Level: Beginner
Charles chen, MBB, Quality and Reliability, Applied Materials
Mason Chen, Black Belt Student, Stanford University OHS
Patrick Giuliano, Statistics SME, Abbott
Poker is a very popular gambling game in casinos and family social events. Except for professionals, most poker players lose money/chips by not applying the proper probability-based logic. This talk examines poker probability concepts by using a novel poker game. The game is based on a partial deck – a total of 16 AKQJ cards – and can be played by up to six players. The authors have used combination formulas and derived generalized formulas of matching probability for each of the possible matching pattern outcomes. The creation of this game was motivated by the desire to simplify the simulation probability of gaming outcomes, and can increase the matching probability significantly on some higher ranked pattern outcomes such as a full house. Given the AKQJ cards available in the game, the winningest patterns reduce to four of a kind, full house, three of a kind and two pairs. With six players, this game is very exciting, since the basic poker probabilities are more simply calculated to inform betting, reducing the emotional investment needed for more risky moves. To study the player’s personality and psychology, each player has been assigned different playing characteristics based on propensity for risk-taking. Several JMP visualization platforms, such as Graph Builder and Distribution, are utilized to plot the winning probability distribution. The actual players’ gaming data is compared to simulated probability through hypothesis proportion testing in JMP. Through participation in the AKQJ game with combined statistical outcome-estimation and psychological risk-taking, real player results can be augmented with worst-case probability (Monte Carlo) simulation. This provides a structure for card players to play their hands in a more rational, data-based way, and in so doing, can help avoid gambling disorders.
