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| How to win at rock-paper-scissors | How to win at rock-paper-scissors |
| (about 2 hours later) | |
| What are your odds of winning rock-paper-scissors? Simple - one in three. At least, that's what chance predicts. | What are your odds of winning rock-paper-scissors? Simple - one in three. At least, that's what chance predicts. |
| But people do not play randomly - they follow hidden patterns that you can predict to win more games than you should, a study has revealed. | But people do not play randomly - they follow hidden patterns that you can predict to win more games than you should, a study has revealed. |
| Winners tend to stick with their winning action, while losers tend to switch to the next action in the sequence "rock-paper-scissors". | Winners tend to stick with their winning action, while losers tend to switch to the next action in the sequence "rock-paper-scissors". |
| Anticipating these moves could give you a winning edge, say scientists. | Anticipating these moves could give you a winning edge, say scientists. |
| Their strategy was revealed in a massive rock-paper-scissors tournament at Zhejiang University in China, documented on the Arxiv server. | Their strategy was revealed in a massive rock-paper-scissors tournament at Zhejiang University in China, documented on the Arxiv server. |
| Scientists recruited 360 students and divided them into groups of six. Each competitor played 300 rounds of rock-paper-scissors against other members of their group. | Scientists recruited 360 students and divided them into groups of six. Each competitor played 300 rounds of rock-paper-scissors against other members of their group. |
| As an incentive, the winners were paid - in proportion to their number of victories. | As an incentive, the winners were paid - in proportion to their number of victories. |
| To play smart, classical game theory suggests players should completely randomise their choices - to remain unpredictable and not be anticipated by opponents. | To play smart, classical game theory suggests players should completely randomise their choices - to remain unpredictable and not be anticipated by opponents. |
| This pattern - where both players select rock, paper or scissors with equal probability in each round - is known as the Nash equilibrium. | This pattern - where both players select rock, paper or scissors with equal probability in each round - is known as the Nash equilibrium. |
| The strategy is named after game theory pioneer John Forbes Nash Jr, subject of the 2001 Hollywood film A Beautiful Mind. | The strategy is named after game theory pioneer John Forbes Nash Jr, subject of the 2001 Hollywood film A Beautiful Mind. |
| And indeed - in the Chinese tournament players in all groups chose each action about a third of the time, exactly as expected if their choices were random. | |
| However, on closer inspection, the organisers noticed a surprising pattern of behaviour. | |
| When players won a round, they tended to repeat their winning rock, paper or scissors more often than would be expected at random (one in three). | When players won a round, they tended to repeat their winning rock, paper or scissors more often than would be expected at random (one in three). |
| Hidden psychology | Hidden psychology |
| Losers, on the other hand, tended to switch to a different action. And they did so in order of the name of the game - moving from rock, to paper, to scissors. | |
| After losing with a rock, for example, a player was more likely to play paper in the next round than the "one in three" rule would predict. | After losing with a rock, for example, a player was more likely to play paper in the next round than the "one in three" rule would predict. |
| This "win-stay lose-shift" strategy is known in game theory as a conditional response - and it may be hard-wired into the human brain, the researchers say. | This "win-stay lose-shift" strategy is known in game theory as a conditional response - and it may be hard-wired into the human brain, the researchers say. |
| Anticipating this pattern - and thereby trumping your opponent - "may offer higher pay-offs to individual players" they write. | Anticipating this pattern - and thereby trumping your opponent - "may offer higher pay-offs to individual players" they write. |
| "The game of rock-paper-scissors exhibits collective cyclic motions which cannot be understood by the Nash equilibrium concept. | "The game of rock-paper-scissors exhibits collective cyclic motions which cannot be understood by the Nash equilibrium concept. |
| "Whether conditional response is a basic decision-making mechanism of the human brain or just a consequence of more fundamental neural mechanisms is a challenging question for future studies." | "Whether conditional response is a basic decision-making mechanism of the human brain or just a consequence of more fundamental neural mechanisms is a challenging question for future studies." |
| Though it is only a simple game, rock-paper-scissors is seen as a useful model for studying competitive behaviour in humans - in financial trading for example. | Though it is only a simple game, rock-paper-scissors is seen as a useful model for studying competitive behaviour in humans - in financial trading for example. |
| A previous experiment found that players unconsciously mimic the actions of their opponents - a surprising result because advantage is usually gained by acting differently. | A previous experiment found that players unconsciously mimic the actions of their opponents - a surprising result because advantage is usually gained by acting differently. |
| The Chinese scientists now plan to investigate the underlying psychology behind the seemingly irrational choices players make when competing. | |
| In the meantime, anyone curious to test if their "winning strategy" really works need look no further than the UK championship. |