Contents
0. Preface
0.1. Acknowledgements
1. The Basics
1.1. Notation and Combination
1.1.1. Notation
1.1.2. Combinations
1.1.3. Position Names
1.1.4. Exercises
1.2. Range and Distribution
1.2.1. Range
1.2.2. Distribution
1.2.3. Probability space
1.2.4. Exercises
1.3. Equity
1.3.1. Equity
1.3.2. Equity on the Flop
1.3.3. Exercises
1.4. Pot Odds
1.4.1. Pot Odds
1.4.2. Comparing Equity and Pot Odds
1.4.3. Exercises
1.5. Expected Value
1.5.1. Expected Value
1.5.2. Exercises
2. Game Theory
2.1. Game Theory Basics
2.1.1. A Very Brief History of Game Theory
2.1.2. Types of Games
2.1.3. Information and Knowledge
2.1.4. Strategic Form
2.1.5. Exercises
2.2. Game Trees and Extensive Form
2.2.1. Game Trees
2.2.2. Extensive Form
2.2.3. Backward Induction
2.2.4. Exercises
2.3. Minimax and Information sets
2.3.1. Information Sets
2.3.2. The Minimax Theorem
2.3.3. Exercises
2.4. Nash Equilibria and Indifference
2.4.1. Nash Equilibrium
2.4.2. The Indifference Principle
2.4.3. Indifference in Poker
2.4.4. Exercises
3. Half-Street Discrete Distribution Games
3.1. Alpha and Omega
3.1.1. Risk and Reward
3.1.2. Nuts and Air
3.1.3. Exercises
3.2. AKQ Games
3.2.1. Half-Street AKQ Game
3.2.2. Modified Half-Street AKQ Game
3.2.3. Modified Half-Street AKQJ Game
3.2.4. Half-Street AKQJT Game
3.2.5. Exercises
3.3. The Chopping Game
3.3.1. Half-Street Chopping Game
3.3.2. Extended Half-Street Chopping Game
3.3.3. Exercises
4. Continuous Probability Games
4.1. Limit [0, 1] Games
4.1.1. Half-Street Limit [0, 1] Game
4.1.2. Exercises
4.2. Extended Limit [0, 1] Games
4.2.1. One-bet Limit [0, 1] Game
4.2.2. Exercises
4.3. Multiway [0, 1] Games
4.3.1. The 3-Player Limit [0, 1] Game
4.3.2. Exercises
5. Multi-Street Games
5.1. Two-Street AKQ
5.1.1. Limit Two-Street Nuts and Air Game
5.1.2. No-Limit Two-Street Nuts and Air Game
5.1.3. No-Limit Two-Street AKQJ Game
5.1.4. Exercises
5.2. Defending with Draws
5.2.1. The Lonely Draw
5.2.2. Calling with Air
5.2.3. Implied Odds
5.2.4. Exercises
5.3. Attacking with Draws
5.3.1. Draw Bluffs when In-Position
5.3.2. Draw Bluffs when Out-of-Position
5.3.3. Exercises
6. Raises and Check-Raises
6.1. No-Limit AKQ
6.1.1. No-Limit AKQ Game
6.1.2. Exercises
6.2. Defending by Raising
6.2.1. AKQJ Game with a Check-Raise
6.2.2. Limit AKQJ Game with Raises
6.2.3. Exercises
6.3. [0, 1] Games with Raises
6.3.1. Limit [0, 1] Game with a Check-Raise
6.3.2. Exercises
7. Computational Models
7.1. Artificial Intelligence and Poker
7.1.1. Cepheus and Heads-Up Limit Hold’em
7.1.2. Libratus and Heads-Up No-Limit Hold’em
7.1.3. Pluribus and Multiplayer No-Limit Hold’em
7.2. Regret Minimization
7.2.1. Regret
7.2.2. Regret Matching
7.2.3. Regret Matching+
7.2.4. Counterfactual Regret Minimization
7.2.5. Counterfactual Regret Minimization+
7.2.6. Monte Carlo Counterfactual Regret Minimization
7.2.7. Discounted Counterfactual Regret Minimization
7.2.8. Instant Counterfactual Regret Minimization
7.3. Abstraction
7.3.1. Suit Isomorphism
7.3.2. Action Abstraction
7.3.3. Action Translation
7.3.4. Information Abstraction
7.3.5. Deep Counterfactual Regret Minimization
7.4. Subgame Solving
7.4.1. Safe and Unsafe Subgame Solving
7.4.2. Nested Subgame Solving
7.4.3. Depth-Limited Subgame Solving
