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On semi-restricted Rock, Paper, Scissors
- Publication Year :
- 2024
-
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.<br />Comment: 12 pages
- Subjects :
- Mathematics - Probability
Mathematics - Combinatorics
60C05, 91A05
Subjects
Details
- Database :
- arXiv
- Publication Type :
- Report
- Accession number :
- edsarx.2402.14676
- Document Type :
- Working Paper