Rock, Paper, Scissors

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For the Catatonia album, see Paper Scissors Stone (album).

Rock, Paper, Scissors is a hand game most often played by children. It is often used as a selection method in a similar way to coin flipping, Odd or Even, 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.

It is also known by many other names such as: Rochambeau, Paper Scissors Stone/Rock (UK),Scissors, Paper, Rock (Australia), Paper Scissors Rock (NZ), Ching Chong Cha (South Africa), Jiandao Shítou Bu (China), Janken (Japan), Schnick, Schnack, Schnuck (Germany), Morra Cinese (Italy), Piedra, Papel o Tijera (Spain), Pedra, Papel, Tesoura (Portugal), Chin chan pu (Mexico), and Gawibawibo (Korea).

Various sports may use Rock, Paper, Scissors to determine which team gets the opening play (rather than a coin toss). Similarly, uncertain calls, or even the whole game in case of rain, may be decided by the game. 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 gambling sites as a novelty betting.

Contents 1 Game play 2 Cheating 3 Variations 4 Mathematics 4.1 Non-transitivity 4.2 Commutativity and non-associativity 5 Pop culture trivia 5.1 Federal case 5.2 Auction house RPS match 6 Evolutionary strategy 7 Tournaments 7.1 WRPS sanctioned tournaments 7.1.1 World Championship results since 2002 7.1.2 Tour events 7.2 USARPS Tournaments 8 Notes 9 References 10 External links

[edit] Game play

Each of the three basic hand-signs ( from left to right: rock, paper and scissors ) beats one of the other two.

The players count together to 3 counts, most commonly either using the name of the game (e.g. Rock! Paper! Scissors! or Ro! Sham! Bo!) or simply numbers. At the end of the third count, the players simultaneously change their fists into any of three "objects", which they then "throw" by extending it towards their opponent. An alternate introduction frequently used is "Rock, paper, scissor SHOOT" (or "one, two, three, shoot, etc.), throwing on "shoot".

• Rock: represented by a closed fist.
• Scissors : represented by the index and middle fingers extended toward the opposing player, mimicking a pair of scissors.
• Paper: represented by an open hand with the palm facing downwards and the fingers facing towards the opponent, resembling a flat piece of paper.

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

1. Rock smashes (or breaks or blunts) Scissors (rock wins)
2. Scissors cut Paper (scissors win)
3. Paper covers Rock (paper wins)

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

In some styles of play, the winner of each round has the opportunity to "use" the weapon on the opponent's weapon; excessive force is acceptable only if prior consent has been given. For example, a winner who has thrown rock may punch at the opponent's scissors, paper may slap at the rock, and scissors may "cut" the paper (though the latter has very little effect, especially in the forceful variation).

Frequently, the game is played in a "best 2 out of 3" match.

[edit] Cheating

One of the first tricks learned by a Rock-Paper-Scissors novice is to hold back a throw of paper until the last possible moment to dupe an opponent into believing that one may actually be throwing a rock. Both paper and scissors have this ability; however, unless one is employing a "double-back" strategy, cloaking a paper throw is likely to draw an instinctive paper from one's opponent. If the throw is accidentally revealed too late, that is, not revealed until the thrower's arm breaks the plane where the thrower's arm is perpendicular to the thrower's torso (at a 90 degree angle), this is considered a foul. In such a case the referee will assign a throw of rock, even if this is not what the thrower intended. This is known as a "forced rock."

A common variation on the opening ritual is to have both players hold their hands behind their backs and reveal their already formed throw after the count of three. The intention is to prevent any sort of timing based cheating.

Another way to cheat is to prime three times instead, if the opponent primed twice only, the other could see his opponent's throw without revealing his own, claiming that he thought "I thought we are doing three primes". Note: 'priming' is the number of bounces one does before revealing the throw.

Yet another method of cheating is to play scissors but put it right up to the other player's eyes. The other player might then without realizing it put his/her hand up to block it. The cheater would then claim, "Scissors beats paper."

[edit] Variations

Main article: Rock, Paper, Scissors variations

There are many different variations of Rock, Paper, Scissors which range from simple changes in the names of the objects to increasing the number of players or objects. While interesting, most rule variations suffer from one problem or another, making them less interesting games.

A simple American variation is Pirate, Cowboy, Ninja (Cowboy beating Ninja, Pirate beating Cowboy, Ninja beating Pirate). This version is performed with the players starting standing back to back, taking three paces in opposite directions and then turning and revealing their choice.

Versions of Rock, Paper, Scissors are also observed in many different cultures. It is usually known by direct translations of "Rock, Paper, Scissors" although some cultures have slightly different names or even entirely different elements representing the different objects. For example in Japan there is a variation which uses a tiger, a chief and the chief's mother as the three elements (the tiger beating the chief's mother, the chief beating the tiger and the chief's mother beating the chief). In Indonesia another version is played with the elements as an elephant, a man and an ant (the elephant crushing the man, the man crushing the ant and ant humorously defeating the elephant by crawling into the animal's ear and making it go insane).^[1]

Malaysians use water instead of paper, and in place of scissors is a bird, made by holding the fingertips together, forming the shape of a beak. The bird drinks up the water, the water sinks the rock, and the rock kills the bird.

The Chinese and Koreans use Cloth along with Rock and Scissors, while the Japanese have adopted Paper. Minor variation is also observed in the standard game play.^{[citation needed]}

The Indians play a variant called Chi-Ku-Ba with slightly different hand formations. Ku is rock formation, held the same; Chi is a scissors with the two fingers closed instead of open; Ba is paper but held vertically with all fingers open like a full hand, with the fingers separated from each other. Chi-Ku-Ba is played with two hands instead of one; after you lose one hand, only the other hand remains in the game. Unlike the rock-scissors-paper rule, there is no asymmetric cycle. One has to play exactly what the other player plays to stay in the game. It is very tough to maintain a draw with two hands, as you get combinations like this, Chi-Chi, Chi-Ku or Ku-Chi, Chi-Ba or Ba-Chi, Ku-Ku, Ku-Ba or Ba-Ku, & Ba-Ba. ^{[citation needed]}

[edit] Mathematics

[edit] Non-transitivity

Rock, Paper, Scissors 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 Rock, Paper, Scissors: 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, Rock-Paper- Scissors could be called "antitransitive" because if A strictly defeats B, and B strictly defeats C, A necessarily loses against C.

[edit] Commutativity and non-associativity

Rock, Paper, Scissors also provides an example of a magma that is commutative but not associative, by defining a binary operation on the set {rock, paper, scissors} in which the product of a pair is defined to be the "winner".

[edit] Pop culture trivia

Main article: List of pop culture references to Rock, Paper, Scissors

Because of its widespread use by children and adults, Rock Paper Scissors has received substantial references in popular culture. Seinfeld, The Simpsons, and That 70s Show all poke fun at particular characters' incompetence at understanding the game rules. In other shows, mischievous characters are often able to "win" the game by deploying new objects which beat all the others and are subsequently able to convince their slow-witted competitor that deploying the new object is a legitimate move. In video games, intransitive relationships (like Rock, Paper, Scissors) often appear either in strategy choices or in weapons' abilities.

"Rock is Dead. Long live Paper and Scissors." is a popular t-shirt among young people wishing to express disdain for the lack of quality rock music available.

[edit] Federal case

In 2006, Federal Judge Gregory Presnell from the Middle District of Florida ordered opposing sides in a lengthy court case to settle a trivial (but lengthily debated) point over the appropriate place for a deposition using the game of rock-paper-scissors.^[2] The ruling in Avista Management v. Wausau Underwriters stated:

Upon consideration of the Motion – the latest in a series of Gordian knots that the parties have been unable to untangle without enlisting the assistance of the federal courts – it is ORDERED that said Motion is DENIED. Instead, the Court will fashion a new form of alternative dispute resolution, to wit: at 4:00 P.M. on Friday, June 30, 2006, counsel shall convene at a neutral site agreeable to both parties. If counsel cannot agree on a neutral site, they shall meet on the front steps of the Sam M. Gibbons U.S. Courthouse, 801 North Florida Ave., Tampa, Florida 33602. Each lawyer shall be entitled to be accompanied by one paralegal who shall act as an attendant and witness. At that time and location, counsel shall engage in one (1) game of "rock, paper, scissors." The winner of this engagement shall be entitled to select the location for the 30(b)(6) deposition to be held somewhere in Hillsborough County during the period July 11-12, 2006.[3]

[edit] Auction house RPS match

When Takashi Hashiyama, CEO of a Japanese television equipment manufacturer, decided to auction off the collection of Impressionist paintings owned by his corporation, including works by Cézanne, Picasso and van Gogh, he contacted two leading U.S. auction houses, Christie's International and Sotheby's Holdings, seeking their proposals on how they would bring the collection to the market as well as how they would maximize the profits from the sale. Both firms made elaborate proposals, but neither was persuasive enough to get Hashiyama’s business. Willing to split up the collection into separate auctions, Hashiyama asked the firms to decide between themselves who would get the Cézanne's "Large Trees Under the Jas de Bouffan", worth $12-16 million. They could not decide—enter Rock, Paper, Scissors.

Hashiyama told the two firms to play RPS to decide who would get the rights to the auction, explaining, "It probably looks strange to others, but I believe this is the best way to decide between two things which are equally good."

The auction houses had a weekend to come up with a choice. Christie's went to experts: 11-year-old twin daughters of an employee, who suggested "scissors" because "Everybody expects you to choose 'rock'." Sotheby's admitted that they treated it as a game of chance and had no particular strategy for the game, but went with "paper".

Christie's won the match, with millions of commission that went to the auction house.

[edit] Evolutionary strategy

Biologist Barry Sinervo from the University of California, Santa Cruz has discovered a Rock-Paper-Scissors evolutionary strategy in the mating behaviour of the side-blotched lizard species Uta stansburiana. Males have either orange, blue or yellow throats and each type follows a fixed, heritable mating strategy:^[4]

• Orange-throated males are strongest and do not form strong pair bonds; instead, they fight blue-throated males for their females. Yellow-throated males, however, manage to snatch females away from them for mating.
• Blue-throated males are middle-sized and form strong pair bonds. While they are outcompeted by orange-throated males, they can defend against yellow-throated ones.
• Yellow-throated males are smallest, and their coloration mimics females. Under this disguise, they can approach orange-throated males but not the stronger-bonding blue-throated specimens and mate while the orange-throats are engaged in fights.

This can be summarized as "orange beats blue, blue beats yellow, and yellow beats orange", which is similar to the rules of rock, paper, scissors. The proportion of each male type in a population is similar in the long run, but fluctuates widely in the short term. For periods of 4-5 years, one strategy predominates, after which it declines in frequency as the strategy that manages to exploit its weakness increases. This corresponds to the stable pattern of the game in the replicator dynamics where the dynamical system follows closed orbits around the mixed strategy Nash equilibrium (Sinervo & Lively, 1996; Sinervo, 2001; Alonzo & Sinervo, 2001; Sinervo & Clobert, 2001; Sinervo & Zamudio, 2001).

[edit] Tournaments

The World RPS Society [1] has been holding the world championships in Canada for the past 5 years. Hundreds of competitors from all over the world come to compete in these championships and during the first 4 years, home grown Canadian talent won the coveted trophy.

The latest winner is Bob 'The Rock' Cooper, from London, UK. He defeated 496 competitors to take the title, winning with a pair of scissors.

Bob is quickly gaining cult status now in the UK, and has his own fansite: [2]

Bob's great popularity has insprired his fans to be petitioning the BBC to re-open the nominations for the Sports Personality of the Year Awards 2006.

[edit] WRPS sanctioned tournaments

Starting in 2002, the World Rock Paper Scissors Society (WRPS) standardized a set of rules for international play^[5] and has overseen annual International World Championships. These open, competitive championships have been widely attended by players from around the world and have attracted widespread international media attention.^{[6][7][8][9][10]} WRPS events are noted for their large cash prizes, elaborate staging, and colourful competitors.^[11] In 2004, the championships were broadcast on the U.S. television network Fox Sports Net.

Professional poker player Phil Gordon conducted what he called "The World Series of Rock-Paper-Scissors" during the 2005 World Series of Poker in which 64 contestants of the WSOP competed in a tournament similar to the NCAA tournament.

[edit] World Championship results since 2002

Year	Host City	Medal	Champion	Gender	Nationality
2002[12]	Toronto		Peter Lovering	Male	Canadian
			Moe Asem	Male	Canadian
			Dave Ferris	Male	Canadian
2003[13]			Rob Krueger	Male	Canadian
			Marc Rigaux	Male	Canadian
			Patrick Merry	Male	Canadian
2004[14]			Lee Rammage	Male	Canadian
			Heather Birrell	Female	Canadian
			Chris Berggeren	Male	American
2005[15]			Andrew Bergel	Male	Canadian
			Stan Long	Male	American
			Stewart Waldman	Male	American
2006[16]			Bob Cooper	Male	Scottish
			Bryan Bennett	Male	American
			Tom Smith	Male	American

[edit] Tour events

In addition to the International World Championships the WRPS also endorses or sanctions a year-round series of tournaments world wide. "Endorsed" tournaments agree to abide by the WRPS standardized international rules of play and code of conduct, while "Sanctioned" tournaments will net the winner a trip to compete at the International World Championships. Some of the major events of this tour include:

• Roshambo Winery RPS Championships, Healdsburg, California
• RPS Keystone Classic, Philadelphia, Pennsylvania
• RPS Philadelphia City League Championship Series, Philadelphia, Pennsylvania
• Rocksdam RPS Charity Tournament, Potsdam, New York
• Atlantic Yards Smackdown, Brooklyn, New York
• RPS Australian Championships
• RPS New Zealand Championships
• Norwegian RPS Championships

[edit] USARPS Tournaments

USARPS League is an organization sponsored by Bud Light. USARPS has been often criticised by the World RPS Society for poor officiating. Matti Leshem is the co-commissioner of the USA Rock Paper Scissors League

In April 2006, the inaugural USA Rock Paper Scissors League Championship was held in Las Vegas, Nevada. Following months of regional qualifying tournaments held across the US, 257 players were flown to Las Vegas for a single-elimination tournament at the House of Blues where the winner received $50,000. The tournament was shown on the A&E Network on June 12, 2006.

At the first USA Rock Paper Scissors League Championship, "Drill" McGill defeated "Fast Twitch" Twitchel to win the tournament.

[edit] Notes

1. ^ What's the origin of "Rock, Paper, Scissors"?. Straight Dope (2001-07-10). Retrieved on 2006-08-20.
2. ^ "Exasperated judge resorts to child's game", Associated Press, 2006-06-26. Retrieved on 2006-08-20.
3. ^ Presnell, Gregory (June 7, 2006). Order of the court: Avista Management vs. Wausau Underwriters Insurance Co.. CNN.com. Retrieved on 2006-06-08.
4. ^ Sinervo, Barry (2001-02-20). The rock-paper-scissors game and the evolution of alternative male strategies. Retrieved on 2006-08-20.
5. ^ Game Basics. World Rock Paper Scissors Society. Retrieved on 2006-08-20.
6. ^ Hruby, Patrick. "Fists fly in game of strategy", Washington Times, 2004-12-10. Retrieved on 2006-08-20.
7. ^ "2003 World Rock Paper Scissors Championship", All Things Considered, National Public Radio, 2003-10-24. Retrieved on 2006-08-20.
8. ^ "Rock, Paper, Scissors A Sport?", CBS News, 2003-10-23. Retrieved on 2006-08-20.
9. ^ "Rock Paper Scissors contest being held", Associated Press, 2003-10-27. Retrieved on 2006-08-20.
10. ^ Park, Michael Y.. "Rock, Paper, Scissors, the Sport", Fox News, 2006-03-20. Retrieved on 2006-08-20.
11. ^ Gallery. World RPS society (2005-11-13). Retrieved on 2006-08-20.
12. ^ 2002 International Rock Paper Scissors Championships Official Results. World RPS society. Retrieved on 2006-08-20.
13. ^ 2003 Championships Official Results. World RPS society. Retrieved on 2006-08-20.
14. ^ 2004 Championships Official Results. World RPS society. Retrieved on 2006-08-20.
15. ^ 2005 Championships Official Results. World RPS society. Retrieved on 2006-08-20.
16. ^ 2006 Championships Official Results. World RPS society. Retrieved on 2006-11-16.

[edit] References

• Alonzo, Suzanne H. & Sinervo, Barry (2001): Mate choice games, context-dependent good genes, and genetic cycles in the side-blotched lizard, Uta stansburiana. Behavioral Ecology Sociobiology 49(2-3): 176–186. DOI:10.1007/s002650000265 (HTML abstract)
• Culin, Stewart (1895): Korean Games, With Notes on the Corresponding Games at China and Japan. (evidence of nonexistence of Rock, Paper, Scissors in the West)
• Gomme, Alice Bertha (1894, 1898): The traditional games of England, Scotland, and Ireland, 2 vols. (more evidence of nonexistence of Rock, Paper, Scissors in the West)
• Opie, Iona & Opie, Peter (1969): Children's Games in Street and Playground Oxford University Press, London. (Details some variants on Rock, Paper, Scissors such as 'Man, Earwig, Elephant' in Indonesia, and presents evidence for the existence of 'finger throwing games' in Egypt as early as 2000 B.C.)
• Sinervo, Barry (2001): Runaway social games, genetic cycles driven by alternative male and female strategies, and the origin of morphs. Genetica 112-113(1): 417-434. DOI:10.1023/A:1013360426789 (HTML abstract)
• Sinervo, Barry & Clobert, Jean (2003): Morphs, Dispersal Behavior, Genetic Similarity, and the Evolution of Cooperation. Science 300(5627): 1949-1951. DOI:10.1126/science.1083109 (HTML abstract) Supporting Online Material
• Sinervo, Barry & Lively, C. M. (1996): The Rock-Paper-Scissors Game and the evolution of alternative male strategies. Nature 380: 240-243. DOI:10.1038/380240a0 (HTML abstract)
• Sinervo, Barry & Zamudio, K. R. (2001): The Evolution of Alternative Reproductive Strategies: Fitness Differential, Heritability, and Genetic Correlation Between the Sexes. Journal of Heredity 92(2): 198-205. PDF fulltext
• Sogawa, Tsuneo (2000): Janken. Monthly Sinica 11(5). [Article in Japanese]
• Walker, Douglas & Walker, Graham (2004): The Official Rock Paper Scissors Strategy Guide. Fireside. (RPS strategy, tips and culture from the World Rock Paper Scissors Society).

[edit] External links

• Switzerland Interplanetary Rock Paper Scissors Championship
• USA Rock Paper Scissors League
• Roshambo Winery's Annual Championships
• PRPS Format, Rules and Strategy
• World Rock Paper Scissors Society
• Rock, Paper, Scissors in Flash
• Stanford University's RoshamBot, an artificial intelligence RPS player
• Article from Forbes FYI

view	Topics in game theory
Definitions	Normal form game · Extensive form game · Cooperative game · Information set · Preference
Equilibrium concepts	Nash equilibrium · Subgame perfection · Bayes-Nash · Trembling hand · Correlated equilibrium · Sequential equilibrium · Quasi-perfect equilibrium · Evolutionarily stable strategy
Strategies	Dominant strategies · Mixed strategy · Grim trigger · Tit for Tat
Classes of games	Symmetric game · Perfect information · Dynamic game · Repeated game · Signaling game · Cheap talk · Zero-sum game · Mechanism design
Games	Prisoner's dilemma · Coordination game · Chicken · Battle of the sexes · Stag hunt · Matching pennies · Ultimatum game · Minority game · Rock, Paper, Scissors · Pirate game · Dictator game
Theorems	Minimax theorem · Purification theorems · Folk theorem · Revelation principle · Arrow's Theorem
Related topics	Mathematics · Economics · Behavioral economics · Evolutionary game theory · Population genetics · Behavioral ecology · Adaptive dynamics · List of game theorists