Introduction to Probability
by Charles M. Grinstead, J. Laurie Snell
Undergraduate probability theory covering discrete and continuous random variables, expected value, distributions, and limit theorems.
More resources on Probability Theory
probabilitycourse.com
ProbabilityCourse.com is an online learning resource that provides a structured probability course with clear explanations, worked examples, and practice problems covering topics from basics to advanced theory.
Wolfram MathWorld
MathWorld is an online mathematics encyclopedia from Wolfram Research offering detailed, browsable articles on topics across the math spectrum, including algebra, geometry, calculus, and number theory. Each entry includes definitions, theorems, formulas, diagrams, worked examples, and links to further reading.
seeing-theory.brown.edu
Seeing Theory is an interactive, browser-based resource from Brown University that uses visual simulations to explain fundamental probability and statistics concepts. It offers interactive demos and explanations on topics like probability, distributions, sampling, the central limit theorem, confidence intervals, hypothesis testing, and Bayesian reasoning.
Blackjack Attack: Playing the Pros' Way
Don Schlesinger's statistical treatment of professional-level counting: bet-spreading efficiency, risk-of-ruin calculations, the Illustrious 18 index plays, and the bankroll needed to survive variance as a counter.
Card Counting in Blackjack
Mathematical explanation of card counting from actuary Michael Shackleford, covering running count, true count conversion, the Hi-Lo system, and a breakdown of which playing decisions (standing, insurance, doubling) counting most affects.
Probability Theory: The Logic of Science
Jaynes derives probability as extended logic from consistency requirements rather than from frequencies, then applies it to inference problems across physics and science. Reframes probability as the arithmetic of reasoning under incomplete information and dissolves the split between probability theory and statistical inference.