How to rock paper and scissors

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Anthropology / Mathematics / Myths / Psychology

We’ve all used rock-paper-scissors to resolve a dispute. Is there a foolproof winning strategy?

Want to win at rock-paper-scissors?

The earwig and the elephant

When all else fails, rock-paper-scissors (also known as RPS) is an excellent way to make a decision. The rules are simple. At an agreed moment – usually after two or three ‘primes’ to get in sync, two people each make a symbol with their hand. The symbols are rock (closed fist), paper (flat hand) and scissors (index and middle fingers form a V to represent scissor blades).

There is an agreed hierarchy to determine who wins each round: rock breaks scissors, scissors cuts paper, paper covers rock. Despite considerable debate as to whether the rock smashes the scissors or blunts them, the outcome is the same. There are three possible results: win, lose or tie.

There’s plenty of discussion about the origins of RPS – it probably dates back to the Chinese Han Dynasty. The Japanese version, Junken, has a long history and continues to play an important role in Japan today. There are many variations on the theme: for example, the tiger, village chief and village chief’s mother (who trumps the village chief). My personal favourite – earwig-man-elephant – hails from Indonesia. Earwig beats elephant because it crawls up the elephant’s trunk and eats its brain. The game is also sometimes called Rochambeau or Roshambo (remember the Southpark episode?)

Just a kid’s game?

At one level, RPS is a kid’s game, good for settling playground disputes. Among adults, it can decide who should pay for a round of drinks. But don’t be fooled: RPS is a cultural phenomenon.

International competitions offer five-figure prize money. The World RPS Society has an Internationally Recognised Throwing System of hand symbols. There’s also a Player’s Responsibility Code including the sage advice “Think twice before using RPS for life-threatening decisions.”

Why do we love RPS so much? Because despite the deceptively simple rules, there’s a whole world of strategy.

RPS is written off as a kids’ game … but when you delve into it, it’s one of the purest forms of competition that two minds can have with each other – Professional rock-paper-scissors player Jason Simmon

Let’s talk strategy

We tend to think RPS is a fair way to resolve disputes because the winner is decided by chance. Each player picks a hand symbol at random meaning each has an equal likelihood of winning that round.

Except that we are lousy at being random. We follow patterns and if you understand those patterns, you suddenly have a distinct advantage over your opponent. You can find a variety of RPS strategy guides and most suggest different tactics depending on your opponent’s gender and level of experience. For example, inexperienced men tend to lead with rock whereas most women lead with scissors. If you’re not convinced experience makes any difference, play against a computer first in Novice mode, then in Veteran mode where the computer “pits over 200,000 rounds of previous experience against you.” Experience matters.

Recent studies have revealed on average, we choose each action about a third of the time, which is what you would expect if our choices were random. But closer inspection shows there are predictable patterns to our choices. In a study of 360 students playing 300 rounds of RPS, the patterns were clear.

Players who won the last round will most likely stick with the same action. If it worked once, it may well work again.

Importantly, players who lost the last round will most likely switch to the next action in a clockwise direction (where R → P → S is clockwise). This is the tendency you can exploit to your advantage.

Can you always win?

The latest research led to dozens of claims that with maths on your side, you can always win at rock-paper-scissors.

The latest research findings can definitely up your chances of winning. If your opponent just won with rock (because you played scissors), you should choose paper next because they are likely to play rock again. If your opponent lost, you should respond to the likelihood that they will switch from rock to paper to scissors in that order by playing the actions in the opposite order. For every scenario, the research predicts which action will most likely win you the next round.

But the problem here is that if your opponent has also read up on strategy, your plans may be foiled. I don’t think you can ever be guaranteed of winning.

Unless, of course, you’re a robot. The Janken robot wins RPS every time because it recognises in one millisecond what shape your hand is forming and almost simultaneously makes the winning action.

Time to channel your inner robot.

Links and stuff

2 Comments

  1. You are awesome! – At last – a strategy to ensure I always beat the kids on a RPS match.

    By the way, I did a RPS cartoon a few months back and discovered the World RPS society website during my research. I must admit, I thought it was a joke at first, but it’s real – they really do take the game seriously.

    Thanks for another wonderful post

    • Thanks Marti! Ooh, I’ll find your cartoon to share on the FB page. I know, very seriously. And check out the prize money!!

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