<p>Video poker is a casino game based on five-card draw poker played on a computerized console. Video poker allows players an opportunity for some control of the random events that determine whether they win or lose. This means that making the right play can increase a player's return in the long run. For that reason, optimal strategy hand-rank tables for various types of video poker games have been recently published and established to help players improve their return (Ethier, 2010). Ethier posed a number of open problems in his recent book, <em>The Doctrine of Chances: Probabilitistic Aspects of Gambling</em> among which were some in video poker. In this thesis we consider the most popular video poker games: Jacks or Better, Double Bonus, and Joker Wild. Ethier produced an optimal strategy hand-rank table for Jacks or Better. We expand on his method to produce optimal hand-rank tables for Double Bonus, and Joker Wild. The method involves enumerating all possible discards, computing the expected returns, and then finding a way to rank them according to optimal discard based on the payoffs. The methodology combines combinatorics with probability and C++ programming. For Double Bonus and Joker Wild new terminologies are introduced in order to illustrate how different cards can affect the magnitude of expected return of a particular hand. Furthermore, ranks whose organization and specification are noteworthy in the hand-rank tables are examined and provided with in-depth explanations and supporting examples. The final result is a hand-rank table for use by the player. The player chooses that discard which ranks highest in the hand-rank table corresponding to potential final hands.</p> / Master of Science (MSc)