Mathematics > Probability
[Submitted on 22 Feb 2024 (v1), last revised 2 May 2024 (this version, v2)]
Title:On semi-restricted Rock, Paper, Scissors
View PDF HTML (experimental)Abstract:Spiro, Surya and Zeng (Electron. J. Combin. 2023; arXiv:2207.11272) recently studied a semi-restricted variant of the well-known game Rock, Paper, Scissors; in this variant the game is played for $3n$ rounds, but one of the two players is restricted and has to use each of the three moves exactly $n$ times. They find the optimal strategy, and they show that it results in an expected score for the unrestricted player $\Theta(\sqrt{n})$; they conjecture, based on numerical evidence, that the expectation is $\approx 1.46\sqrt{n}$.
We analyse the result of the strategy further and show that the average is $\sim c \sqrt{n}$ with $c=3\sqrt{3}/2\sqrt{\pi}=1.466$, verifying the conjecture. We also find the asymptotic distribution of the score, and compute its variance.
Submission history
From: Svante Janson [view email][v1] Thu, 22 Feb 2024 16:30:01 UTC (20 KB)
[v2] Thu, 2 May 2024 11:56:16 UTC (23 KB)
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