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# Rock Paper Scissors: Win Every Time

#### A recent study reveals the two tricks you need to win every time.

The last time I played Rock-Paper-Scissors (RPS), I lost and had to not only settle a bar tab, but also do the washing-up the following day. I’m now quite confident that won’t happen again.

In RPS, there are three options to play: rock, paper or scissors, and there are two outcomes: you win, or you lose. If you were playing against a computer, which is unpredictable and void of human emotions or expectations, you would simply play each option a third of the time. This is called ‘Classical Game Theory’. But how could we take the complexity of human decision making into account if I were to play against you, a fellow human?

Researchers based at Zhejiang University in China recruited 360 students from different disciplines at the university. The students were divided into groups of six and were then made to play 300 rounds of RPS (approximately 90-150 minutes) within their respective group. You can read their paper, but be warned: It’s brimming with complex mathematical equations and graphs! The researchers came to two main conclusions after having collected all the data. Let’s delve into them and get a glimpse of your opponent’s mind.

1. If your opponent wins a round of RPS, they will be statistically more likely  to use the same option the next time they play against you. For example, if they played scissors and you lost with paper, they will most likely play scissors again in the next round. To win, you should play rock to beat their scissors.

2.If your opponent loses a round, they will most likely play the option that will beat the option you played in the last round. This means that you should play the option that will beat their option that beats what you previously played. For example, if your opponent loses with paper against your scissors, they will most likely play rock in the next round, as they are assuming you will play scissors again. This means that you should play paper in order to beat their rock. Are you still with me? If not, just play what they played previously.

All of this can be summarized in the easy-to-follow video below, made by the Mathematical Sciences Research Institute (MSRI), featuring Dr Hannah Fry, a young lecturer at University College London who is also involved in public engagement activities and academic stand-up.

With this strategy in mind, it’s time to gather your opponents and raise your stakes!

References:
Wang, Z., Xu, B. and Zhou, H-J. (2014) Social cycling and conditional responses in the Rock-Paper-Scissors game. Scientific Reports. 4:5830. doi:10.1038/srep05830.

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• ##### Parag
February 10, 2015, 20:26

Great fun. My kids will love to hear this. Do you know how much this strategy will increase you chances of winning?

• ##### Elisabeth Buhl Thubron@Parag
February 11, 2015, 12:38

Hi Parag, I’m glad to hear you enjoyed the article! The authors report that players will increase their chances of winning by 10% when compared to using the mixed-strategy method (this is where players randomize their action choices so opponents can’t exploit them). With the ‘win-stay lose-shift’ strategy in mind I’m sure your kids will thoroughly enjoy trying to out-think each other!

• ##### Elisabeth Buhl Thubron
February 11, 2015, 12:42

Hi Parag, I’m glad to hear you enjoyed the article! The authors report that players will increase their chances of winning by 10% when compared to using the mixed-strategy method (this is where players randomize their action choices so opponents can’t exploit them). With the ‘win-stay lose-shift’ strategy in mind I’m sure your kids will thoroughly enjoy trying to out-think each other!