I will define Markov chains and stochastic matrices (transition matrices) and then show how it can be applied to Yahtzee. We will find the probability of rolling a Yahtzee (given only three rolls), the average number of rolls one would need to get a Yahtzee (if given any number of rolls), and see that there is an optimal strategy when playing Yahtzee. Well look at a few interesting scenarios where the optimal strategy may contradict your own strategy.