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Title: Game of pure chance with restricted boundary
Authors: Ho Hon Leung
Thotsaporn “Aek” Thanatipanonda
Mahidol University
United Arab Emirates University
Keywords: Mathematics
Issue Date: 1-Jan-2020
Citation: Discrete Applied Mathematics. (2020)
Abstract: © 2020 We consider various probabilistic games with piles for one player or two players. In each round of the game, a player randomly chooses to add a or b chips to his pile under the condition that a and b are not necessarily positive. If a player has a negative number of chips after making his play, then the number of chips he collects will stay at 0 and the game will continue. All the games we considered satisfy these rules. The game ends when one collects n chips for the first time. Each player is allowed to start with s chips where s≥0. We consider various cases of (a,b) including the pairs (1,−1) and (2,−1) in particular. We investigate the probability generating functions of the number of turns required to end the games. We derive interesting recurrence relations for the sequences of such functions in n and write these generating functions as rational functions. As an application, we derive other statistics for the games which include the average number of turns required to end the game and other higher moments.
ISSN: 0166218X
Appears in Collections:Scopus 2020

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