Rock-paper-scissors
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225698882
2008-07-14T23:34:12Z
Cretog8
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[[WP:UNDO|Undid]] revision 225695311 by [[Special:Contributions/66.97.227.157|66.97.227.157]] ([[User talk:66.97.227.157|talk]])
{{Mergefrom|Janken|date=January 2008}}
{{Refimprove|date=June 2008}}
{{for|the Catatonia album|Paper Scissors Stone (album)}}
[[Image:Rock paper scissors.jpg|thumb|250px|Rock-paper-scissors chart]]
{{Spoken Wikipedia|Rock,_Paper,_Scissors.ogg|2006-07-13}}
'''Rock-paper-scissors''' (also known as '''''[[jan-ken-pon]]''''', '''rochambeau''' (sometimes spelled '''roshambo'''), '''ching-chang-wulla''', and many derived terms<ref>{{cite web |url=http://www.sfgate.com/cgi-bin/article.cgi?f=/c/a/2003/03/16/BA251812.DTL |title=Ready, set ... Roshambo! Contestants vie for $1,000 purse in Rock, Scissors, Paper contest|accessdate=2007-11-20 |format= |work=[[San Francisco Chronicle]] }}</ref>), is a popular two-person [[hand game]].
The game is often used as a [[selection method]] in a similar way to [[coin flipping]] or [[drawing straws]] 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.{{Fact|date=February 2008}} It is also often used as a method for creating appropriately non-biased random results in [[live action role-playing game]]s, as it requires no equipment. It is also used in some [[online gambling]] sites as a form of novelty betting.
== Game play ==
{| border="0" cellpadding="2" cellspacing="1" rules="cols" align="right" style="margin-left: 1em; margin-bottom: 0.5em; width: 210px; background: #dcdcdc;"
| [[Image:SssStein.jpg]] || [[Image:SssPapier.jpg]] || [[Image:SssSchere.jpg]]
|-
|colspan=3| <small>Each of the three basic hand-signs ( from left to right: rock, paper and scissors ) beats one of the other two.</small>
|}
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 (often played in the Northeastern United States involves a fourth count—"SHOOT"—before players throw their gesture.
* '''Rock''', represented by a closed fist.
* '''Paper''', represented by an open hand.
* '''Scissors''', represented by the index and middle fingers extended.
The objective is to select a gesture which defeats that of the opponent. Gestures are resolved as follows:
* Rock breaks or blunts scissors; rock wins.
* Paper covers rock; paper wins.
* Scissors cut paper; scissors wins.
If both players choose the same gesture, the game is tied and played again. The average number of plays required to decide a winner is 1.5 (see [[#Mathematics]] below).
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.
RPS is frequently played in a "best two out of three" match, and tournament players often prepare sequences of three gestures ahead of time.<ref name="Lawrence Journal-World">Steve Vockrodt, [http://www2.ljworld.com/news/2007/apr/08/student_rivals_throw_down_rock_paper_scissors_tour/ "Student rivals throw down at rock, paper, scissors tournament"], ''[[Lawrence Journal-World]]'', [[April 8]], [[2007]], retrieved [[April 13]], [[2007]].</ref><ref name="Fox News">Michael Y. Park, [http://www.foxnews.com/story/0,2933,188380,00.html "Rock, Paper, Scissors, the Sport"], ''[[Fox News]]'', [[March 20]], [[2006]], retrieved [[April 13]], [[2007]].</ref>
Jason Simmons, a competitive RPS champion, claims that women tend to start with scissors,<ref name="Morning E-dition">[[Steve Inskeep]], [http://www.npr.org/templates/story/story.php?storyId=6466715 "In the News and On the Air: Iraq, Paper, Scissors"], ''[[Morning E-dition]]'', [[NPR.org]], [[November 10]], [[2006]]. Retrieved [[April 13]], [[2007]]</ref> 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.<ref name="How to beat anyone">Graham Walker, [http://www.worldrps.com/index.php?option=com_content&task=view&id=256&Itemid=37 "How to beat anyone at Rock Paper Scissors"], World RPS Society, 2006, Retrieved [[April 13]], [[2007]].</ref>
During the 17th century, Japanese children played a street game where 2 teams would meet on opposite ends of a field and then send individual runners off towards each others "Camp". These runners would follow a prescribed course passing several landmarks such as a tree, a rock, a wagon rut or whatever was around; whenever/wherever the two runners would meet up, they would stop and "Challenge" each other to "Rock-Paper-Scissors" or as the Japanese say, "Jan Ken Pon" until one runner won. The two runners would quickly continue running, but with the losing runner racing back to his own "Camp" in disgrace. His only hope for redemption was to get back to his own Camp faster than the runner who beat him at RPS/JKP. If he could pass or "tag" his first landmark before the other team's runner does, then his team was allowed to send a fresh runner out towards their first landmark and intercept the other team's runner and "Challenge" them to RPS/JKP and possibly send that runner back along the route to his own camp. The first team to get all of their runners into the other's camp was declared the winner. This idea has recently been adapted into a board game called "Hand2Hand".
==Terminology==
The exact name of the game can vary, with the three components appearing in a different order, or with "stone" in place of "rock". Non-English-speakers often refer to the game by their words for "rock-paper-scissors" (though not necessarily in that order).
== Mathematics ==
===Expected number of rounds to determine a winner===
The [[expected value]] for the number of rounds required to decide a winner, given that <math>p_x</math> is the probability of reaching round x, is
:<math>\sum_{n=1}^\infty n(p_n -p_{n+1})</math>. In each round of RPS there is a 1/3 probability of a tie, so this equals
:<math>\sum_{n=1}^\infty n((\tfrac{1}{3})^{n-1} - (\tfrac{1}{3})^n)</math>. Regrouping (which is permitted since terms converge to zero) then leads to the [[geometric series]]
:<math> \sum_{n=0}^\infty (\tfrac{1}{3})^n</math>, which converges to 1.5.
=== Non-transitivity ===
RPS is also often used as an example of the mathematical concept of [[intransitivity|non-transitivity]]. A [[transitive relation]] ''R'' is one for which ''a R b'' and ''b R c'' implies ''a R c''. A [[reflexive relation|reflexive]], [[antisymmetric relation|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.
==Variations==
Players have developed numerous cultural and personal variations on the game, from simply playing the same game with different objects, to expanding into more 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.<ref>{{cite web
| title = The Myth of Dynamite Exposed
| url = http://www.worldrps.com/article4.html
| author = [[The World RPS Society|World RPS Society]]
| accessdate = 2007-11-09
| date = [[2002]] }})</ref>
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.<ref>{{cite web
| title = Children's Games in Street and Playground
| url = http://www.creekcats.com/pnprice/rochamtrue.html
| author = Iona and Peter Opie
| accessdate = 2008-03-10}}</ref>
== Analogies in nature and computing ==
=== 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), or simple elemental trinities such as fire, water and air. 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 Pokemon, in which attacks have varied effectiveness based on 17 elemental types.)
=== Mating strategies ===
[[Image:Uta3.jpg|thumb|300px|The Common Side-blotched Lizard (''Uta stansburiana'') exhibits a RPS pattern in its different mating strategies.]]
Biologist [[Barry Sinervo]] from the [[University of California, Santa Cruz]] has discovered an RPS [[Evolution|evolutionary strategy]] in the [[mating behaviour]] of the [[side-blotched lizard]] species ''[[Common side-blotched lizard|Uta stansburiana]]''. Males have either orange, blue or yellow throats and each type follows a fixed, heritable mating strategy:<ref>{{cite web | title = The rock-paper-scissors game and the evolution of alternative male strategies | url = http://bio.research.ucsc.edu/~barrylab/lizardland/male_lizards.overview.html | author = [[Barry Sinervo|Sinervo, Barry]] | accessdate = 2006-08-20 | date = [[2001-02-20]] }}</ref>
* 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 [[Mimicry|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]]{{Fact|date=September 2007}} (Sinervo & Lively, 1996; Sinervo, 2001; Alonzo & Sinervo, 2001; Sinervo & Clobert, 2003; Sinervo & Zamudio, 2001).
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]] (Nature. 2002 Jul 11;418(6894):171-4.). The antibiotics in question are the [[bacteriocins]] - more specifically, [[bacteriocins|colicins]] produced by ''[[Escherichia coli]]''. Biologist [[Benjamin C. Kirkup, Jr.]] further demonstrated that the [[bacteriocins|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 between [[antibiotic]] producing and antibiotic sensitive strains, because antibiotic resistant strains would out-compete the producing strains, providing an environment in which sensitive strains could successfully become established again (Nature. 2004 Mar 25;428(6981):412-4.).
== Cultural references ==
Because of its widespread use, the game has received substantial references in popular culture. Many television series poke fun at particular characters' incompetence at understanding the rules, or show how mischievous characters are often able to "win" the game by inventing new objects which beat all the others.
==== 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 (law)|deposition]] using the game of rock-paper-scissors.<ref>{{cite news | url = http://seattletimes.nwsource.com/html/nationworld/2003052251_game10.html | title = Exasperated judge resorts to child's game | publisher = [[Associated Press]] | date = [[2006-06-26]] | accessdate = 2006-08-20 }}</ref> The ruling in ''Avista Management v. Wausau Underwriters'' stated:
{{quotation|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.|<ref>{{cite web| url=http://money.cnn.com/2006/06/07/magazines/fortune/judgerps_fortune/index.htm| publisher=CNN.com| accessdate=2006-06-08| title=Order of the court: Avista Management vs. Wausau Underwriters Insurance Co.| year=June 7, 2006| first=Gregory| last=Presnell}}</ref>}}
The public release of this judicial order, requiring counsel to resort to a childish game to resolve a dispute, was widely circulated among area lawyers. It served the function of [[shaming]] the respective law firms regarding their litigation conduct.{{Fact|date=February 2008}}
==== Auction house RPS match ====
[[Image:Paul Cézanne 076.jpg|thumb|''Large Trees Under the Jas de Bouffan'' sold for $11,776,000 at Christie's<ref name="CityReview">[http://www.thecityreview.com/s05cimp1.html Art/Auctions logo, Impressionist & Modern Art, Christie's, 7PM, May 4, 2005, Sale 1514].</ref>.]]
When [[Takashi Hashiyama]], CEO of [[Maspro Denkoh|a Japanese television equipment manufacturer]], decided to auction off the collection of [[Impressionist]] paintings owned by his corporation, including works by [[Paul Cézanne|Cézanne]], [[Pablo Picasso|Picasso]] and [[Vincent Van Gogh|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.
The houses were unable to reach a decision. Hashiyama told the two firms to play RPS, to decide who would get the rights to the auction, explaining that "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 of move. Christie's went to the 11-year-old twin daughters of an employee, who suggested "scissors" because "Everybody expects you to choose 'rock'." Sotheby's said that they treated it as a [[game of chance]] and had no particular strategy for the game, but went with "paper".<ref>{{Citation
| last =Vogel
| first =Carol
| title =Rock, Paper, Payoff: Child's Play Wins Auction House an Art Sale
| newspaper = [[New York Times]]
| year =2005
|date=April 29
| url = http://www.nytimes.com/2005/04/29/arts/design/29scis.html}}
</ref>
Christie's won the match, with millions of dollars of commission for the auction house.
== Tournaments ==
== World Record ==
=== WRPS sanctioned tournaments ===
Starting in 2002, the [[World Rock Paper Scissors Society]] (WRPS) standardized a set of rules for international play<ref>{{cite web | title = Game Basics | work = [[World Rock Paper Scissors Society]] | url = http://www.worldrps.com/index.php?option=com_content&task=view&id=14&Itemid=31 | accessdate = 2006-08-20 }}</ref> 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.<ref>{{cite news
| date = [[2004-12-10]]
| url = http://www.washingtontimes.com/national/20041210-120729-4008r.htm
| title = Fists fly in game of strategy
| first = Patrick
| last = Hruby
| publisher = [[Washington Times]]
| accessdate = 2006-08-20
}}</ref><ref>{{cite news
| title = 2003 World Rock Paper Scissors Championship
| url = http://www.npr.org/templates/story/story.php?storyId=1477870
| date = [[2003-10-24]]
| work = All Things Considered
| publisher = [[National Public Radio]]
| accessdate = 2006-08-20
}}</ref><ref>{{cite news | url = http://www.cbsnews.com/stories/2003/10/29/earlyshow/contributors/melindamurphy/main580709.shtml
| title = Rock, Paper, Scissors A Sport?
| date = [[2003-10-23]]
| publisher = CBS News
| accessdate = 2006-08-20
}}</ref><ref>{{cite news
| url = http://www.usatoday.com/news/offbeat/2003-10-27-rock-paper_x.htm
| title = Rock Paper Scissors contest being held
| publisher = [[Associated Press]]
| date = [[2003-10-27]]
| accessdate = 2006-08-20
}}</ref><ref>{{cite news
| url = http://www.foxnews.com/story/0,2933,188380,00.html
| title = Rock, Paper, Scissors, the Sport
| first = Michael Y.
| last = Park
| publisher = [[Fox News]]
| date = [[2006-03-20]]
| accessdate = 2006-08-20
}}</ref> WRPS events are noted for their large cash prizes, elaborate staging, and colorful competitors.<ref>{{cite web | url = http://www.worldrps.com/index.php?option=com_gallery2&Itemid=30 | title = Gallery | work = World RPS society | date = [[2005-11-13]] | accessdate = 2006-08-20 }}</ref>
In 2004, the championships were broadcast on the U.S. television network [[Fox Sports Net]].
=== USARPS Tournaments ===
[[USA Rock Paper Scissors League]] (USARPS) is the principal rock-paper-scissors league of the United States. It is sponsored by [[Bud Light]]. Matti Leshem is the co-commissioner of the USARPS.
In April 2006, the inaugural USARPS 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]].
The $50,000 2007 USARPS Tournament took place at the Las Vegas Mandalay Bay in May 2007.
In 2008, Sean Sears beat out 300 other contestants and walked out of the Mandalay Bay Hotel & Casino with $50,000. He is currently scheduled to compete in the International Rock Paper Scissors Federation Championship in Beijing, China this August.
=== National XtremeRPS Competition 2007-2008 ===
The XtremeRPS National Competition<ref>{{cite web | title = XTreme RPS Competition by Showtime Entertainment | url = http://www.rpsrocks.com | accessdate = 2007-01-07 }}</ref> is a US nationwide RPS competition with Preliminary Qualifying contests starting in January 2007 and ending in May 2008, followed by regional finals in June and July 2008. The national finals will be held in [[Des Moines]] in August 2008, with a chance to win up to $5,000.
=== 2008 World Record Attempt ===
East Coast restaurant chain [[California Tortilla]] are planning to host a World Record RPS Tournament on Thursday, July 17 at the [[Merriweather Post Pavilion]], attempting to break the record for the highest number of participants in such a tournament. The champion will win free burritos for a year, and the tournament will be followed by a [[Steve Miller Band]] concert.<ref>http://californiatortilla.com/RPSContest.html</ref>
== Notes ==
{{reflist|2}}
== References ==<!-- Genetica 112–113: 417–434 -->
* '''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)
* [[Alice Gomme|'''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)
* [[Peter and Iona Opie|'''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 (journal)|Science]]'' '''300'''(5627): 1949-1951. {{DOI|10.1126/science.1083109}} (HTML abstract) [http://www.sciencemag.org/cgi/content/full/sci;300/5627/1949/DC1 Supporting Online Material]
* '''Sinervo''', Barry & '''Lively''', C. M. (1996): The Rock-Paper-Scissors Game and the evolution of alternative male strategies. ''[[Nature (journal)|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. [http://jhered.oxfordjournals.org/cgi/reprint/92/2/198.pdf 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).
== External links ==
*[http://www.usarps.com USA Rock Paper Scissors League]
*[http://www.rpsrocks.com XtremeRPS National Competition 2007-2008]
*[http://www.roshambowinery.com Roshambo Winery's Annual Championships]
*[http://www.chessandpoker.com/rps_rock_paper_scissors_strategy.html PRPS Format, Rules and Strategy]
*[http://www.worldrps.com/ World Rock Paper Scissors Society]
*[http://chappie.stanford.edu/cgi-bin/roshambot Stanford University's RoshamBot], an [[artificial intelligence]] RPS player
*[http://www.trajanmagazine.com/content/2008/rockpaperscissors.php Trajan Magazine article on 2008 USARPS results]
*{{cite web
| url = http://www.forbes.com/execpicks/fyi/2005/0407/061.html
| title = Throwing for The Gold
| accessdate = 2007-04-09
| last = Abrams
| first = Michael
| date = [[2004-07-05]]
| work = Pursuits
| publisher = ''[[Forbes]] FYI''
}}
{{Game theory}}
{{Gestures}}
[[Category:Rock-paper-scissors|*]]
[[Category:Hand games]]
[[Category:Game theory]]
[[Category:Children's games]]
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