--- title: Probability & Statistics description: This field covers the mathematical analysis of random phenomena and data collection. Learners will understand how to model uncertainty, calculate probabilities, analyze datasets, and draw valid statistical inferences from sample data. category: mathematics subcategory: mathematics difficulty: beginner, intermediate, advanced url: /subject/probability-and-statistics --- # Probability & Statistics This field covers the mathematical analysis of random phenomena and data collection. Learners will understand how to model uncertainty, calculate probabilities, analyze datasets, and draw valid statistical inferences from sample data. ## Available Resources 1 Videos • 4 Books • 5 Courses • 5 Websites • 2 Papers ## Books ### 1. Probability Theory: The Logic of Science **Author:** E. T. Jaynes Upgrades epistemology by treating probability as the rigorous logic of science and reasoning under incomplete information. **Difficulty:** Advanced | **Price:** Paid **Link:** https://www.amazon.com/s?k=0521592712&tag=edmonddante07-20 **Tags:** bayesian inference, probability theory, epistemology, statistical inference ### 2. The Mathematics of Poker **Author:** Bill Chen & Jerrod Ankenman 2006. Where the Risk of Ruin mathematics comes from. The most enjoyable book on this list if you like equations. **Difficulty:** Advanced | **Language:** English | **Price:** Paid **Link:** https://www.amazon.com/dp/1886070253?tag=edmonddante07-20 **Tags:** poker, risk of ruin, probability ### 3. The Theory of Gambling and Statistical Logic **Author:** Richard Epstein 2nd edition, 2009. The primary text on gambling mathematics, and heavy going. The place to end up rather than the place to start. **Difficulty:** Advanced | **Language:** English | **Price:** Paid **Link:** https://shop.elsevier.com/books/the-theory-of-gambling-and-statistical-logic/epstein/978-0-12-374940-6 **Tags:** casino mathematics, probability ### 4. Practical Casino Math **Author:** Robert Hannum & Anthony Cabot 2nd edition. The textbook version of Hannum's free casino-math guide; only worth buying for the full treatment. **Difficulty:** Advanced | **Language:** English | **Price:** Paid **Link:** https://www.amazon.com/dp/0942828534?tag=edmonddante07-20 **Tags:** casino mathematics, house edge ## Courses ### 1. Introduction to Statistical Methods in Economics (MIT 14.30) **Author:** Konrad Menzel Probability and statistics for economists: probability theory, random variables and distributions, sampling theory, estimation, confidence intervals and hypothesis testing. Provides 25 lecture note files, problem sets with solutions, and exams. Leaves you ready for a first regression-based econometrics course. **Difficulty:** Intermediate | **Price:** Free **Link:** https://ocw.mit.edu/courses/14-30-introduction-to-statistical-methods-in-economics-spring-2009/ **Tags:** probability, mathematical-statistics, statistical-inference, hypothesis-testing, econometrics ### 2. Statistics Learn statistics fundamentals with this free course from Khan Academy! Master probability, data analysis, and more. **Difficulty:** Beginner | **Price:** Free **Link:** https://www.khanacademy.org/math/statistics-probability **Tags:** introductory-statistics, probability, data-analysis, hypothesis-testing ### 3. Probabilistic Systems Analysis and Applied Probability (MIT 6.041SC) **Author:** John Tsitsiklis Modeling and analysis of uncertainty: probability models, discrete and continuous random variables, Bayesian inference, limit theorems and random processes. Designed for independent study, with lecture videos, slides, recitation and tutorial problems, problem sets and exams with solutions, and TA problem-solving videos. **Difficulty:** Intermediate | **Price:** Free **Link:** https://ocw.mit.edu/courses/6-041sc-probabilistic-systems-analysis-and-applied-probability-fall-2013/ **Tags:** probability, random-variables, bayesian-inference, limit-theorems, random-processes, statistical-inference ### 4. Fat Chance: Probability from the Ground Up **Author:** Benedict Gross, Joseph Harris, Emily Riehl A HarvardX introductory course that builds probability from counting principles: permutations, combinations, the binomial distribution, expected value, conditional probability, and the normal approximation. Learners develop the quantitative reasoning to calculate probabilities and assess risk in everyday and applied settings. **Difficulty:** Beginner | **Language:** English | **Price:** Free **Link:** https://www.edx.org/learn/probability/harvard-university-fat-chance-probability-from-the-ground-up **Tags:** probability, combinatorics, expected-value, binomial-distribution ### 5. Introduction to Probability **Author:** Joe Blitzstein HarvardX's self-paced version of Harvard's Stat 110, taught by Joe Blitzstein. Covers counting and story proofs, conditional probability and Bayes' rule, discrete and continuous random variables, joint distributions, the law of large numbers, the central limit theorem and Markov chains. **Difficulty:** Intermediate | **Language:** English | **Price:** Free **Link:** https://www.edx.org/learn/probability/harvard-university-introduction-to-probability **Tags:** probability, random-variables, bayes-rule, probability-distributions, markov-chains, central-limit-theorem ## Videos ### 1. Introduction to Bayesian data analysis - part 1: What is Bayes? First part of Rasmus Bååth's video introduction to Bayesian data analysis, explaining the approach conceptually before the math. Viewers see how prior information, observed data, and a generative model combine to produce a posterior distribution. **Difficulty:** Beginner | **Price:** Free **Link:** https://www.youtube.com/watch?v=3OJEae7Qb_o **Tags:** bayesian-inference, statistics, lecture, introductory ## Papers ### 1. The Economics of Casino Gambling **Author:** William R. Eadington Free on the AEA site. The source of the house-advantage and standard-deviation table used in casino-math introductions. **Difficulty:** Advanced | **Language:** English | **Price:** Free **Link:** https://www.aeaweb.org/articles?id=10.1257/jep.13.3.173 **Tags:** casino mathematics, house edge, variance ### 2. A Guide to Casino Mathematics **Author:** Robert C. Hannum Free 25-page PDF covering handle, drop, hold, house edge, and the 'theo' formula casinos use to rate players. **Difficulty:** Beginner | **Language:** English | **Price:** Free **Link:** https://www.trendfollowing.com/pdfs/casino_math.pdf **Tags:** casino mathematics, house edge, probability ## Websites ### 1. Gaming Revenue Reports Free primary data, monthly, 2004 to date. Twelve-month rolling win and win percentage by game. **Difficulty:** Intermediate | **Language:** English | **Price:** Free **Link:** https://www.gaming.nv.gov/about-us/gaming-revenue-information-gri/ **Tags:** casino mathematics, house edge ### 2. Wizard of Odds House-edge tables, a rule-variations calculator that prices each rule change individually, and a basic-strategy calculator for any rule set, including European no-hole-card. **Difficulty:** Beginner | **Language:** English | **Price:** Free **Link:** https://wizardofodds.com/ **Tags:** casino mathematics, house edge, blackjack ### 3. stattrek.com StatTrek is an online statistics resource that provides clear tutorials and explanations of probability and statistics. It also features free calculators for distributions, hypothesis tests, confidence intervals, and other statistical methods. **Difficulty:** Intermediate | **Language:** English | **Price:** Free **Link:** https://stattrek.com **Tags:** websites, science-research, scientific-method ### 4. 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. **Difficulty:** Intermediate | **Language:** English | **Price:** Free **Link:** https://probabilitycourse.com **Tags:** websites, technology-computer-science, data-science--ai ### 5. 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. **Difficulty:** Intermediate | **Language:** English | **Price:** Free **Link:** https://seeing-theory.brown.edu **Tags:** websites, technology-computer-science, data-science--ai ## Youtubes ### 1. Statistical Rethinking 2023 (Full Lecture Course) **Author:** Richard McElreath McElreath's full Bayesian course, taught around causal DAGs: why a regression coefficient answers a question only once confounds, colliders, and post-treatment bias are specified. Covers generative simulation, MCMC, multilevel models, and measurement error, with R and Stan code. **Difficulty:** Advanced | **Language:** English | **Price:** Free **Link:** https://www.youtube.com/playlist?list=PLDcUM9US4XdPz-KxHM4XHt7uUVGWWVSus **Tags:** bayesian statistics, causal inference, r, stan, multilevel models --- *This content is part of Dantes.io - Your Treasure Map to Knowledge* *Curated by humans at Dantes.io. Personal study use welcome; republishing this curation requires permission (team@dantes.io).* View this page online: https://dantes.io/subject/probability-and-statistics