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Winning big at hold’em requires practical math knowledge, which is precisely what this book will teach you. The ability to make quick and accurate mathematical decisions is crucial for your winnings at the table. The mission of this book is to drill these important poker math skills into you, giving you a distinct advantage over the other players at your table.

Both of the authors of this book graduated with degrees in Mathematics from Caltech. Collin Moshman is the best-selling author of Sit ‘n Go Strategy and Heads-Up No-Limit Hold’em. Douglas Zare is a mathematician and poker coach famous for his in-depth analyses.

The authors use their extensive math, poker, and coaching backgrounds to present the most important hold’em math concepts designed to immediately increase your winrate at the tables.

You will learn to:
- Understand the fundamental probabilities and statistics underlying Hold’em
- Count hand combinations while playing
- Master expected value calculations
- Play optimally with game theory
- Seize full advantage of the latest software
- Utilize deductive logic to put your opponent on a specific hand range
And more!

Poker is a fun game, but it’s even more fun when you win. Whether you play cash games or tournaments, high-stakes or low-stakes, online or live poker, The Math of Hold’em will give you the significant edge you need over your opponents.

Introduction
Part One: The Fundamentals
Introduction
Pot Odds
Expected Value
            Expected Value in Poker
            Relative Expected Value
            Definition of +EV
            Drilling Down
            Conclusion
Effective Stack Depth
Counting Hand Combinations
Basic Probabilities
            Pre-flop
            Ranges
Flop
Hitting the Flop
Dangerous Ranks
River
Outs to Percentages
2-to-4 Rule
Backdoor Draws and Redraws
Winning without Improving
Percentages to odds
Calling Decisions Based on Outs, Odds, and Percentages
            Implied Odds
                        Reverse Implied Odds
Hot and Cold Equity
            Pre-flop Match-Ups
            Ranges
            Re-steals
            Post-flop
                        Domination
            Overpairs
            Draws
            Overcards
            Sets
            Miscellaneous Examples
            Post-flop Equity vs. Ranges
            Post-flop Equity Against Random Hands
Other Factors
            Conditional Probability and Bayes’ Theorem
            Sklansky Dollar Accounting
                        Traps
Part Two: Advanced Expected Value
Introduction
            Equity Against a Pre-flop Range
            Equity Against a Post-flop Range
            Making the Fold or Call Decision
            EV of Value Bets and Bluffs
            Determining the EV of a Semibluff All-in
                        Pre-flop
            Showing an Immediate Profit
            Later Profit
            Metagame Math
            Split-Pot Math
            More Expected Value Examples
            Common Mistakes
                        Using a Bad Baseline
                        The Sunk-Cost Fallacy
            Philosophy
Part Three: Game Theory
            Introduction
            Rock-Paper-Scissors (Roshambo)
                        Nash Equilibrium
                        Note of Caution
                        Sequential Rock-Paper-Scissors
            The Game of Chicken
                        Sequential Chicken
            The Bluffing Game
                        Basic Bluffing Game
                        Drilling Down
                        Deviations
                        Mixed Strategies in Models, but Pure Strategies in Poker
                        Bettor Strength
                                    Bet Size
                                    Bluffing in No-Limit
                        Caller Strength
                                    Showdown Value
                                    Value Bluffs
                        Bluffing Two Streets
                        Choosing a Bet Size
                        Bluffing Three Streets
                        Complications
            Conclusion
Part Four: Tournaments
            Introduction
            Blind Levels
                        High Blinds
                        Medium Blinds
Low Blinds
Adjusting to Future Blind Increases
            Re-stealing
            Tournament Equity
                        Independent Chip Model (ICM)
                        Sit-and-go Tournaments
            Calling Pushes/Bubble Math
            Converting Chips to Cash Heads Up
            Adjusting for the Antes
                        Effective Big Binds
            Heads-Up Push/Fold Strategies
            Zare’s Golden Rule
            Satellites
Part Five: Statistics and Variance
            Introduction
            Standard Deviation
                        Standard Deviations in Poker
            Central Limit Theorem
            The Long Run
            How Rapidly do Statistics Converge?
            Downswings
                        Looking Backwards
                        Downswing Formulas
            Bankroll Management
                        For Winning Players Only
                        Goals
                        Psychology
                        Kelly Criterion
                        The Key Bankroll Formula
                        Applying the Key Formula
                        Instantaneous Risk of Ruin
                        Moving Up
                                    Stages
                        Calculations
                        Splitting Tables across Stakes
                        Multitabling
                        Flawed Bankroll Management Ideas
                                    Fixed Number of Buy-ins
                                    Stop-Losses
                                    Anecdotal Downswings
Part Six: Crucial Hold’em Mathematical Concepts
            Introduction
            Beating the Rake
                        Cash Games
            Sets
                        What Can Go Wrong?
                                    Not Getting to See a Flop
                                    Behind with Flopped Set
                                    Not Getting Paid Off
                                    Being Outdrawn
                        Ideal Conditions
                        Favorable Conditions
                        The 5-10 Rule
                        Curtis vs. Farha Revisited
                        Set-Mining Tips
                        Combating Set-Miners
            Hit-to-Win Math
                        When Fit-or-Fold is Correct
            Logic
            Math versus Instincts
            The Free Card Play
            Bet-Sizing
Part Seven: Software
            Introduction
            Poker Equity Calculators
            Hold’em Manager (HEM)
                        Heads-Up Display
                        Results Tracking
                        Database Analysis
            Finding Leaks using Software
            Extreme or Happy Medium
            Aggregated Statistics
            Averages vs. Totals
            Linked Categories
            Linked Statistics
            Blinds
            Social Statistics
Cardrunners EV
ICM Explorer
SitNGoWizard
            Note of Caution
Nash Equilibrium Calculator
Sharkscope
Appendix- Hand Rankings