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From Wikipedia:

Rock-paper-scissors

Rock-paper-scissors (also known as paper-scissors-rock, scissors-paper-stone, jan-ken-pon, rochambeau (sometimes spelled roshambo) and many derived terms), is a two-person hand game.

 

The game is often used as a selection method in a similar way to coin flipping, drawing straws, or throwing dice to randomly select a person for some purpose. However, unlike truly random selections, it can be played with skill if the game extends over many sessions, as a player can often recognize and exploit the non-random behavior of an opponent.

 

Sportspeople often use the game (both officially and unofficially, in place of a coin toss) to decide on opening plays. Similarly, uncertain calls, or even the whole game in case of rain, may be so decided. It is also often used as a method for creating appropriately non-biased random results in live action role-playing games, as it requires no equipment. It is also used in some online gambling sites as a form of novelty betting.

 

Game play

The players both count aloud to three, or speak the name of the game (e.g. "Rock! Paper! Scissors!" or "Ro! Cham! Beau!"), each time raising one hand in a fist and swinging it down on the count. On the third count (saying "scissors!" or "Beau!" ), the players change their hands into one of three gestures, which they then "throw" by extending it towards their opponent. A variation on this version (played in the United States) involves a fourth count—"SHOOT"—before players throw their gesture.

 

Rock, represented by a clenched fist.

 

Paper, represented by an open hand, with the fingers connected.

 

Scissors, represented by the index and middle fingers extended and separated.

 

The objective is to select a gesture which defeats that of the opponent. Gestures are resolved as follows:

 

Rock blunts or breaks scissors; rock wins.

 

Paper covers or captures rock; paper wins.

 

Scissors cut paper; scissors win.

 

If both players choose the same gesture, the game is tied and the players throw again. If the gestures chosen on each throw were truly random, the average number of throws required to decide a winner would be 1.5.

 

In some variations of the game, the winner of each round "uses" the weapon on the opponent's weapon, to demonstrate that they have won. Otherwise the game is settled.

 

Rock-paper-scissors (RPS) is frequently played in a "best two out of three" match, and tournament players often prepare sequences of three gestures ahead of time.

 

Jason Simmons, a competitive RPS champion, claims that women tend to start with scissors,while the World RPS Society states that males have a tendency to lead with rock. At World RPS tournaments, scissors is statistically the least common throw.

 

Mathematics: intransitivity

RPS is also often used as an example of the mathematical concept of non-transitive relations. A transitive relation R is one for which a R b and b R c implies a R c. A reflexive, antisymmetric, and transitive relation on a set is known as a partial ordering, from which notions of "greater" and "less" follow. A game option which is "greater" than another is closer to being optimal, but such a notion does not exist in RPS: The relation used to determine which throws defeat which is non-transitive. Rock defeats scissors, and scissors defeat paper, but rock loses to paper. In fact, RPS could be called "intransitive" because A is greater than B, and B is greater than C, yet A is not greater than C. The game is thus an example of a Strange loop, or apparent hierarchy that returns to an earlier level.

 

In knot theory and braid theory, the Borromean rings and the standard braid exhibit rock-paper-scissors ordering. This gives rise to what is called the Brunnian property: any pair of Borromean rings is unlinked, and any two strands of a standard braid are not braided around each other, so if any one ring or strand is removed they will come apart, but the overall link or braid does not come apart.

 

Additional weapons

With an odd number of choices, each beats half the weapons and loses to half the weapons. No even number of weapons can be made balanced, unless some pairs of weapons result in a draw; there will always be some weapons superior to others. These also lose some of the aesthetic elegance of the game, which is otherwise one of the simplest possible games of skill.

 

An example of an unbalanced four-weapon game adds "dynamite" as a trump. Dynamite, expressed as the extended index finger or thumb, always defeats rock, but is defeated by scissors. The paper-dynamite relationship is disputed; using it as a trump generally implies that "dynamite shreds paper," but there are those who claim that the paper would supposedly smother the wick. Because of this dispute (and the potential unfair advantage that would result), organized rock-paper-scissors contests never use dynamite.

 

One popular balanced five-weapon expansion, invented by Sam Kass,[8] adds "Spock" and "lizard" to the standard three. "Spock" is signified with the Star Trek Vulcan salute, while "lizard" is shown by forming the hand into a sock-puppet-like mouth. Spock smashes scissors and vaporizes rock; he is poisoned by lizard and disproved by paper. Lizard poisons Spock and eats paper; it is crushed by rock and decapitated by scissors. This variant was covered in a 2005 article of The Times, and appeared in an episode of the sitcom The Big Bang Theory in 2008.

 

"The Ultimate Rock, Paper, Scissors Chart", contains no fewer than 25 possible hand shapes.

 

A new "most terrifyingly complex" game of RPS was posted online in 2006 that has 101 different gestures and 5050 possible non-tie outcomes. All information on playing is available online but a poster and a booklet outlining the gestures and outcomes were also made available for purchase. A notable difference from the 25 hand shape version is that now nuke beats wolf rather than the other way around.

 

Different weapons

A variation found in Indonesia is composed of an earwig, a human, and an elephant. The earwig is able to climb into the elephant's ear and drive it insane, while the human crushes the earwig and the elephant crushes the human.

 

The popular television series That '70s Show mentions a nuclear war-like version. The cockroach survives the nuclear bomb, the nuclear bomb destroys the foot (or human as it may apply), and the foot/human crushes the cockroach.

 

The Discovery Kids television series Endurance uses an elimination scheme that involves wood, water, and fire. (The operating premise is that fire "burns", and therefore defeats wood; wood "floats on" and defeats water; and water extinguishes fire.)

 

Rock-paper-scissors analogies in video games

Combat or strategy-based video games often feature RPS-like cycles in their characters' or units' effectiveness against others. These often attempt to emulate cycles in real-world combat (such as where cavalry are effective against archers, archers have an edge over spearmen, and spearmen are strongest against cavalry.) Such game mechanics can make a game somewhat self-balancing, by preventing any one simple strategy from dominating gameplay.

 

Many card-based video games in Japan use the RPS system as their core fighting system, with the winner of each round being able to carry out their designated attack. (A popular game involving an extended RPS strategy is Pokémon, in which attacks have varied effectiveness based on 17 elemental types.)

 

Some class-based first-person shooter games, such as Team Fortress 2, use the same self-balancing mechanism. Certain classes are designed with clear strength or weaknesses against other classes, which encourages players to respond to the changing battlefield and coordinate their efforts.

 

Rock-paper-scissors also featured in Sega's 1986 video game Alex Kidd in Miracle world. At the end of certain levels, the player would need to beat a computer character in a best-of-three game of rock-paper-scissors, in order to pass to the next level.

 

Rock-paper-scissors analogies in nature

Lizard mating strategies

The common side-blotched lizard (Uta stansburiana) exhibits a RPS pattern in its mating strategies. Of its three color types of males, "orange beats blue, blue beats yellow, and yellow beats orange" in competition for females, which is similar to the rules of rock-paper-scissors.

Coliform bacteria

Some bacteria also exhibit a rock-paper-scissors dynamic when they engage in antibiotic production. The theory for this finding was demonstrated by computer simulation and in the laboratory by Benjamin Kerr, working at Stanford University with Brendan Bohannan. The antibiotics in question are the bacteriocins - more specifically, colicins produced by Escherichia coli. Biologist Benjamin C. Kirkup, Jr. further demonstrated that the colicins were active as E. coli compete with each other in the intestines of mice, and that the rock-paper-scissors dynamics allowed for the continued competition among strains: antibiotic-producers defeat antibiotic-sensitives; antibiotic-resisters multiply and withstand and out-compete the antibiotic-producers, letting antibiotic-sensitives multiply and out-compete others; until antibiotic-producers multiply again.