How to Win at Rock-Paper-Scissors, According to Math

December 24, 2015 | Elizabeth Knowles

black outlines of three hands: rock, paper, scissors
Photo credit: Mazeo/Open Clipart

It’s not as random of a game as you might think. 

Since every action in rock-paper-scissors has an equally likely winning and losing reaction, you might think that it is all up to chance and that there is no such thing as a winning strategy. Zhijian Wang from the Zhejiang University in China studied real players to determine whether an optimal strategy exists.

For his study, he had 72 students play 300 rounds of rock-paper-scissors, each through computers, so no body language could be seen. After playing for about two hours, they received a payout based on their number of wins.

Wang noticed that winning players tended to stick with their actions in the next round. Knowing this can help you come up with a winning strategy of your own. Here are some tips:

  • If your opponent just won, he or she is most likely to play the same action again. Play the one that will beat that — the one neither of you played in the previous round.

  • If you just won, play what your opponent just played because he or she is likely to think you will stick with your strategy.

Some other statistics about the game can help you win as well.

  • Men tend to open with rock. If you are playing against a man, start with paper.

  • Scissors is the opening move statistically most likely to win. Try that if you’re playing against a woman.

Game theory is the area of mathematics that studies how people interact when they have to make decisions that affect each other.

In rock-paper-scissors, the researchers have hypothesized that sticking with a winning strategy might be a conditional response hard-wired into the brain. That’s what they intend to study through further research.

As the World RPS Society says: “Like chess or fencing, the rules are simple, but the game itself is as complex as the mind of your opponent.”


You might also like: How Many Squares Are Actually on a Checkerboard?  

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