##### Department of Mathematics,

University of California San Diego

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### Food for Thought

## Sam Spiro

#### UCSD

## Semi-restricted Rock, Paper, Scissors

##### Abstract:

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. We show that a certain greedy strategy is the unique optimal strategy for Rei in this game, and that Norman's expected score is $\Theta(\sqrt{n})$. We also prove several general theorems about semi-restricted games arising from digraphs. This is joint work with Erlang Surya, Yuanfan Wang, Ji Zeng.

### May 2, 2022

### 4:00 PM

AP&M 5402

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