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Win at Rock-Paper-Scissors Every Time, With Math

Don't let your little brother read this.

If you've ever been on a playground, you should know the rules of the most elegant of games: rock smashes scissors, scissors cuts paper, paper covers rock.

To have a bullet-proof tactic for this 4,000-year-old game (which was probably known as scarab-papyrus-stone in Egypt) can be lifesaving—or at least secure you the last piece of pizza.

With a large scale field experiment, game theory researchers at the University of Hangzhou in China just ensured that you will never ever have to bring the trash outside again. They published the ultimate tactic to winning rock-paper-scissors​.


In the experiment, 360 students from the Zhejiang University in Hangzhou were drafted to play a game of rock-paper-scissors for hours with one another. Each pair played a total of 300 rounds per game. Their decisions were summarized by mathematicians in a paper, which surprisingly shed a lot of light on human tactical decisions made under pressure.

First, humans tend to repeat their successful strategies (if it worked once, it's going to work again). Second, losers try to change their tactics.

Make shameless use of these facts.

Since people generally act predictably irrational, the Chinese game researchers were able to identify the following strategies for a sure victory:

  • The first strategy is the countertactic. Let's say you played scissors and your opponent played rock. The chance that your opponent will confidently play rock again is now very high. What that means to you: anticipate that and play paper. In other words: play the option that wasn't played in the previous round.
  • The second strategy is to mirror. If you just won, play what your opponent just played, because he or she will think that you are going to play the same gesture again.

Image: ​OpenClipart

Look at the triangle in the picture above. You want to cycle backwards, against the direction of the arrows. That's it.

This elaborate tactic lies at the intersection of math and psychology. It's based on game theory, the science behind how humans make decisions in competitive situations.


At Numberphile, the strategy is explained in detail once again (with a pleasant British accent):

All of you who are dreaming of participating in the world championship of rock-paper-scissors (prize money: $10,000!) should refer to the pro strategy tips published by the "​World Rock Paper Scissor Society."

  • Men tend to open a game with rock (little power demonstration). Take advantage of that information.
  • Dazzle your opponent with the truth: Declare which decision you are going to make and follow through—no one would think that you were actually planning on playing exactly what you just announced anyways.
  • Play scissors first. Statistically, this opening move wins the most.

Two years ago, scientists at the University of Tokyo already developed a robot that is able to win rock-paper-scissors in 100 percent of games. It has a great advantage though: its sensor technology is so susceptible that within milliseconds it can predict the movements of humans, and counter them. Well, it's actually a swindle robot, since that's hardly a fair strategy.

For further education, we recommend the 208-page "​Official Rock-Paper-Scissors Strategy Guide" which also answers urgent questions, such as: "Does the rock sand down the scissors or does it simply destroy it?" and "Is rock-paper-scissors a sport?"

Rock Paper Scissors 25, a variant of the game. Image: David Lovelace/​RPS 25

Playing the above shown variant, featuring 25 possible gestures developed by rock-paper-scissors expert David Lovelace, you may want to take the latter question into consideration. Be careful with all complex game extensions though: the odds of a game are only balanced if every hand gesture can be defeated as often as it can defeat others.

Keep this simple hint in mind and don't lose your nerves. With this advice, it should be fairly easy to win the next game of rock-paper-scissors to decide who gets to ride shotgun or who is responsible for cleaning the dishes. And if no sparring partner is available, you can challenge a computer at The New York Times and put your tactic to the test.

This article was translated from ​Motherboard Germany.