How to Win at Rock-Paper-Scissors
If you’ve ever played Rock-Paper-Scissors, you’ll have wondered about the strategy that is most likely to beat your opponent. And you’re not alone. Game theorists have long puzzled over this and other similar games in the hope of finding the ultimate approach.
It turns out that the best strategy is to choose your weapon at random. Over the long run, that makes it equally likely that you will win, tie, or lose. This is known as the mixed strategy Nash equilibrium in which every player chooses the three actions with equal probability in each round.
And that’s how the game is usually played. Various small-scale experiments that record the way real people play Rock-Paper-Scissors show that this is indeed the strategy that eventually evolves.
Or so game theorists had thought. Today, Zhijian Wang at Zhejiang University in China and a couple of pals say that there is more to Rock-Paper-Scissors than anyone imagined. Their work shows that the strategy of real players looks random on average but actually consists of predictable patterns that a wily opponent could exploit to gain a vital edge.
Zhijian and co carried out their experiments with 360 students recruited from Zhejiang University and divided into 60 groups of six players. In each group, the players played 300 rounds of Rock-Paper-Scissors against each other with their actions carefully recorded.
As an incentive, the winners were paid in local currency in proportion to the number of their victories. To test how this incentive influenced the strategy, Zhijian and co varied the payout for different groups. If a loss is worth nothing and a tie worth 1, the winning payout varied from 1.1 to 100.
The results reveal a surprising pattern of behavior. On average, the players in all the groups chose each action about a third of the time, which is exactly as expected if their choices were random.
But a closer inspection of their behavior reveals something else. Zhijian and co say that players who win tend to stick with the same action while those who lose switch to the next action in a clockwise direction (where R → P → S is clockwise).
This is known in game theory as a conditional response and has never been observed before in Rock-Paper-Scissors experiments. Zhijian and co speculate that this is probably because previous experiments have all been done on a much smaller scale.
“This game exhibits collective cyclic motions which cannot be understood by the Nash Equilibrium concept but are successfully explained by the empirical data-inspired conditional response mechanism,” say Zhijian and co.
In fact, a “win-stay, lose-shift” strategy is entirely plausible from a psychological point of view: people tend to stick with a winning strategy.
Zhijian and co hope to investigate this psychological aspect in more detail in future studies. An interesting question is how this kind of response is “built in” to the brain. “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,” they say.
The discovery also has practical implications. If humans inevitably use a predictable strategy when playing Rock-Paper-Scissors, that’s a weakness that can be exploited. “Our theoretical calculations reveal that this new strategy may offer higher payoffs to individual players in comparison with the NE mixed strategy,” they say.
That might be worth bearing in mind the next time you take on all comers at your local watering hole.
Ref: http://arxiv.org/abs/1404.5199 : Social Cycling And Conditional Responses In The Rock-Paper-Scissors Game
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