On semi-restricted Rock, Paper, Scissors
Fuente:
arXiv
Salvato in:
| Autore principale: | |
|---|---|
| Natura: | Preprint |
| Pubblicazione: |
2024
|
| Soggetti: | |
| Accesso online: | |
| Tags: |
Aggiungi Tag
Nessun Tag, puoi essere il primo ad aggiungerne!!
|
| _version_ | 1866910430966841344 |
|---|---|
| author | Janson, Svante |
| author_facet | Janson, Svante |
| contents | 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 $Θ(\sqrt{n})$; 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 $c=3\sqrt{3}/2\sqrtπ=1.466$, verifying the conjecture. We also find the asymptotic distribution of the score, and compute its variance. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2402_14676 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | On semi-restricted Rock, Paper, Scissors Janson, Svante Probability Combinatorics 60C05, 91A05 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 $Θ(\sqrt{n})$; 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 $c=3\sqrt{3}/2\sqrtπ=1.466$, verifying the conjecture. We also find the asymptotic distribution of the score, and compute its variance. |
| title | On semi-restricted Rock, Paper, Scissors |
| topic | Probability Combinatorics 60C05, 91A05 |
| url | https://arxiv.org/abs/2402.14676 |