New Study Shows Rock-Paper-Scissors Game Could be Predicted

By | May 05, 2014 11:08 AM EDT

A new study changes the way researchers look at the age-old popular schoolyard game of rock-paper-scissors.

Chinese mathematicians with the Zhejiang University recently published the results of their wide encompassing test on the Arxiv website, involving 360 students divided into groups of six for 300 rounds at 90 to 150 minutes each.

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The test subjects were randomly paired with each player's strategy and record closely monitored with monetary incentives for victories. The goal of the study was to discover what in game theory is called "conditional response" as opposed to randomized chance.

For decades, the so called Nash Equilibrium was one of the principal game theories around. Formulated by Nobel Prize-winning mathematician and subject of Hollywood film A Beautiful Mind, John Forbes Nash, Jr., the principle implies that in any given game where the player is faced with equal randomized options to victory, they will make their choice at random for maximum unpredictability against an opponent.

Researchers Dr Zhijian Wang, Dr Bin Xu and Dr Hai-Jun Zhou, were however dubious as to how it applied to rock-paper-scissors, a game first invented in China during the Han Dynasty around two thousand years ago, and speculated if human behavior wasn't more premeditated than that.

The Nash Equilibrium would predict that each player, win or lose, would continue to make randomized choices as to what hand to play next as the smarter play. The study conclusively proved this false.

Though players would choose each of the three options exactly one third of the time, as what the Nash Equilibrium would predict, but a pattern of the order of the choices made soon emerged upon close inspection.

Players who won would keep playing the same winning hand over and over until they lost and players who lost would proceed to change their hand in a "clockwise" direction, going from rock, to paper, to scissors. This is detailed in the study as the "win-stay lose-shift" strategy.

Thus, the easiest way to win rock-paper-scissors is if you lose, you next play the hand that would beat your opponent's last hand. That is, if you lost to rock, you next play paper as odds are your opponent will keep playing rock until a loss. If you however win, you can pretty safely anticipate your opponent to change to the next hand in the clockwise-line. If you win over paper, your opponent is most likely to use scissors in the next round.

The reason for this, Dr Wang claims, may be hard-wired collective cyclic motions of the human 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" the researchers say.

The study may however very well be useful in predicting other patterns of competitive behavior and game theory. Theories that would be applicable to anything from financial trading to competitive sports, among other things.

How these new findings fit in with a previous study by the Proceedings of the Royal Society of Biological Sciences is unclear. That study found that players of rock-paper-scissors frequently unconsciously imitate their opponent, an effect called automatic imitation, something which may seem counterintuitive as conventional logic dictates victory is secured by acting differently than your opponent.

Zhejiang University, founded in 1897, was one of the first modern academies of secondary education in China and is considered one of the most prestigious universities in the country, once called the "Oriental Cambridge" by British scholar Joseph Needham.

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