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On two combination rules for 0-1-sequences. (English) Zbl 0861.90150

Two players compete with each other by successively taking part in a series of win-or-lose games for one person. The player having more successes at the end is the winner, where the two termination rules (i) stop as soon as one player has reached \(N\) successes and (ii) stop after the \(N\)th trial are considered. The effect of the following two switching rules is studied: (1) alternate between the players, (2) the current player continues iff he or she was successful in the last trial. The aim of the paper is to derive surprisingly simple relations between the corresponding sets of winning sequences of trials and, in the case that the outcomes of the trials are random, between the probabilities of winning.

MSC:

91A60 Probabilistic games; gambling
91A20 Multistage and repeated games
90C05 Linear programming
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