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Published online by Cambridge University Press: 23 August 2024
This Article is a follow-up to a recent Gazette Article about a probabilistic betting game studied by Abdin et al. [1]. We examine the speed of convergence of the probability needed to investigate this game by giving concrete examples, using the large deviation, which is a valuable tool for estimating probabilities of repeated trials (see [2], [3, Chapter 6], [4, Section 5.11]). Moreover, to get a deep understanding of the game, we study fairness when it is repeated infinite times. Let us call it fairness in the sense of infinity, whose exact definition will be given in the final section.