Rock Paper Scissors

The rules

• Rock crushes scissors.
• Paper covers rock.
• Scissors cuts paper.

Matching throws are a draw. Each gesture beats one and loses to one, which is what stops any single choice being the right one.

Can the Bot opponent see your choice?

No. The Bot’s throw is decided before yours is recorded, every round. Both opponents work the same way in that respect — the difference is what they base the choice on.

• Fair picks at random, without seeing your choice. It ignores everything you have played.
• Learns your patterns counts what you have thrown after recent sequences, predicts your next throw and plays the gesture that beats it. It only acts once it has seen the same pattern lead to the same throw twice.

Why a fair opponent cannot be beaten

Against an opponent that chooses rock, paper, and scissors independently and uniformly at random, every strategy wins one third of the time in the long run. Always rock, always alternate, copy their last throw — none can improve your expected result against a genuinely random opponent.

That is the game’s Nash equilibrium: throwing uniformly at random is unexploitable, and both players doing it makes the game a coin toss nobody can improve on. It also means a perfectly fair opponent is not very interesting, which is why the second mode exists.

Why people lose to a pattern-hunting opponent

People often produce predictable patterns when they try to choose randomly:

• Repeats feel wrong. Asked to be unpredictable, people throw the same gesture twice in a row far less often than chance would.
• Losing changes behaviour. Players tend to switch after a loss and stick after a win, which is itself a pattern.
• Rock is a common opening. Some RPS datasets and player surveys report rock being chosen more often as a first throw, although the size of that effect depends on the population and setting.

None of this helps against the fair opponent — its throws are independent of your choices. It is exactly the kind of predictability the pattern-hunting opponent is looking for. To avoid giving it a pattern to exploit, use an independent source of randomness rather than trying to "feel" random.

Rock paper scissors lizard Spock

The five-gesture version adds lizard and Spock, so each gesture beats two others and loses to two. If both players choose uniformly at random, draws occur in one fifth of rounds rather than one third.

• Scissors cuts paper, and decapitates lizard.
• Paper covers rock, and disproves Spock.
• Rock crushes lizard, and crushes scissors.
• Lizard poisons Spock, and eats paper.
• Spock smashes scissors, and vaporizes rock.

The Lizard Spock variant was created by Sam Kass and Karen Bryla and later became widely known through The Big Bang Theory.

Is there a winning strategy?

Against a uniformly random opponent, there is no throw that gives you an advantage. Against a human, however, predictable habits can sometimes be exploited.

That is the game's Nash equilibrium: choosing each gesture uniformly at random cannot be exploited by the other player. Against the fair mode here, you can win or lose individual rounds and even short matches, but no choice of strategy gives you a long-run advantage.

Frequently asked questions