Thirty kids in a classroom throw at the same moment. How many rounds before one of them is left standing? One estimate says about 63,917. At two seconds a throw, that is roughly thirty-five and a half hours. But look closely: that number is not the count of rounds to a winner.

Add players and rock-paper-scissors stops producing winners

A round resolves under exactly one condition: precisely two of the three shapes have to appear. Everyone throwing the same shape is a tie. All three shapes appearing is also a tie. The probability that n players settle a round works out to 3(2^n-2)/3^n.

  • 2 players → 1.5 throws
  • 3 players → 1.5 throws
  • 5 players → about 2.7
  • 8 players → about 8.6
  • 9 players → about 12.9
  • 20 players → about 1,108
  • 30 players → about 63,917

Two and three players land on the same figure because adding a third hand multiplies the winning patterns and the total outcomes by the same three.

"Nine players" is not a mathematical answer. It is a patience setting.

The estimate comes from a report published on August 28, 2026 by Yasuo Uetake, a senior researcher in the insurance research department at the NLI Research Institute, asking how many people can actually play rock-paper-scissors. He lands on nine because if ten throws is treated as the practical ceiling, the line falls between eight and nine players.

So nine is not something mathematics handed down. Stretch your tolerance to fifteen throws and nine players becomes workable. Lose interest after five and six is your ceiling. The math only says there is a wall. Where the wall sits depends on how long you can stand there with your fist out. Every figure here assumes each player picks among the three shapes uniformly at random. Real classrooms have habits and glances, and the numbers drift accordingly.

Of 64,201 throws, only 4.61 decide anything

Those 63,917 throws are only the average wait until the first round that is not a tie. And when that round finally lands, nobody has won. Thirty players simply split into two groups.

Count all the way down to a single survivor and the average comes to about 64,201 throws. The entire rest of the tournament costs roughly 284 more. Eliminating the other twenty-nine is rounding error. Some 99.6 percent of the time is spent waiting for round one to break.

Of those 64,201 throws, an average of 4.61 actually settle anything. Every other throw is a tie. The wall is not "picking one person out of a crowd." It is "a crowd throwing at the same time."

So Japanese kids cut the hands down to two

Japanese playgrounds had another way of doing it long ago, run by children, with a chant. Nobody throws scissors. Everyone shows rock or paper, and the group splits by which one you picked.

Cut the options to two and the only tie left is everyone happening to match. With thirty players, the odds of that are about one in 500 million. The group splits on the first throw, essentially every time. Push the team-splitting tool all the way to picking one person, with the smaller group carrying on each round, and 64,201 rounds become an average of 4.2.

High schoolers have checked the same thing. A student research paper published by Koshigaya-Kita High School in Saitama calculated that from five players up it is faster to split, and that dividing six players into three and three pulls the average down from 6.22 throws to 4.42.

The chant itself is nowhere near standard. When the Japanese site J-Town Net gathered reader submissions, 67 responses produced about 50 different versions: "Guu to paa de wakkareemashotto" in Kanagawa, "Guppa de kunde mo monku nashi" in Kyoto, "Guppa no soroi zone" in Kochi. Presumably none of those children ever worked out an expected value. The answer came out right anyway.

The same wall stands in every schoolyard

Rock-paper-scissors is not a Japanese-only game. Ken games are described as having reached Japan from China in the 17th century as a drinking game, and janken as having reached the West in the 20th.

The other solution turns up everywhere too: the counting-out rhyme. Players drop out as the last syllable lands on them, and the rhyme repeats until one is left. There is no such thing as a tie, so it always ends. Japan has its own, "dochira ni shiyou kana," and the lines that follow it vary not just by region but by school. The same scatter as the rock-or-paper chants.

When you had to choose one person out of twenty, what did the kids in your country do?

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