Mathematics of Games of Chance

This course delves into the mathematical concepts relevant to analysing games of chance. Topics covered include probabilities, odds, house advantages, fairness assessments, variance, risk evaluation, statistical tests for game honesty, optimal strategies, random walks, the gambler’s ruin, the Kelly criterion, and estimating gaming revenue. The course illustrates these concepts using examples from various games, including Lottery, Roulette, Blackjack, Poker, and Bridge. The course aims to introduce the mathematical analysis of games of chance, focusing on their applications to probabilistic computing. Selected topics include conditional expectation, discrete martingales, Markov chains, house advantage, craps, video poker, gambler’s ruin, slots, and betting systems, which encompass strategic skills. This course also includes a scientific computation component.