Insightology

Rock Paper Scissors (RPS) is serious business. Serious enough to have an RPS World Championship. The next one is in October in Toronto. Why all the interest? Isn't it simply a children's game? As it turns out not only is it easy enough for a small child to play, it is difficult enough for an adult to master because of its unique nature, and complex enough for mathematicians to become interested.

The basic game consists of two players standing close enough not to touch with outstretched arms. The number of games (single, two out of three etc) is agreed upon beforehand. Number of primes (essentially number of times hands are revved before using) is also agreed upon beforehand. Players can choose to play any of the three hands in any game. There are rules for what is acceptable and what is not. For example, when playing paper, using a "vertical" paper (which looks similar to a handshake) is considered bad form. The game is set-up such that no one hand is best: rock beats scissors, scissors beats paper and paper beats rock.

So what is so difficult about this? Because there is no one dominant hand, every game (and series) becomes a battle of wits between the players where one is trying to guess the other's move. What is the best strategy to use? Randomness in hand selection may be the best strategy as it prevents the other player from guessing correctly. Randomness does not mean never choosing the last hand played. In fact, a common strategy to defeat amateurs is to bank on the fact that they consciously try to avoid repeating hands. For example, if an inexperienced player plays rock twice, chances are very good he may not play that again because they think thrice makes them predictable. Other tips can be found here .

Why is this game interesting to mathematicians? One reason is that it involves game theory. The simplest version involves two people competing with each other in a finite number of games. In order to win one needs to outwit the other since the possible strategies are limited and known to both. The dynamics of game theory can be mathematically modeled and optimal strategies derived. Another reason why RPS is interesting to mathematicians is that it has a property called non-transitivity. Transitivity is when A is better than B, B is better than C and therefore A is better than C. Clearly that doesn't happen here. The non-transitive nature makes mathematicians search for optimal strategies to play the game as well as invent other games (such as dice-based ones) that mimic the properties of RPS. Biologists have found examples of RPS in the natural world where such strategies lead to stability in systems .