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Maths of Planet Earth | Limitless Applications

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Published on June 11th, 2014 | by Liam

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How well do humans play rock-paper-scissors?

Maths+StatsA count of three, and two adversaries throw their signs. A fist and a flat palm, and the fight is over – paper beats rock. Rock-paper-scissors is played around the world, from playgrounds to court-rooms. And although the rules are simple, there’s plenty for a mathematician to investigate.

Rock-paper-scissors (RPS) is different from games like chess or naughts-and-crosses, because there is no ‘best move’. No matter which action you pick, there is one action that will beat you, and one action that you will beat. If you can find a pattern in your opponent’s choices, you can better predict their moves – and hopefully pick moves to beat them!

Chinese researchers decided to investigate. First, the researchers needed lots of rounds of RPS to get the information they wanted. They got 360 students, arranged them in groups of six, and asked each group to play 300 rounds of RPS. This gave the researchers 18 000 rounds to study.

From all of this data, the researchers noticed that rock was the most popular choice, and scissors was the least popular. However, these differences were quite small, only a few actions in every hundred games played. Looking deeper into the results, the researchers found a much more interesting pattern. When someone won, they tended to use the same action in the next round. When they lost, they were more likely to change in a predictable way, from rock to scissors, from scissors to paper, and from paper to rock.

This ‘win-stay, lose-switch’ strategy is quite common in everyday life. When a product is successful, stores keep selling it – but if the product is unsuccessful, they might try selling something different.

Win-stay, lose-switch is not a good rock-paper-scissors strategy. A well programmed computer could use this pattern to beat most humans. But the patterns that make us bad at rock-paper-scissors might help us make good decisions in much more important situations in our daily life.

More information
How to win at rock-paper-scissors
Play against a very good computer program

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