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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
