Rock Paper Scissors

Rock beats scissors, scissors beats paper, and paper beats rock. Against a fair random opponent nobody has an edge: each result happens one third of the time. Switch to smart mode and the computer looks for patterns in your choices.

How to play

1. Choose rock, paper or scissors (or press R, P or S).
2. The computer picks at the same moment and the winner is shown.
3. Your record and pick percentages update after each round.

The probability of winning

There are 3 × 3 = 9 equally likely pairs of moves when both players pick at random. In 3 you win, in 3 you lose and in 3 you tie, so P(win) = P(lose) = P(tie) = 1/3. Over 30 rounds against the fair computer, you should expect about 10 wins, but random luck often gives 7 or 13.

Are you really random?

People are bad at being random: many avoid repeating a move, or follow a cycle. The page runs a chi-square test on your picks. With 3 options, χ² = Σ (observed − expected)² ÷ expected. A value above 5.99 means your choices are uneven enough that the difference is unlikely to be chance (5% level, 2 degrees of freedom). The smart computer exploits such habits.

Rock paper scissors probability quiz: 10 questions

Test yourself with 10 multiple-choice questions. Choose an answer and press Submit to see if you are right and why. Your score appears at the end.

Frequently asked questions

Is there a way to always win at rock paper scissors?

Not against a truly random opponent: every move wins 1/3 of the time. Against people, spotting patterns can help, which is what the smart computer does to you.

What does the smart computer do?

It counts which move you tend to play after each of your moves and plays what beats your most likely next pick, with a little randomness mixed in.

What is the chi-square test here?

A statistics test that checks whether your rock, paper and scissors counts are close to equal, as they would be if you picked at random.

Why does the fair computer sometimes win many times in a row?

Streaks happen by chance. The chance of losing 3 in a row is (1/3)³ = 1/27, so in a long session it will happen.

Can I play with the keyboard?

Yes: R for rock, P for paper, S for scissors.

Sources

• OpenStax Introductory Statistics 2e: Goodness-of-Fit Test
• NIST/SEMATECH e-Handbook: Chi-Square Goodness-of-Fit Test

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