Introduction to Probability with Texas H o l d 'em Examples

Probability Basics
Meaning of Probability
Basic Terminology
Axioms of Probability
Venn Diagrams
General Addition Rule

Counting Problems
Sample Spaces with Equally Probable Events
Multiplicative Counting Rule
Permutations
Combinations

Conditional Probability and Independence
Conditional Probability
Independence
Multiplication Rules
Bayes’ Rule and Structured Hand Analysis

Expected Value and Variance
Cumulative Distribution Function and Probability Mass Function
Expected Value
Pot Odds
Luck and Skill in Texas Hold’em
Variance and Standard Deviation
Markov and Chebyshev Inequalities
Moment Generating Functions

Discrete Random Variables
Bernoulli Random Variables
Binomial Random Variables
Geometric Random Variables
Negative Binomial Random Variables
Poisson Random Variables

Continuous Random Variables
Probability Density Functions
Expected Value, Variance, and Standard Deviation
Uniform Random Variables
Exponential Random Variables
Normal Random Variables
Pareto Random Variables
Continuous Prior and Posterior Distributions

Collections of Random Variables
Expected Value and Variance of Sums of Random Variables
Conditional Expectation Laws of Large Numbers and the Fundamental Theorem of Poker
Central Limit Theorem
Confidence Intervals for the Sample Mean
Random Walks

Simulation and Approximation Using Computers

Appendix A: Abbreviated Rules of Texas Hold’em
Appendix B: Glossary of Poker Terms
Appendix C: Solutions to Selected Odd-Numbered Exercises

References and Suggested Reading

Index