论文标题
半限制岩石，纸，剪刀
Semi-restricted Rock, Paper, Scissors
论文作者
论文摘要
考虑以下岩石，纸，剪刀（RPS）的变体，由REI和Norman演奏。该游戏由$ 3N $的RPS组成，其中Rei（受限的玩家）必须在$ 3N $回合中使用岩石，纸和剪刀的每一个$ n $ times，而诺曼则可以正常比赛而无需任何限制。回答Spiro的问题，我们表明某种贪婪的策略是此游戏中REI的独特最佳策略，而Norman的预期分数为$θ（\ sqrt {n}）$。此外，我们研究了一般零和游戏的半限制版本，并证明了有关其最佳策略和预期分数的许多结果，这特别意味着我们对半限制RPS的结果。
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 $Θ(\sqrt{n})$. 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.
