On fair coin-tossing games

Robert Chen and Alan Zame

Journal of Multivariate Analysis, 1979, vol. 9, issue 1, 150-156

Abstract: Let [Omega] be a finite set with k elements and for each integer n [greater, double equals] 1 let [Omega]n = [Omega] - [Omega] - ... - [Omega] (n-tuple) and 11 and aj [not equal to] aj+1 for some 1 [less, double equals] j [less, double equals] n - 1}. Let {Ym} be a sequence of independent and identically distributed random variables such that P(Y1 = a) = k-1 for all a in [Omega]. In this paper, we obtain some very surprising and interesting results about the first occurrence of elements in [Omega]n and in [Omega]n with respect to the stochastic process {Ym}. The results here provide us with a better and deeper understanding of the fair coin-tossing (k-sided) process.

Keywords: fair; coin-tossing; process; fair; coin-tossing; game; the; renewal; theorem; the; Conway; Algorithm; stopping; time; the; taboo; first; passage; probability (search for similar items in EconPapers)
Date: 1979
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Citations: View citations in EconPapers (2)

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