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Commercial poker solvers emerged around 2015, these are paid software used by poker players to study the game and improve their strategies and whose purpose is to find the best way to play in certain poker situations. Unfortunately for us, their implementation is a black box. As poker players and computer science students, we asked ourselves two questions. Why did the most popular poker solvers appear during this period? How to implement our own poker solver? We answer these questions in this thesis. We review the scientific literature and find that in 2015 the Heads-Up Limit Texas Hold’em poker variant has been weakly solved for the first time by a computer program called Cepheus. This poker variant contains 1014 decision points and has been a challenge for artificial intelligence for over 10 years. We find that the best poker AIs after this period face the same challenges and use techniques that have commonalities to solve them. We describe the challenges and techniques used to create a poker solver. The most common challenges are related to the size of a poker game, the computing power and memory required to solve and store a strategy for a game of this magnitude. We implement a poker solver capable of solving abstractions of different poker variants on a home computer using techniques such as Couterfactual Regret Minimization (CFR) and game abstractions. We also create tools to read and study the strategies calculated by our solver. At the end of this thesis, we show that our results are consistent with the results obtained by commercial poker solvers and we discuss ways to improve our implementation and to solve poker situations in games as big as No Limit Texas Hold’em.

poker --- solver --- counterfactual regret minimization --- cfr --- Nash equilibrium --- imperfect information games --- games theory --- Ingénierie, informatique & technologie > Sciences informatiques

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This book contributes to the literature on conflict and terrorism through a selection of articles that deal with theoretical, methodological and empirical issues related to the topic. The papers study important problems, are original in their approach and innovative in the techniques used. This will be useful for researchers in the fields of game theory, economics and political sciences.

Economic history --- European Union (EU), spatial autoregression and connectivity --- alliance --- strategic free riding --- Nash equilibrium --- terror cycles --- terror paths --- counterterror policy --- conflict dynamics --- asymmetric conflict --- continuous game --- national security --- Blotto game --- imperfect information --- machine learning --- terrorism --- game theory --- hybrid threats --- state competition --- prospect theory --- grand strategy --- retaliation --- counterterror --- coalition --- backlash --- conflict --- contests --- momentum