This project applies techniques from game theory and linear programming to find the optimal strategies of two variants of poker. A set of optimal poker strategies describe a Nash equilibrium, where no player can improve their outcome by changing their own strategy, given the strategies of their opponent(s). We first consider Kuhn Poker as a simple application of our methodology. We then turn our attention to 2-7 Draw Poker, a modern variant onto which little previous research is focused. However, the techniques that we use are incapable of solving large, full-scale variants of poker such as 2-7 Draw. Therefore, we utilize several abstractions techniques to render a computationally-feasible LP that retains the underlying spirit of the game. We use the Gambit software package to build and solve LPs whose solutions are the optimal strategies for each game.


Moynihan, Matthew




game theory, linear programming, poker

Publication Date


Degree Granted

Bachelor of Arts

Document Type

Senior Independent Study Thesis Exemplar



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