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( √ 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.