Rock paper scissors, against a computer that cannot cheat.

Rock paper scissors is a hand game for two players who choose one of three moves at the same moment. This page lets you play it against the computer or a friend, in a single round or a match, and adds the five-move version with lizard and Spock. It also keeps the score, remembers your record on this device, and shows that the computer plays fair.

How to play

1. Under Moves, pick Rock, paper, scissors or the five-move version.
2. Pick Computer plays: Fair, at random for a game of pure luck, or Smart, learns your habits for a computer that studies what you throw.
3. Pick Play against: The computer or A friend on this device, and a Match length from Best of 1 to Best of 7, or Endless.
4. Click a move, or press its key: R for rock, P for paper, S for scissors, L for lizard and K for Spock. If Count down before the reveal is on, you see Rock, Paper, Scissors before both hands appear.
5. Read the line under the hands. It names the winning move and the verb, such as "Rock crushes scissors". A tie is played again.
6. When someone has enough rounds, the match ends. A best of 3 is first to 2 wins, a best of 5 first to 3, and a best of 7 first to 4. Press Play again for a new match.
7. With a friend, Player 1 clicks first while Player 2 looks away, the choice is hidden, then Player 2 clicks and both hands are shown.

The rules

The first three rows are the classic game. The other seven are added when you pick the five-move version, and Rock crushes scissors in both.

The odds against a random computer

In the classic game there are 3 times 3, which is 9, pairs of moves. In 3 of them both players chose the same, in 3 you win and in 3 you lose. So whatever you choose, you win 1 round in 3, lose 1 in 3 and tie 1 in 3. No pattern of your own beats a computer that chooses at random, which is what Fair mode does. In the five-move game there are 25 pairs: 5 ties, 10 wins and 10 losses, so you win 2 in 5, lose 2 in 5 and tie 1 in 5.

Once ties are replayed, every decisive round is 50 to 50, and so is a match of any length. Winning three rounds in a row in the classic game has a chance of 1 in 27, which is 3.7%, and winning at least one of three rounds is 1 minus 2/3 cubed, 19 in 27, or about 70.4%. The Computer's moves so far panel counts what the computer has played this session, so you can see it spread out in fair mode, though a short run will never be exactly even.

Why you can trust the computer

Against a person, the danger is the other player seeing your move first. Here the computer picks its move with your browser's secure random numbers before you click, and shows Computer locked in and a code. The code is the start of a SHA-256 hash of the move and a secret number. After the round, the page shows the move and the number. If you hash them together, in the form move:number, you get the same start, which proves the move was fixed before you chose. A tool such as the one built into your computer's terminal, or any SHA-256 page, can do the check.

Playing a friend

On one device, the choice has to be hidden. Player 1 clicks, the hands show a question mark, and Player 2 clicks. The keys are turned off in this mode so nobody can press a key by accident. This also works as a way to settle a small bet, who goes first or who pays.

The smart computer

In smart mode the computer keeps a count of your throws: how often you play each move, and which move you tend to play after each of your previous moves. Before each round it guesses your next throw from the count of what you played after your last move. If it has seen fewer than 3 throws after that move, it uses your overall counts instead, and with fewer than 3 throws in all it plays at random. It then plays the move that beats its guess. One round in five it plays at random, so it is not fully predictable. The guess is made before you click, so the fingerprint still proves the move was fixed first, and it never looks at your click. The counts stay in your browser, and Forget my throws clears them.

What this means for you: a player who throws at random still wins, loses and ties one third of the time each, because no guess can beat a pattern that is not there. A player who leans on a move, for example rock after a loss, will see the computer catch on. The Your throws so far panel shows your own spread, so you can see whether you have a habit.

Does strategy matter?

Against the fair computer, no. Its move is chosen at random and fixed before you click, so it has no habits to learn and your choices have no effect on its next one. You can always choose rock, or cycle through the three, and the odds stay at one third. Against the smart computer, strategy means avoiding patterns, and the best pattern is none. Against a real person, a pattern can help only if the person has one.

How long a match lasts

Ties are played again and do not count, so a match is decided by the rounds that have a winner. The number needed depends on the length you pick:

A longer match does not favour anyone when both sides win at the same rate. It only makes the result harder to put down to a lucky streak, so pick best of 1 for a quick call and best of 5 or 7 for something that matters to the players.

To flip a coin instead, use flip a coin. For bigger draws use the dice roller, the random name picker or the .