Rock, Paper, Scissors, Science!

By Kelley Northam

From determining who goes first to deciding what movie to watch, Rock Paper Scissors (RPS) is one of the most common games. If you need a refresher, RPS is where two players simultaneously choose one of three options: rock (beats scissors), scissors (beats paper), or paper (beats rock), forming the shapes with their hands. You win once you “throw” the option that beats your opponent’s.

Although it may seem simple, the science behind RPS is surprisingly complex when you consider probability, psychology, and game theory.

Probably Pick Paper

Probability is a branch of mathematics that deals with the occurrence of events and how likely they are to happen. In RPS, each option has a statistically equal (33.3 percent) chance of winning, but probability-wise, the odds are less even.

According to the World Rock Paper Scissors Association (WRPSA), 35 percent of players throw rock first, 29 percent paper, and 26 percent scissors. Since most people pick rock first, you have a slightly better chance of winning the first round if you pick paper.

Psyched Out

Psychology, the study of the human mind and behavior, also plays a role in RPS. A study published in Scientific Reports, “Social cycling and conditional responses in the Rock-Paper-Scissors game”, suggests that RPS is a game of psychology because you can exploit an opponent’s patterns to win.

The study suggests that if you lose, your opponent is likely to repeat the winning option in the next round. So, after a loss, jump two options ahead in the sequence to win. For example, if you lost against paper, expect paper and play scissors.

If you win, your opponent is likely to move to the next option in the sequence. So, when you win, play the next option in the sequence to win again. For example, if your opponent lost using paper, expect scissors and play rock.

Common Game, Uncommon Game Theory

The game theory behind RPS is also unique. Game theory is the study of how players strategize to make decisions, and a key concept is a pure-strategy Nash equilibrium. This is a scenario where if your opponent plays the same option every time, it would be optimal to continue playing your initial option. In RPS, this would look like one player always throwing rock and the other always throwing scissors, so one player would always lose.

So, in RPS, a mixed-strategy Nash equilibrium is optimal. In this scenario, at least one player randomizes their choices, making their moves less predictable. If you threw paper and your opponent threw scissors, you could switch to paper next and win if they throw rock.

Now that you know the science behind RPS, grab a friend and flex your newfound skills!