Is rock paper scissors luck or skill?
Strategy · · 4 min read
Ask ten people whether rock paper scissors is a game of luck and most will say yes, obviously. Ask the people who have played it for money, or written programs to play it, and they will say no, not quite. Both sides are right, and the difference is the number of rounds.
This article separates the two: where the luck really is, where the skill comes from, how many rounds it takes for skill to show, and a way to find out which one you are relying on.
One throw is pure chance
Take a single throw between two strangers. Rock, paper and scissors each beat one sign and lose to one, so no sign is better than another. Whatever you choose, you win, lose or draw with the same probability — one in three each. There is no clever first throw against someone you know nothing about, and there is nothing to practise.
That is why it works as a tie-breaker. A coin has two sides; rock paper scissors has three, and as long as it is played once, it is just as fair as the coin. Everything people call “skill” lives outside that single throw: in what happened before it, and in what the other person thinks you will do.
Over a match, people stop being random
Play five or ten rounds against the same person and the game changes, because people cannot produce random sequences. They avoid repeating a sign too often, they react to winning and losing, and they try to guess what you are about to do — which is itself a pattern. A 2014 experiment at Zhejiang University, with 360 players and thousands of rounds, found that winners tended to repeat their sign and losers tended to switch, and in a predictable direction.
Skill in rock paper scissors is simply two things done better than the other person: predicting their next throw from what they have done so far, and keeping your own throws unreadable. The patterns themselves are in how to win at rock paper scissors; here is what they add up to:
- Prediction: spotting that your opponent repeats after a win, or shifts after a loss, before they notice it themselves.
- Deception: breaking your own habits on purpose, so the same reading fails when it is tried on you.
- Nerve: a read is only worth something if you act on it, and a player who always retreats to “safe” rock is easy to beat.
The evidence that skill exists
If the game were only luck, nobody could stay ahead of the field for long. Three cases where somebody did:
- In 2005 a Japanese electronics company, Maspro Denkoh, let Christie’s and Sotheby’s decide by one round of rock paper scissors which auction house would sell its art collection, worth around twenty million dollars. Christie’s asked the eleven-year-old twin daughters of an employee for advice. Their reasoning: everyone expects rock, so an opponent will play paper, so play scissors. Christie’s played scissors; Sotheby’s played paper.
- In 1999 the computer scientist Darse Billings ran a tournament for rock paper scissors programs. A program that plays at random cannot lose on average, but it cannot win either — and the winner, Iocaine Powder, finished far ahead of the field by modelling what each opponent was predicting and playing one step past it.
- From 2002 the World RPS Society held championships in Toronto with hundreds of entrants, and the same handful of players kept reaching the late rounds. Over a single throw that is impossible; over a tournament it is what skill looks like.
How many rounds before skill shows?
More than most people play. In a short match the better player wins more often, but not by much, and a lucky run is enough to hide the difference. The numbers for a player with no skill at all, picking each sign at random:
That is the honest version of “luck or skill”. In one throw, luck is everything. In a best-of-five, it is still most of the story. Over a hundred rounds, it is background noise, and what remains is whoever reads better.
- Over 100 rounds they win about 33, give or take 5. Winning 43 or more by luck alone happens roughly one time in forty.
- A match to five round wins between a slightly better player and a slightly worse one is still close to a coin flip — the edge needs more rounds to show.
A random bot cannot be beaten — try it
Duelto’s practice bot picks each sign at random, with no memory of what either of you played. That makes it the cleanest test there is: you can play it right now, without an account, and over twenty or thirty rounds you will end up close to a third of the wins, however hard you try. Nobody can do better against a random opponent, and if you feel you are “on a streak”, that is what a streak of luck feels like.
Then play a person. Against a human opponent your win rate stops being a third, in one direction or the other, and the gap between those two results is exactly the skill in the game.
So: luck or skill?
Luck for one throw, skill over many, and the match length decides which one you are playing. Games built on top of rock paper scissors make the skill part bigger: in RPS Board, the throws are hidden pieces on a board, so reading your opponent starts before the first fight and the random part is only the last resort when two equal pieces meet.