Rock Paper Scissors Simulator
Play against the computer or run thousands of rock–paper–scissors simulations. Explore strategies, randomness, and win rates with live stats.
1 Choose your move
Tip: Try patterns (e.g., Rock → Paper → Scissors) and see how the computer responds.
2 Round result
Make your first move!
Your stats vs computer
Recent rounds
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How the rock paper scissors simulator works
This simulator models the classic game of rock–paper–scissors (RPS) using simple probability rules. Each round, both players choose one of three moves:
- Rock beats Scissors
- Paper beats Rock
- Scissors beat Paper
In Play Mode, you manually choose your move and the computer responds using a fair random strategy (each move has probability 1/3). The tool tracks your wins, losses, draws, and streaks over time.
In Experiment Mode, both players are controlled by strategies. You can simulate thousands of rounds to see how different strategies perform against each other.
Strategy types
- Random – Rock, paper, and scissors are chosen with equal probability (33.33% each).
- Always Rock / Paper / Scissors – The player always chooses the same move.
- Custom probabilities – You specify the probability of each move (they should sum to 100%).
Probability model
Suppose Player A chooses Rock, Paper, Scissors with probabilities \(p_R, p_P, p_S\) and Player B chooses them with \(q_R, q_P, q_S\).
Expected win rate for Player A:
Player A wins when:
- A plays Rock and B plays Scissors: \(p_R \cdot q_S\)
- A plays Paper and B plays Rock: \(p_P \cdot q_R\)
- A plays Scissors and B plays Paper: \(p_S \cdot q_P\)
So the expected long-run win probability for A is:
\[ P(\text{A wins}) = p_R q_S + p_P q_R + p_S q_P \]
Similarly:
\[ P(\text{B wins}) = q_R p_S + q_P p_R + q_S p_P \] \[ P(\text{draw}) = p_R q_R + p_P q_P + p_S q_S \]
When both players use the fair random strategy (\(p_R = p_P = p_S = 1/3\) and \(q_R = q_P = q_S = 1/3\)), each outcome has probability:
- \(P(\text{A wins}) = 1/3\)
- \(P(\text{B wins}) = 1/3\)
- \(P(\text{draw}) = 1/3\)
Using the simulator for experiments
You can use Experiment Mode to:
- Verify that random vs random converges to ~33% wins, losses, and draws.
- Test how a biased player (e.g., 60% Rock) performs against a fair opponent.
- Explore how long win streaks appear purely by chance.
Because the simulator uses pseudo-random numbers, results will vary slightly each time, but with more rounds the percentages should approach the theoretical values above.