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Samurai Survival Statistics: A Monte-Carlo Approach to Game-Theoretical Sudden Death Interactions
Version 1
: Received: 18 November 2022 / Approved: 22 November 2022 / Online: 22 November 2022 (10:11:05 CET)
How to cite: Garcia, P. Samurai Survival Statistics: A Monte-Carlo Approach to Game-Theoretical Sudden Death Interactions. Preprints 2022, 2022110419. https://doi.org/10.20944/preprints202211.0419.v1 Garcia, P. Samurai Survival Statistics: A Monte-Carlo Approach to Game-Theoretical Sudden Death Interactions. Preprints 2022, 2022110419. https://doi.org/10.20944/preprints202211.0419.v1
Abstract
Sword-duels are interesting, from a game-theoretical perspective, as they correspond to sudden-death interactions between players (i.e., defeat means removal from the game), and where victory/defeat depend on not just skill, but also luck. Analyzing probabilities of victory streaks, given a certain level of self and others' skill, is thus relevant for any application domain that can be modeled in the same way. This paper takes inspiration from Miyamoto Musashi, famously undefeated for 61 duels, and implements a Markov-chain Monte-Carlo simulation approach to evaluate this scenario. Results suggest that a 61 victory streak can be probabilistically observed when skill level is roughly 6.5 times that of the average duelist, and with 95\% confidence when skill level is roughly 1000 times that of the average duelist. More generally, this paper provides a method for determining chances of victory streaks in game-theoretical sudden-death encounters, when both "skill" and "luck" contribute to the outcome of the encounter. Specific scenarios can be modeled by modifying the utilized Markov chain and adjusting sampled distributions as required.
Keywords
Samurai; Miyamoto Musashi; Monte-Carlo; Markov; Probability
Subject
Computer Science and Mathematics, Probability and Statistics
Copyright: This is an open access article distributed under the Creative Commons Attribution License which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.
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