To win at rock-paper-scissors, put on a blindfold

By Ed Yong | July 19, 2011 7:00 pm

In 2007, one Jamie Langridge became $50,000 richer after winning intense national tournament in Las Vegas. Langridge beat his opponent decisively, with a classic open-hand technique. The sport? Rock-paper-scissors.

Rock-paper-scissors seems deceptively simple. Pairs of opponents display one of three hand gestures. Paper covers rock, rock blunts scissors, and scissors cut paper. It’s so straightforward that children the world over learn to play it. But this is not just a game of chance. Played at the highest level, it becomes a game of psychological strategy, one that justifies five-figure trophies in large competitions and even the publication of strategy guides.

Such advanced games are possible because people don’t choose their hand shapes randomly. They are affected by moves that have gone before, and what other people are doing. Consider a new experiment by Richard Cook at University College London. Cook asked 45 people to face off against each other in several rounds of rock-paper-scissors, in exchange for real money. In every game, either one or both players were blindfolded.

Cook found that the players drew with each other more often when one of them could see (36.3% of the matches) than when both were blindfolded (33.3% of them). The latter figure was exactly the proportion of draws you’d expect if the players were choosing randomly; the former was significantly higher than chance.

Cook devised this study because he was interested in the idea that we all automatically and unconsciously imitate one another. There’s plenty of evidence that we do indeed copy one another, from obvious gestures like touching our face to subtle movements like tensing our muscles. But it’s not clear whether these actions are truly involuntary in the way that the knee-jerk reflex is. To find out, Cook wanted to see if people can stop themselves from performing these acts of mimicry.

That’s why he turned to rock-paper-scissors. Here is a game where you have to avoid imitating your opponent in order to win – the rules implicitly encourage people to avoid copying what their adversaries do. The results of Cook’s face-offs suggest that the sighted player has a slight tendency to imitate the blindfolded one – that’s why a blindfolded player will draw more often against a sighted one than another blindfolded opponent. And indeed, players were particularly likely to imitate rocks and scissors.

The sighted players weren’t using any obvious strategies. Their gestures weren’t related to the ones their opponents made in the previous round, or the one before that. Instead, Cook thinks that they were acting involuntarily.

The timing of their moves supports his conclusion. There simply isn’t enough time to see what the other player does and make a conscious decision to ape it. If the players were doing that, there would have been a noticeable delay, and an overseeing referee would have notified the researchers. There was, however, enough time for the brain to process signals from the eyes, and send instructions to the arm without any conscious thought. It takes at least 200 milliseconds to do this, and in his experiments, Cook saw that the sighted players made their move more than 200 milliseconds after their opponent on around half of the games.

Cook invokes the idea of mirror neurons, which fire both when animals act and when they see others performing the same actions. According to this interpretation, the sight of someone else’s falling hand would trigger neurons that encode the same movement in our brains, nudging us towards doing the same thing. The existence of mirror neurons in the human brain is controversial (they’re only formally been identified in monkeys), but Cook notes that playing rock-paper-scissors lights up parts of the brain where human mirror neurons are supposed to lie.

Of course, Cook says, “The tendency to imitate need not be overwhelming.” People can overcome it if they have enough concentration, motivation or experience, which is presumably why folks like Jamie Langridge can walk away with big tournament prizes.

Now, what happens when people play rock-paper-scissors-lizard-Spock?

Some novice-level tips for rock-paper-scissors:

  1. Paper first, or perhaps scissors. Rookies tend to lead with rock, so paper could score an easy opening victory. However, if you’re playing an experienced player, they will know this. If they think you’re a rookie, they’ll play paper; if they think you know what you’re doing, they’ll play scissors. In this case, scissors if your best bet – it will either draw or win.
  2. When in doubt, paper. Rock is the most popular move and scissors is the least popular.
  3. Lose to their last move. When players have no plan, they often play the move that will beat their last one. If they threw paper, they’ll do scissors next, so you should play rock.
  4. Spot double runs. People are unlikely to play three of the same move in a row. If they throw two rocks, their next move will probably be scissors or paper, so you should play scissors for, at worst, a draw.
  5. And if you want to take this far too seriously

Reference: Cook, Bird, Lunser, Huck & Heyes. 2011. Automatic imitation in a strategic context: players of rock–paper–scissors imitate opponents’ gestures. Proc Roy Soc B. http://dx.doi.org/10.1098/rspb.2011.1024

Image by Wizardhat

Comments (10)

  1. Great article! However, the “far too seriously” link near the end is broken. Because obviously, I wanted. And couldn’t. Aww.

  2. MT-LA

    I look forward to using my new found powers of Rock-Paper-Scissors to make sure I never have to drive again.

  3. The psych world sure is going to mirror neurons for explanations these days. In time, we will see which ones are legit and which ones aren’t.

    Btw – Seems like there are international competition for anything these days, beer pong, hot dog eating, and rock-paper-scissors….

  4. errors

    err non-randomness at the 3% level may be statistically significant, but you’re not going to win multiple tournaments because of that kind of advantage.

  5. Naga

    How is it that avoiding imitating your opponent makes you win???

  6. afbach

    The “Far too seriously” link is probably:
    http://www.chessandpoker.com/rps_rock_paper_scissors_strategy.html

    or, maybe the same thing:
    http://cowboyszone.com/forums/archive/index.php/t-79362.html

    I googled the phrase in the href:
    “they can gain a surprising depth of knowledge about how the game will play out concerning forced draws or forced results. Let’s learn how.”

  7. Chris M.

    If you’re interested in trying your skill versus a learning algorithm, the New York Times recently featured this web tool:

    http://www.nytimes.com/interactive/science/rock-paper-scissors.html

    You can use either a novice computer that learns based only on the moves you make, or a veteran computer that has the move history of everyone who has played the game on the site. Both are interesting!

    And thanks for using the narrow definition of mirror neurons here; the original paper described them as just responding to an action, whether that action was performed by the monkey or the experimenter. Most of the speculation about further uses hasn’t been well-proven.

  8. sprawld

    advanced-level tips for beating someone who’s read NERS’ novice-level tips

    1. Go with rock first, rock is strong
    2. When you’re opponent doesn’t know what to do, they’ll play paper. When you don’t know what to do, chances are your opponent will; so no need to worry about paper. For at worst a draw, go for rock
    3. They’ll try to lose to your last move, so the best thing is to play your last move and beat them. Stick with rock.
    4. Go for triple runs, they’ll not expect them. Why not go rock one more time?
    5. And if you want to take this far too seriously…

  9. Super-advanced-level tips for people who read Sprawld’s selection.

    Always play rock. You will lose, but then you can punch your opponent in the face with your already balled-up fist and take their money.

  10. Tk

    1. If players tend to subconsciously copy their opponents’ current moves, resulting in 3% more ties with a 200 ms delay, then the question arises: Can training increase the frequency of this behavior? More importantly, can one train oneself to subconsciously play the move that beats the opponent’s current move? If we took RPS as seriously as Americans take baseball, then this seems like a viable strategy.

    2. Cook presumably rules out the alternative explanation, namely, that the sighted players were reacting to their opponents’ previous moves, using some sort of statistical analysis. One could alternatively design the experiment this way: use a blindfolded confederate who has memorized a precomputed, random sequence of moves. I think this could also be useful for training, see 1 above.

    3. There is a mathematical contradiction between the following three propositions:

    (a) Two blindfolded players throw independently of each other, in the sense that conditioning on one player’s move doesn’t affect the probability distribution of the other player’s concurrent move. (This may be false, but if so, there should be an interesting explanation. Perhaps the blindfolded players were told the outcome of each round before playing the next one? The article doesn’t specify, but that would explain it.)

    (b) Rock is more popular than scissors, on average across naive players (which I’m assuming are the ones used in this study). (I don’t know if this is true, but Ed suggests this in his novice-level tips. In any case, it seems plausible that the frequencies of rock, paper, and scissors would be significantly different from each other, for whatever psychological reasons.)

    (c) Two blindfolded players nevertheless tie exactly one-third of the time. (It seems Cook’s study suggests this is true, but perhaps the data are not conclusive on this point.)

    The problem is, the RMS-AM inequality implies that, assuming (a) and (b), the expected frequency of ties should be strictly greater than 1/3. This is why I’m puzzled. Which of (a), (b), (c) is false?

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