%0 Journal Article
%T Competing Patterns in Bernoulli Sequence of Trials
%A Paul Vrbik
%A Jan Vrbik
%J Applied Mathematics
%P 314-323
%@ 2152-7393
%D 2023
%I Scientific Research Publishing
%R 10.4236/am.2023.145019
%X Consider performing a sequence of Bernoulli trials (each resulting in either a success, denoted S, or a failure F, with a probability of <i>p</i> and <i>q</i> := 1 - <i>p</i> respectively) until one of <i>m</i> specific strings (or patterns) of consecutive outcomes is generated. This can be seen as a game where <i>m</i> players select one such pattern each and the one whose pattern occurs first wins. We present symbolic formulas for the <i>m</i> 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.
%K Competing Patterns
%K Bernoulli Sequence of Trials
%K Game Theory
%U http://www.scirp.org/journal/PaperInformation.aspx?PaperID=125183