A General Formula for the Probability of Winning in Sequential Turn-Based Games
Sakshya Vardhan Mishra
Sakshya Vardhan Mishra, Department of Mathematics, Sunbeam School, Mughalsarai, Chandauli (Uttar Pradesh), India.
Manuscript received on 21 October 2025 | First Revised Manuscript received on 04 January 2026 | Second Revised Manuscript received on 21 March 2026 | Manuscript Accepted on 15 April 2026 | Manuscript published on 30 April 2026 | PP: 22-23 | Volume-6 Issue-1, April 2026 | Retrieval Number: 100.1/ijam.A122606010426 | DOI: 10.54105/ijam.A1226.06010426
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© The Authors. Published by Lattice Science Publication (LSP). This is an open-access article under the CC-BY-NC-ND license (http://creativecommons.org/licenses/by-nc-nd/4.0/)
Abstract: This paper presents a general formula for calculating a player’s probability of winning in a sequential, turn-based game with a constant success probability per trial. The problem extends the classical two-player probability models of dice tossing or coin flipping to an arbitrary number of n players. A compact proof based on the summation of a geometric series is provided, and examples demonstrate the correctness and applicability of the result. This formulation can serve as an educational tool for understanding probabilistic reasoning, sequences, and infinite series.
Keywords: Probability, Successive Trials, Random Experiments, Sequential Games, Geometric Series, Binomial Distribution.
Scope of the Article: Statistics and Probability Theory