Mathematics, Probability and Poker

Contents Chapter 1. Introduction Chapter 2. Some basic concepts Concept of an event Independence Expectation Calculation of simple probabilities Probability and odds Bayes Theorem Chapter 3. Counting methods Combinations and permutations Computation of permutations Computation of combinations How many aces are out? Chapter 4. Concept of a process Chapter 5. Some Paradoxes Chapter 6. Distributions Chapter 11. Mathematical aids to decision making Optimization Theory Decision Theory Game Theory Prisoner's Delimma Chapter 12. Psychology of Irrational Behavior Availability Error Chapter 15. Statistics What is statistics? Chapter 20. General Linear Model Basic model Influence Misc. topics Gary Carson's sites Poker sites Home page Math and Poker Blog Poker Culture Blog Poker Road Trips blog Playing no limit poker blog Road to the 2007 WSOP blog No Limit Poker website List of poker blogs Poker dealer employment Poker Strategy and Tips Articles Poker and Math List of poker blogs Poker dealer employment My Ebooks The Complete Book of Hold'Em Poker (electronic edition) The Complete Book of Casino Poker (electronic edition Other sites Probability Overnight travel blog Free books Politics Drinking Espresso Basic Probability Off Topic Rant Off Topic Rant Blog Top Colleges Princeton American Tradition blog I get my own business cards from them and it's a legit offer. They just charge for postage and it's quality work. Secretary Problem Optimal Stopping and Applications, by Tom Ferguson, an online textbook. Best-Choice problems with dependent criteria, by Tom Ferguson A Natural Vatiation of the Standard Secretary Problem, by Shoou-Re Hsiau and Jiing-Ru Yang, Statisca Sinica, Vol 10, 2000. Decision-Making on the Full Information Secretary Problem, by Michael D. Lee, Tess A. O'Connor, and Matthew B. Welsh Optimal Stopping Constants, by Steven Finch. Buy it now The Complete Book of Hold'Em Poker

Enter your search terms Submit search form Interpretations of probability There are different ways to interpret the meaning of probability. Sometimes probability theorists get into deep debate about the best way of interpretation. We’re only going to barely touch the surface of that debate. Each interpretation has its uses. What is probability? A probability is a number. It’s constrained to be in the range from zero to one. Like .20 or .74. It’s a closed range, 0.0 and 1.0 are included. A probability is a property of an event, an event being a primitive notion of something that occurs. A probability of 0.0 means the event will never happen, 1.0 means it will always happen. Probabilities in between those extremes are subject to various interpretations. There's no particular meaning here. It's just a defintion. How we interprete the meaning of that definition is open to different point of views. Relative frequency Probably the most natural seeming interpretation is a frequency notion. In this interpretation probability reflects the relative frequency of an outcome (or event) if the trial (or experiment, or observation) is repeated over and over. In this interpretation we think of probability as a fraction, a fraction of the time that the event will occur. The probability of heads as an outcome of a coin flip is .50 because it will occur half the time if we flip the coin over and over. This is an empirical view. Not necessarily historical, but empirical, based on observations of the world. Maybe it's about historical observations, maybe about expected future observations. Subjective probability But what about events that don’t repeat themselves over and over again? How do we interpret the concept of the probability of Hillary Clinton winning the 2008 Presidential election? We could think about it in terms of What if the election was repeated over and over? But that doesn’t really make sense, the election outcome will be whatever it is, repeating it under the exact same conditions won’t change the result. The result will be whatever the result is. That’s it. What does probability have to say about that? Certainly it doesn’t say anything about a relative frequency. In that kind of context our interpretation of probability is more of a subjective nature, it’s more a reflection of beliefs about likelihood, not a measure of the fraction of times things occur. It’s in some ways a measure of a degree of certainty about the event occurring. Application of probability to statistics This difference in viewpoint becomes more important when we start trying to apply notions of probability to statistical thought. Statistics is a field of application of probability the two fields developed separately and really only merged strongly in the 20th century. This debate about a frequentists view of probability and a subjective view is at the core of how we use statistical analysis. We’ll get into this more much later. Previous Next Enter your search terms Submit search form

Updates to this website will be announced on the mailing list holdem Click to subscribe to holdem Alspach's Mathematics and Poker Page Brian Alspach used to write a regular column on combinatorics for Poker Digest. He's a retired math professor from Simon Fraser University. Tom Ferguson's home page He's a math ;professor at UCLA and Chris Ferguson's father. MathPages.com A collection of straight-forward introductions to various topics in mathematics and recreational mathematics. Kelly Betting