination of chance and strategy. On a player's turn, he or she begins by rolling five dice. After this roll, a. Chance . To get the maximum average score the strategy is straightforward. After the first throw the player will keep any 5s and 6s. Random chance : High.