Author(s)

Paul Vrbik¹, Jan Vrbik²

¹ITEE, Queensland University, Brisbane, Australia.
²Department of Mathematics and Statistics, Brock University, St. Catharines, Canada.

Consider performing a sequence of Bernoulli trials (each resulting in either a success, denoted S, or a failure F, with a probability of p and q := 1 - p respectively) until one of m specific strings (or patterns) of consecutive outcomes is generated. This can be seen as a game where m players select one such pattern each and the one whose pattern occurs first wins. We present symbolic formulas for the m probabilities of winning, and for the mean number of trials and the corresponding standard deviation to complete this game. Several numerical examples are presented, including a search for optimal strategy.

Competing Patterns, Bernoulli Sequence of Trials, Game Theory

Vrbik, P. and Vrbik, J. (2023) Competing Patterns in Bernoulli Sequence of Trials. Applied Mathematics, 14, 314-323. doi: 10.4236/am.2023.145019.