Semi-Restricted Rock, Paper, Scissors
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Published:2023-12-01
Issue:4
Volume:30
Page:
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ISSN:1077-8926
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Container-title:The Electronic Journal of Combinatorics
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language:
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Short-container-title:Electron. J. Combin.
Author:
Spiro Sam,Surya Erlang,Zeng Ji
Abstract
Consider the following variant of Rock, Paper, Scissors (RPS) played by two players Rei and Norman. The game consists of $3n$ rounds of RPS, with the twist being that Rei (the restricted player) must use each of Rock, Paper, and Scissors exactly $n$ times during the $3n$ rounds, while Norman is allowed to play normally without any restrictions. Answering a question of Spiro, we show that a certain greedy strategy is the unique optimal strategy for Rei in this game, and that Norman's expected score is $\Theta(\sqrt{n})$. Moreover, we study semi-restricted versions of general zero sum games and prove a number of results concerning their optimal strategies and expected scores, which in particular implies our results for semi-restricted RPS.
Publisher
The Electronic Journal of Combinatorics
Subject
Computational Theory and Mathematics,Geometry and Topology,Theoretical Computer Science,Applied Mathematics,Discrete Mathematics and Combinatorics