Study reveals a way to improve chances of winning at rock-paper-scissors

May 2, 2014 by Bob Yirka, report

The Rock-Paper-Scissors game. (A) Each matrix entry specifies the row action’s payoff. (B) Non-transitive dominance relations (R beats S, P beats R, S beats P) among the three actions. (C) The social state plane for a population of size N = 6. Each filled circle denotes a social state (nR, nP , nS); the star marks the centroid c0; the arrows indicate three social state transitions at game rounds t = 1, 2, 3. Credit: arXiv:1404.5199 [physics.soc-ph]
( —A trio of researchers at Zhejiang University in China has found a way for players to improve their odds of winning when playing the hand game rock-paper-scissors. In their paper they've uploaded to the preprint server arXiv, the researchers describe a field study they undertook with a large crowd of volunteers and how it revealed the secret.

Scientists in many fields have studied for thousands of years, some to gain military or social advantage, others to better understand . One stands out, the hand game rock-paper-scissors, likely because of its simplicity, and because it can be used to make group decisions. Plus, it's universal, requiring no or preconceived social notions—therein lies its inherent beauty. Also, it's supposed to be fair, with every player having a 1 in 3 chance of winning any given round. Prior research has suggested that such odds are the case, but now, it appears the experts may have been wrong. In this new effort, the team in China has found that due to human emotion and decision-making strategy, there is a way to better the odds when playing.

To find it, the researchers recruited 300 volunteers from the university and divided them up into 60 groups and had them play the game. Winners were given different amounts of money to make sure that all players were trying to win. As the horde played, swapping teams periodically, the researchers filmed the action and afterwards, studied the tape. They found that players had a slight tendency to repeat a wining throw, and, to give up on a throw if they lost using it more than twice in a row. That meant, the researchers report, that in order to improve their chances of winning, all a player had to do was throw down a gesture that would beat the previous winner or throw down a gesture that would beat one of the other two gestures a prior loser had not just used.

The researchers note that such predictable play is easy to explain—people naturally continue with a winning strategy and avoid those that don't work. They call it the "win-stay, lose-shift" strategy, which because most of the people playing use it, results in any given player winning a third of the time—but, not if they know about the strategy used by their opponents, and their opponents don't. Because the analysis came after the game playing, the researchers didn't have the opportunity to test their theory that they'd found a winning strategy, but now that the cat's out of the bag, it's likely people all over the world will be testing it for them.

Explore further: Want to win in the NHL? Score first—but not until the third

More information: Social cycling and conditional responses in the Rock-Paper-Scissors game, arXiv:1404.5199 [physics.soc-ph]

How humans make decisions in non-cooperative strategic interactions is a challenging question. For the fundamental model system of Rock-Paper-Scissors (RPS) game, classic game theory of infinite rationality predicts the Nash equilibrium (NE) state with every player randomizing her choices to avoid being exploited, while evolutionary game theory of bounded rationality in general predicts persistent cyclic motions, especially for finite populations. However, as empirical studies on human subjects have been relatively sparse, it is still a controversial issue as to which theoretical framework is more appropriate to describe decision making of human subjects. Here we observe population-level cyclic motions in a laboratory experiment of the discrete-time iterated RPS game under the traditional random pairwise-matching protocol. The cycling direction and frequency are not sensitive to the payoff parameter a. This collective behavior contradicts with the NE theory but it is quantitatively explained by a microscopic model of win-lose-tie conditional response without any adjustable parameter. Our theoretical calculations reveal that this new strategy may offer higher payoffs to individual players in comparison with the NE mixed strategy, suggesting that high social efficiency is achievable through optimized conditional response.

Related Stories

Study suggest people act fairly due to spite, not altruism

February 12, 2014

( —A study done by philosophers Patrick Forber of Tufts University and Rory Smead of Northwestern University, suggests fairness in societies evolves out of a fear of spite from others, rather than due to an increase ...

Recommended for you

Coffee-based colloids for direct solar absorption

March 22, 2019

Solar energy is one of the most promising resources to help reduce fossil fuel consumption and mitigate greenhouse gas emissions to power a sustainable future. Devices presently in use to convert solar energy into thermal ...

Physicists reveal why matter dominates universe

March 21, 2019

Physicists in the College of Arts and Sciences at Syracuse University have confirmed that matter and antimatter decay differently for elementary particles containing charmed quarks.

ATLAS experiment observes light scattering off light

March 20, 2019

Light-by-light scattering is a very rare phenomenon in which two photons interact, producing another pair of photons. This process was among the earliest predictions of quantum electrodynamics (QED), the quantum theory of ...

How heavy elements come about in the universe

March 19, 2019

Heavy elements are produced during stellar explosion or on the surfaces of neutron stars through the capture of hydrogen nuclei (protons). This occurs at extremely high temperatures, but at relatively low energies. An international ...


Adjust slider to filter visible comments by rank

Display comments: newest first

3.7 / 5 (3) May 02, 2014
I see China's military research is improving.
1 / 5 (1) May 02, 2014
I knew that 20 years ago.
This game basically stayed the same for all that time.
5 / 5 (1) May 02, 2014
from PDF:" A total number of 360 students of Zhejiang University volunteered to serve as the human subjects of this experiment.~These human subjects were distributed to 60 populations of ~ size ~ 6.~ each population played within themselves ~ for 300 rounds under ~ random pairwise-matching ~ each game round ~ the players are randomly paired ~ compete ~ once"
Apparently the reporter is unable to read plain English, since he completely botches the dscription. The experimenters throw out one of the sessions, because players eventually all began choosing Rock. The estimated advantage of playing the supposed optimum "win-stay, lose-change" strategy is +10%. The experiments were done via computer screen & the opponents were random and never identified specifically. This has little relevance to real Rock-Paper-Scissors game playing, imho. The authors claim that people tended to cycle their choices & didnt choose randomly. So for a two person series, rather than 50-50 you get 60-40? Big Deal
2.5 / 5 (4) May 02, 2014
So for a two person series, rather than 50-50 you get 60-40? Big deal

In other strategy games, the difference between 50/50 and 60/40 is a pretty big deal.

If you are 50/50 in Grand Master league in Starcraft 2, then you are probably just another run of the mill grand master.

If you are 60/40 in Grand Master league you might actually be able to win a match at a WCS event.

If the winner of each throw got $10, and you had 100 throws, then 60/40 is worth $100 more to you than is 50/50.
5 / 5 (1) May 02, 2014
I am glad to see that the Chinese are using their vast collective intellects to work on something that matters. If nothing else, this research may lead to a new episode of the "Big Bang Theory"

My own research has revealed that when I play Rock, Paper, Scissors, and I use a real rock, I win every time.
1 / 5 (1) May 02, 2014
I am glad to see that the Chinese are using their vast collective intellects to work on something that matters. If nothing else, this research may lead to a new episode of the "Big Bang Theory"

My own research has revealed that when I play Rock, Paper, Scissors, and I use a real rock, I win every time.

I think the point here is real world games do not follow the on-paper probabilities. While you can see it intuitively, I guess it's important to prove it by math and experiments.

Maybe it's useless, or maybe it'll be important to some other math problem. Who knows?
5 / 5 (1) May 03, 2014
and in other news, cancer remains uncured and we dont have a working fusion reactor. But this is a perfectly good use of money, time and resources. Rock Paper Scissors.

Please sign in to add a comment. Registration is free, and takes less than a minute. Read more

Click here to reset your password.
Sign in to get notified via email when new comments are made.