On semi-restricted rock, paper, scissors
The electronic journal of combinatorics, Tome 31 (2024) no. 2
Spiro, Surya and Zeng (Electron. J. Combin., 2023) 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.
DOI :
10.37236/12854
Classification :
91A05, 91A20, 60C05
Affiliations des auteurs :
Svante Janson 1
@article{10_37236_12854,
author = {Svante Janson},
title = {On semi-restricted rock, paper, scissors},
journal = {The electronic journal of combinatorics},
year = {2024},
volume = {31},
number = {2},
doi = {10.37236/12854},
zbl = {1545.91004},
url = {http://geodesic.mathdoc.fr/articles/10.37236/12854/}
}
Svante Janson. On semi-restricted rock, paper, scissors. The electronic journal of combinatorics, Tome 31 (2024) no. 2. doi: 10.37236/12854
Cité par Sources :