$1000 for paper? Rock, Paper, Scissors and the Nash Equilibrium

Steve Stapley won $1000 in a rock, paper, scissors contest in McBride last week.
Steve Stapley won $1000 in a rock, paper, scissors contest in McBride last week.

By: Frank Green

Steve Stapley was confident. He hadn’t played rock paper scissors in years, but he knew the rules and he trusted his gut, which he’d fortified with Budweiser, before switching to rye and coke. He said he had no particular strategy except to make his opponents think he had one.

“I just tried to seem real confident, and look at the guy and not his hand,” Stapley said. “Look him in the eye and make him think that I got him figured.”

Stapley cruised through more than half a dozen rounds, losing just one match. In the final, Stapley said his scissors cut Custin Ryan’s paper, and then his paper covered Ryan’s rock. His triumph at McBride’s Pioneer Days tournament earned him $1,000.

According to scientists who’ve studied rock paper scissors—and many have—Stapley was right to play without a strategy. He would’ve done even better playing without his gut. In the long run, they say, randomness is the only way to come out at least even. Anything else, and your opponent can beat you by exploiting the patterns in your play. In other words, Stapley would’ve done well to just follow orders from an algorithm spitting out a meaningless chain of papers, scissors, and rocks.

“If you love rock paper scissors it’s depressing,” said Oliver Schulte, who teaches computer science at Simon Fraser. “Strategizing is pointless.”

And our guts are very predictable. Studies have found that people rarely throw the same thing more than twice in a row, probably because, ironically, they don’t want to be predictable. Another showed that men throw rock far more often than women do. And researchers discovered that people tend to follow up winning a throw by throwing the same thing again, and a losing throw with one that would beat the throw they just lost to. (For example, if Sally threw paper and Brenda threw rock, chances are Sally will throw paper again, and Brenda will throw scissors.)

If you know these human tendencies and your opponent doesn’t, you could beat them that way. But if you both know your research, the habits of your mind can only betray you.

The mathematician John Nash is famous for coming up with the theory that underpins these ideas, which are important for understanding everything from penalty kicks in soccer to the reproductive habits of side-blotched lizards. He’s also the subject of the movie A Beautiful Mind.

But in McBride, people win to give their winnings away. And so Stapley celebrated his victory by donating $100 to the Elks, and spending the rest buying rounds at the McBride Hotel.

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