The classic two‐player gambler's ruin problem with successive events: A generalized variance. Issue 4 (27th March 2021)

• Record Type: Journal Article
• Authors: Hussain, Abid; Cheema, Salman A.
• Is Part Of: Computational and mathematical methods. Volume 3:Issue 4(2021)
• Page Start: n/a
• Page End: n/a
• Publication Date: 2021-03-27
• Subjects: Gambler's ruin problem successive events -- ruin probability -- ruin time -- sss variance of the ruin time; Mathematics -- Data processing -- Periodicals; Numerical analysis -- Periodicals; Numerical analysis; Mathematics -- Data processing; Periodicals; 004.0151
• DOI: 10.1002/cmm4.1156
• Languages: English
• ISSNs: 2577-7408

Abstract

Abstract: In this article, we present the general expressions for the variance of the ruin time of the classic two‐player gambler's ruin problem with successive and nonoverlapping trials. The rationale of this game plan is motivated by its exhibition in the game of tennis, where a player is required to win two consecutive serves to win the point after achieving deuce. This strategy (i.e., decision is based on successive and nonoverlapping trials) is in favor of the player, who plays with a better skill set and reduces the chances of decision based only on luck. We explicitly derive the general expressions of variance up to m successive and non‐overlapping trials for the case of symmetric and asymmetric games. It is proved that the expressions given in literature for the symmetric and asymmetric cases are the sub cases of our proposed expressions. Finally, some special games (i.e., m = 2) are simulated and the results are verified with the proposed formulas.