Introduction to Probability with Texas Hold '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.