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Rock Paper Scissors Decisive Probability

Find the chance that one round of rock paper scissors among n players ends without a tie.

Input

Enter the number of players. We compute the chance that a single round of rock paper scissors is decisive and does not end in a tie.

players

You can enter from 2 to 30 players.

Result

Chance of a decision with 3 players

66.67percent

18 of 27 outcomes are decisive

Tie probability

33.33 percent

Total outcomes

27

Expected rounds to decide

about 1.5 rounds

050100With 2 players the decisive probability is 66.67 percent2With 3 players the decisive probability is 66.67 percent66.673Number of players

Random simulation

Press the button to run many random rounds on the spot and check how closely they match the theory.

How it works

  • The total number of outcomes is 3 to the power n. Each player is assumed to throw rock, paper, or scissors with equal probability.
  • A round is decisive only when exactly two of the three hand types appear. If just one type appears (everyone the same) or all three appear, the round is a tie.
  • The number of decisive outcomes is 3 times 2 to the power n minus 2, that is 3×(2 to the power n − 2). The tie count is the total minus the decisive count.
  • The expected number of rounds until a decision equals 1 divided by the decisive probability p (the mean of a geometric distribution).
  • The random simulation runs only when you press the button and gives an approximate check against the theory. Because the number of trials is finite, results vary slightly each time.

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