The game of Cribbage has a complex way of counting points in the hands that are dealt to each player. Each player has a choice of what cards to keep and what cards to throw into an extra hand, called the crib, that one of the players gets to count towards his score. Ideally, you could try to keep the most points possible in your hand and your crib, or, conversely, the most points in your hand with the fewest points in your opponent’s crib. To add to the fun, a final card is randomly chosen that all three hands share. This thesis deals with finding optimal expected values for each player’s hand and the crib. Unfortunately, finding the exact optimal values is very difficult. However, I have managed to get bounds on the optimal values.