PC Seminar: Semirestricted Rock, Paper, Scissors

Abstract: A semirestricted variant of the well-known game Rock, Paper, Scissors (Swedish: Sten, sax, påse) was recently studied by Spiro et al (Electronic J. Comb. 30 (2023), #P4.32). They assume that two players R (restricted) and N (normal) agree to play 3n rounds, where R is restricted to use each of the three choices exactly n times each, while N can choose freely. Obviously, this gives an advantage to N. How large is the advantage?

The main result of Spiro et al is that the optimal strategy for R is the greedy strategy, playing each round as if it were the last. (I will not give the proof, and I cannot improve on this.) They also show that with optimal play, the expected net score of N is \Theta(\sqrt{n}). In the talk, I will show that with optimal play, the game can be regarded as a twice stopped random walk, and I will show that the expected score is asymptotic to c \sqrt{n}, where c = 3\sqrt{3}/(2\sqrt{\pi}}.

This is a seminar in our seminar series on Probability and Combinatorics (PC).