Abstract
The trials in the classical N-player gamblers' problem are repeated independently until one or more players get bankrupt. In this modern era, everyone wants to earn something in a limited amount of time as well as doesn't lose all his/her amount. In this research, we present a game that is stopped when the number of trials first reaches the minimum of the initial budget set by the players. We executed this game for N players and determined the probability distribution of the fortune for both symmetric and asymmetric games. The exact expressions for the expected fortune and variance of the distribution are derived.
Reference14 articles.
1. Feller, W. (1968). An Introduction to Probability Theory and its Applications, vol. I. New York: John Wiley & Sons.
2. Ogilvy, C. S. (1962). Tomorrow's Math: Unsolved Problems for the Amateur. New York: Oxford University Press.
3. Sandell, D. (1989). A game with three players. Statistics & Probability Letters, 7(1):61-63.
4. Hussain, A., Cheema, S. A., Haroon, S. and Kifayat, T. (2021). The ruin time for 3-player gambler's problem: an approximate formula. Communications in Statistics - Simulation and Computation, 0:1-9. doi: 10.1080/03610918.2021.1888996.
5. Engel, A. (1993). The computer solves the three tower problem. The American Mathematical Monthly, 100(1):62-64.