Rock Paper Scissors: calculate your way to victory

30th Jan 2017

Paper, Scissors, Rock

Everyone knows the rules: rock breaks scissors, scissors cut paper, paper covers rock. But not everyone knows how to win. When each option can equally win, lose or draw, which move do you choose?

The MBNA numbers nerds have looked into the patterns of moves and behaviours behind the game that can, with a few calculations, create an outcome that’s more science than chance.

The odds on your options

With three equally weighted moves, the rational approach would be to throw each one at random, a third of the time.

But, being human, we’re distinctly incapable of choosing our moves at random. This means there is a slight discrepancy in the share of options we tend to play. Paper, for example, only gets played 29.6% of the time. Scissors appear 35% of the time and rock is actually thrown 35.4% of the time.1

the hand game

Since Rock is thrown most often, this potentially means that by throwing Paper you have a marginally higher chance at winning a game. However, when the odds aren’t strong enough to guarantee a win, the secret is in the psychology. And with just a small advantage between moves, how can you improve your chances of winning?

A mind game

Duplicity, misdirection, cunning. Rock Paper Scissors is an intricate mind game, and, as ambassadors of the game declare, it can be ‘as complex as the minds of those playing.’ But there is a science to decision-making and strategy. Some of our responses are even thought to be pre-programmed in our brains, making them unnervingly predictable.

In China, scientists ran an experiment that oversaw 360 students playing 300 rounds2 of Rock Paper Scissors over two hours3 and they recognised a few patterns in play.

Pattern number one: winners tend to repeat their winning move or sequence more often than they would if truly choosing at random. The reason behind this is simple – the mind thinks that whatever worked before should work again.

Hand signs

Pattern number two: people usually switch up their moves after a loss - it’s called the “win-stay, lose-shift”4 strategy - but the resulting sequence tends not to appear at random. After losing, a player is more likely to play their options in order of the game’s name i.e. by choosing Rock, then Paper, then Scissors. Why we choose this particular sequence is unclear; it could be that our flustered minds reach more readily for familiar patterns, but we do know that it’s our emotional response to losing a game that leads us to make more irrational decisions.5

win-stay, lose-shift

An additional pattern recognised by expert players6 is the rookie effect on the first move played in a game.

Pattern number three: males who are new to Rock Paper Scissors tend to play Rock first. It supposedly symbolises a masculine, forceful move, which could make it seem especially important for a first throw. However, females tend to play Scissors first. It could suggest a natural inclination to play a tactical rather than forceful game, but we don’t know for sure.

females play scissors, males play rock

How to win Rock Paper Scissors (some of the time)

To help tip the game in your favour, the number nerds have taken these findings and sussed out a scientific formula for winning with each move in Rock Paper Scissors.

the winning formula

The formula follows two simple rules:

1. After a win, move backwards one manoeuvre in the sequence “rock, paper, scissors.” For example: if you win with Rock, play Scissors; if you win with Paper, play Rock; etc.

2. After losing, play what wasn’t played in the round you lost. So, if you lost with Scissors, play Paper.

To make it easier to remember, the number nerds have condensed these rules into three formulas for calculating your next manoeuvre.

Win or Lose with Rock = Play Scissors
Win or Lose with Scissors = Play Paper
Win or Lose with Paper = Play Rock

Put simply, all you have to do is play backwards from your first move through ‘Rock, Paper, Scissors!’

Of course, your opponent may already be aware of these strategies, in which case, you’ll either have to switch up this strategy or think on your feet!

If all else fails, throw a curve ball

Chances are, the formula won’t work out in every game. So you may still need to swerve from science from time to time. If you’re caught on a losing streak, here are a couple of cunning moves that might just give you the edge.

1. Announce your next move
Telling people what you’re about to throw might seem a little reckless but it’s also a classic misdirection tactic. Unless your opponent knows you’re ballsy enough to throw a move you’ve just broadcast, you can assume they’ll shy away from taking the bait.

2. Double up
This plucky move is about forcing yourself to counter your natural inclination to randomise and throw the same move three times in a row. Throw Rock twice, and your opponent probably won’t expect you to have the nerve to throw it a third time.

Now you know the science behind Rock Paper Scissors why not test out our formula and throw a few daring moves to see if it leads you to success.

Playing Rock Paper Scissors is one way to settle everyday debates over who does the chores or pays for the next round, but what do you do when stuck making a solo decision? Our spending decision flow charts are built for decision-making in three everyday situations to help you save money.

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