Semi-restricted Rock, Paper, Scissors
Sam Spiro, Erlang Surya, Ji Zeng

TL;DR
This paper analyzes a semi-restricted variant of Rock, Paper, Scissors where one player must use each move equally, showing the optimal strategy and expected scores, and extends the analysis to general zero-sum games.
Contribution
It introduces and solves a semi-restricted RPS game, establishing the optimal strategy for the restricted player and analyzing expected scores, and generalizes results to other zero-sum games.
Findings
Greedy strategy is uniquely optimal for the restricted player.
Expected score for the unrestricted player is proportional to the square root of n.
Results extend to semi-restricted versions of general zero-sum games.
Abstract
Consider the following variant of Rock, Paper, Scissors (RPS) played by two players Rei and Norman. The game consists of rounds of RPS, with the twist being that Rei (the restricted player) must use each of Rock, Paper, and Scissors exactly times during the 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 . 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.
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Taxonomy
TopicsComputability, Logic, AI Algorithms · Artificial Intelligence in Games · Benford’s Law and Fraud Detection
