Abstract
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.
Talk to us
Join us for a 30 min session where you can share your feedback and ask us any queries you have
Disclaimer: All third-party content on this website/platform is and will remain the property of their respective owners and is provided on "as is" basis without any warranties, express or implied. Use of third-party content does not indicate any affiliation, sponsorship with or endorsement by them. Any references to third-party content is to identify the corresponding services and shall be considered fair use under The CopyrightLaw.