Gin Rummy is a popular two-player card game involving choices to draw and discard cards to form sets of matching cards. Unlike other popular games such as Chess, Poker, and Go, there is little formal artificial intelligence research about how to make good decisions when playing Gin Rummy. In this paper, we develop an agent that plays Gin Rummy through a combination of known and expected card values, modeling the opponent to predict their cards of interest, and a conservative approach to assessing when to end the hand. In addition to discussing our observations about Gin Rummy that inspired our agent's design and how the agent works, we evaluate the relative importance of various features employed by our agent by competing agents which implement various subsets of those features.