Syllabus. Statistics 35b: Introduction to Probability with Applications to Poker.
Prof. Rick Paik Schoenberg.
Lectures: MW 8:30-9:50am, Royce 160.

Office hours: Mondays, 1:00-2:20pm, MS 8965. Or by email appointment.

email: frederic@stat.ucla.edu

Course webpage: http://www.stat.ucla.edu/~frederic/35b/W07

Description: Exploration of some main topics in introductory probability theory, especially discrete probability problems, that are useful in wide variety of scientific applications. Topics include conditional probability and conditional expectation, combinatorics, laws of large numbers, central limit theorem, Bayes theorem, univariate distributions, Markov processes, and Brownian motion. Examination of computer simulation in depth and discussion of computational approximations of solutions to complex problems using R, with examples of situations and concepts that arise naturally when playing Texas Hold'em and other games.

Grading:
Class participation (5%).
Homework (20%).
Computer project A (10%).
Computer project B (15%).
Midterm. (20%).
Final exam. (30%).
Computer Project A will be due on Monday, Feb 12, at 11:00pm.
The midterm will be on Wednesday, Feb 28.
Computer Project B will be due on Friday, March 9, at 11:00pm.
The final exam is Thursday, March 22, from 3:00pm-6:00pm.

Computer Project A (to be submitted by EMAIL to me by Monday, Feb 12, at 11:00pm):
Design and write an R function which takes as inputs the variables listed and described at the course webpage, and which returns an integer indicating a fold or all-in bet. Please try to make sure that your code does not contain a syntax or other computational bug. Your code, once submitted, will be in the public domain and free for others to read and use. Submit your R function to me by email at frederic@stat.ucla.edu .

Computer Project B will be similar to project A, but will involve more variables and may have more complicated output. This will take as inputs the variables listed and described at the course webpage, and will return an integer indicating whether to fold, call, bet, or raise, and in the latter two cases, how much to bet.

Note: your code must in some way be different from the examples at code1.html and examplesfromclass.txt. In the class meeting immediately after your code is submitted, one member of your group must quickly summarize your code in two sentences or so.

Homeworks will be due each Wednesday, beginning with HW1 which is due Wednesday Jan 17. Homeworks must be handed in at the beginning of class, or may be slipped under my office door (MS 8965) any time before class. Each homework assignment is graded out of 10 points. Homeworks handed in between 8:35 and 8:40 will be given a one-point deduction. Those handed in between 8:40 and 8:50 will be given a two-point deduction. Homeworks handed in between 8:50 and 9:50 will be given a three-point deduction. Homeworks submitted after 4:20pm will not be accepted. Homeworks must be submitted in hard copy, rather than by email or fax.

Rough Outline:
Week 1: Introductory material. Counting problems, combinations, permutations, multiplication rules for counting, axioms of probability, gambing addicition, rules of hold'em.
Week 2: Addition and multiplication rules for probability, simulation, R.
Week 3: Conditional probability, independence, odds ratio, Bayes' rule.
Week 4: Random variables, probability mass functions, distribution functions, densities, expected value, pot odds.
Week 5: Variance, standard deviation, discrete istributions (Bernoulli, binomial, Poisson, geometric, negative binomial, hypergeometric), continuous distributions (uniform, normal, exponential).
Week 6: Computer project A.
Week 7: Laws of large numbers.
Week 8: Review and midterm.
Week 9: Central limit theorem, checking and testing results, Markov processes.
Week 10: Computer project B and review.