Rock Paper Scissors: The Game Theory Behind It
Rock paper scissors looks like pure chance and is not, because the opponent is a person. The Rock Paper Scissors tool plays against the computer, and the theory behind it is genuinely interesting.
The unbeatable strategy, and why nobody uses it
The game has a known optimal solution: play each option exactly one third of the time, at random. Against that, no opponent can do better than break even over the long run. It is the textbook example of a mixed-strategy equilibrium.
The catch is that it is unbeatable and it is also unwinnable. Perfect randomness guarantees a draw against a good opponent and gives up any chance of exploiting a bad one.
And people cannot do it anyway. Humans are terrible at being random - we avoid repeating ourselves, we think a pattern looks suspicious when it is natural, and we react to what just happened. Every one of those is exploitable.
The patterns people actually fall into
Studies of real play, including large tournaments, find reliable tendencies.
Rock is the most common opening, particularly among men and among inexperienced players. It feels strong. So paper is the statistically better first throw.
Winners tend to repeat their winning throw. Losers tend to switch, and often switch to whatever just beat them. So if you lost to paper, your opponent may well play paper again - and if you won with rock, they are likely to play paper next, which means switching to scissors is the move.
People rarely play the same thing three times running, so after two identical throws the third is unlikely to match.
None of this is certain. All of it is better than guessing, which is what makes the game a competition rather than a coin flip.
Playing against a computer is a different game
An opponent playing genuinely randomly cannot be read, so against a random computer the game really is chance and you will converge on a third each.
An opponent that *learns* is a different matter - it will find your patterns faster than you find its, because it does not get bored or sentimental. Which is a useful demonstration of how hard it is to be unpredictable on purpose: if you want to beat a learning opponent, you need actual randomness, and for that you need something like the Coin Flip or the Random Number Generator rather than your own judgement.
The variants
Rock paper scissors lizard Spock adds two options, making ten outcomes instead of three and roughly halving the chance of a draw.
Any such game needs an odd number of options, each beating half the others, for the symmetry to work. Five, seven and larger odd numbers all produce valid games, and none is more balanced than the original three - just slower to draw.
Common questions
What should I open with?
Paper, because rock is the most common first throw.
Does the three-two-one count matter?
It synchronises the reveal, which is the only thing stopping either player reacting to the other.
Can a computer be beaten?
A random one, only by luck. A learning one, only with real randomness.
Fancy a round?