Consider the following variant of Rock, Paper, Scissors (RPS) played by two players Rei and Norman. The game consists of $3n$ rounds of RPS, with the twist being that Rei (the restricted player) must use each of Rock, Paper, and Scissors exactly $n$ times during the $3n$ 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 $\Theta(\sqrt{n})$. 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.
@article{10_37236_11563,
author = {Sam Spiro and Erlang Surya and Ji Zeng},
title = {Semi-restricted rock, paper, scissors},
journal = {The electronic journal of combinatorics},
year = {2023},
volume = {30},
number = {4},
doi = {10.37236/11563},
zbl = {1534.91010},
url = {http://geodesic.mathdoc.fr/articles/10.37236/11563/}
}
TY - JOUR
AU - Sam Spiro
AU - Erlang Surya
AU - Ji Zeng
TI - Semi-restricted rock, paper, scissors
JO - The electronic journal of combinatorics
PY - 2023
VL - 30
IS - 4
UR - http://geodesic.mathdoc.fr/articles/10.37236/11563/
DO - 10.37236/11563
ID - 10_37236_11563
ER -
%0 Journal Article
%A Sam Spiro
%A Erlang Surya
%A Ji Zeng
%T Semi-restricted rock, paper, scissors
%J The electronic journal of combinatorics
%D 2023
%V 30
%N 4
%U http://geodesic.mathdoc.fr/articles/10.37236/11563/
%R 10.37236/11563
%F 10_37236_11563
Sam Spiro; Erlang Surya; Ji Zeng. Semi-restricted rock, paper, scissors. The electronic journal of combinatorics, Tome 30 (2023) no. 4. doi: 10.37236/11563
