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# Rock, Paper, Scissors

The game of Rock, Paper, Scissors (sometimes with its elements permuted and/or Rock replaced with Stone, but also known as Roshambo, Rochambeau, Janken, Mora or JanKenPon) is a whimsical hand game most often played by children. It is often used in a similar way to coin flipping, throwing dice or drawing straws to randomly select a person for some purpose, though unlike truly random selections it can be played with skill if the game extends over many sessions, because one can often recognize and exploit the non-random behavior of an opponent.

Rochambeau is also often used as an example of the mathematical concept of non-transitivity. 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 Rochambeau: 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, Rochambeau could be called "antitransitive"'' because if A strictly defeats B, and B strictly defeats C, A necessarily loses against C.)

 Table of contents 1 Game play 2 Strategies 3 Cheating 4 Variations 5 Odd or Even 6 Tournaments 7 Other games reduce to Rock, Paper, Scissors 8 History 9 External links

## Game play

{| border="0" cellpadding="2" cellspacing="1" bgcolor="#dcdcdc" rules="cols" align="right" style="margin-left:0.5em;"

||||||| |- ||||||| |- ||||||| |- ||||||| |- | colspan=8| "Hand-signs" in Rock, Paper, Scissors. The
gray hands point to the winning sign. A fist
denotes a tie. |- |}

Two players each make a fist. They count together "1...2...3...Go!" or "Rocks...Paper...Scissors... Shoot!" while simultaneously bouncing their fists. On "Shoot," or "Go," each player simultaneously changes their fist into one of three "weapons":

The objective is to defeat the opponent by selecting a weapon which defeats their choice under the following rules:

1. Rock blunts Scissors (rock wins)
2. Paper covers Rock (paper wins)
3. Scissors cuts Paper (scissors win)

If players choose the same weapon, the game is a tie and is played over.

Often times, the short game is repeated many times so that the person who wins two out of three or three out of five times wins the entire game.

## Strategies

Strategy between human players obviously involves using psychology to attempt to predict or influence opponent behavior. It is considered acceptable to use deceptive speech ("I'm going to play a rock") to influence your opponent.

Mathematically optimal play (according to game theory) is a simple matter of selecting randomly, and so the game may be considered trivial in that sense when played in a way that eliminates psychology, as with a computer. But "optimal" in this sense means only "incapable of being defeated more than expected by chance", while it does not imply that the random strategy is best at taking advantage of a suboptimal opponent. In fact, if the opponent is human or a non-random program, it is almost certain that he plays suboptimally and that a modified strategy can exploit that weakness. This is easily demonstrated by Roshambot, a computer program that easily defeats some human players (as does its author Perry Friedman, who won an \$800 competition against seven opponents including former world poker champion Phil Hellmuth in August 2001). University of Alberta Ph.D. student and poker player Darse Billings organizes a computer Roshambo competition to explore these possibilities, and their application to computer game play in other fields (notably poker, in which exploiting an opponent's non-random behavior is an important part of strategy).

## Cheating

One of the first tricks learned by a Roshambo novice is to hold back a throw of paper until the last possible moment to dupe an opponent into believing that you may actually be throwing a rock. This allows you the extra few milliseconds for fine-tuning your approach and delivery. Both paper and scissors have this ability, however unless you are employing a "double-back" strategy, cloaking a paper throw is likely to draw an instinctive paper from your opponent.

The opening ritual before the actual throws are made ("1..2..3..Go!"), called "priming", is intended to get both players in sync so as to ensure simultaneous delivery of throws. This can be used to an advantage when two players are meeting for the first time, since it is often unclear as to what the priming speed will be. The tendency is to default to the priming speed of the faster player. This allows the faster priming player the luxury of dictating the flow of play and causes their opponent to dedicate more energy to "catching the prime" rather than concentrating on delivering an effective throw.

## Variations

One of the most simple variations is called Cat Microwave Tinfoil. In Cat Microwave Tinfoil, Cat beats tinfoil by ripping it up, tinfoil beats microwave by starting a fire, and microwave beats cat by cooking it. This version was created because, to the creators of Cat Microwave Tinfoil, it doesn't make sense that paper beats rock by covering it (as it doesn't damage the rock, while on the other hand it can destroy the paper by tearing it).

Players often add other "weapons" to the game on a ad-hoc basis, but it is very likely that this will result in an unbalanced game. In particular, four (or any even number) of weapons cannot be made balanced, unless some pairs of weapons result in a draw; there will always be some weapons that will be superior to others. It also loses some of the aesthetic simplicity of the game, which is otherwise one of the simplest possible games of skill. For example, "dynamite", expressed as the extended index finger, defeats only rock, but is defeated by either scissors or paper. Therefore, anything dynamite will beat, paper will beat; and anything dynamite will tie, paper will tie or beat. Given that paper performs better by tying against another paper, it is always better to use paper than to use dynamite, and dynamite is useless. In game theory, it is said that paper has weak dominance over dynamite.

There exists a five-weapon variation called Rock Paper Scissors Spock Lizard, which is carefully crafted so that each weapon defeats exactly two other weapons, and is defeated by exactly two other weapons. Specifically, rock defeats scissors and lizard, paper defeats rock and Spock, scissors defeat paper and lizard, Spock defeats scissors and rock, and lizard defeats Spock and paper. This also works for 7, 9, 11, etc.. As long as there are an odd number of weapons, a balanced game can be created, with each weapon beating half the weapons and losing to half the weapons. The advantage of playing with more weapons is that ties become increasingly unlikely.

It is also possible to play the game with more than just 2 people. This variant works remarkably well, even for large groups of players. The rules are the same, with the following exceptions:

## Odd or Even

A similar game, for which much of the same thoughts apply is Odd or Even: Player A gets to select odd or even. Then both players act as above, only this time the "weapons" are just "one" (a fist with outstretched thumb) or "two" (a fist with outstretched thumb and forefinger). The values signified by the players are added, player A winning with a correct prediction about the result.

With a choice between two values (it does not matter that they are 1 and 2, only that they are not both odd or even) the game is balanced, and A has no benefit from making the call. But would you allow three (or any odd number) values to choose from, either odd or even would be a more probable outcome with both players acting randomly. (That is because n choices make n2 possible outcomes. Squares of even numbers are even, squares of odd numbers odd.)

## Tournaments

There are Roshambo tournaments held occasionally. The websites announcing the tournaments, and the tournaments themselves (if they exist), are not completely serious. Some of the Roshambo websites spoof comparable sites for other games. A real Roshambo tournament would be an interesting psychological exercise. Obviously, the strategy dictated by game theory is to pick each choice 1/3 of the time randomly. However, a human cannot be truly random, and the skill in the tournament would involve exploiting your opponent's nonrandom throws.

In Japan, Janken tournaments are often held on television variety programs, especially between popular actors, and the game is also often used by advertising kiosks as tool for audience participation.

## History

It originated in Egypt at around 2000 BC and was then passed to Greece and then on to the Romans. In ancient Rome it was named Micatio and playing it was called micare digitis, literally to "flash the fingers". As time passed the name became Mora which is a corruption of the verb micare. It was so common in ancient Rome that there was a proverb to denote a honest person: Dignus est quicum in tenebris mices, which meant: So trustworthy, that one might play Mora with him in the dark. It was so common that micatio was used to settle disputes over merchandise sales in Roman forums. This practice was later banned by Apronius, prefect of the city.