Glaz, JosephKulldorff, MartinPozdnyakov, VladimirSteele, J Michael2023-05-232023-05-232006-03-012017-09-11https://repository.upenn.edu/handle/20.500.14332/47493Methods using gambling teams and martingales are developed and applied to find formulas for the expected value and the generating function of the waiting time until one observes an element of a finite collection of patterns in a sequence which is generated by a two-state first or higher order Markov chain.This article has been published in a revised form in Journal of Applied Probability [10.1017/S0021900200001418]. This version is free to view and download for private research and study only. Not for re-distribution, re-sale or use in derivative works. © Cambridge University Press.Gamblingteamswaiting timespatternssuccess runsfailure runsMarkov chainsmartingalesstopping timesgenerating functionsBusinessStatistics and ProbabilityArticle