Rock paper scissors

Rock paper scissors (also known by other permutations such as scissors paper rock, scissors paper stone or ro-sham-bo) is a hand game usually played between two people, in which each player simultaneously forms one of three shapes with an outstretched hand. These shapes are "rock" (a closed fist), "paper" (a flat hand), and "scissors" (a fist with the index finger and middle finger extended, forming a V). "Scissors" is identical to the two-fingered V sign (also indicating "victory" or "peace") except that it is pointed horizontally instead of being held upright in the air. A simultaneous, zero-sum game, it has only two possible outcomes: a draw, or a win for one player and a loss for the other.

For other uses, see Rock paper scissors (disambiguation).
Rock paper scissors
A chart showing how the three game elements interact
Genre(s)Hand game
Players2
Setup timeNone
Playing timeInstant
Random chanceNone to some, depending on the skill level of those playing
Skill(s) requiredPsychology

A player who decides to play rock will beat another player who has chosen scissors ("rock crushes scissors" or sometimes "blunts scissors"[1]), but will lose to one who has played paper ("paper covers rock"); a play of paper will lose to a play of scissors ("scissors cuts paper"). If both players choose the same shape, the game is tied and is usually immediately replayed to break the tie. The type of game originated in China and spread with increased contact with East Asia, while developing different variants in signs over time. Other names for the game in the English-speaking world include roshambo and other orderings of the three items, with "rock" sometimes being called "stone".[2][3][4]

Rock paper scissors is often used as a fair choosing method between two people, similar to coin flipping, drawing straws, or throwing dice in order to settle a dispute or make an unbiased group decision. Unlike truly random selection methods, however, rock paper scissors can be played with a degree of skill by recognizing and exploiting non-random behavior in opponents.[5][6]

Gameplay
Each of the three basic handsigns (from left to right: rock, paper, and scissors) beats one of the other two, and loses to the other.

The players may count aloud to three, or speak the name of the game (e.g. "Rock! Paper! Scissors!"), either raising one hand in a fist and swinging it down with each syllable or holding it behind their back. They then "throw" by extending it towards their opponent. Variations include a version where players throw immediately on the third count (thus throwing on the count of "Scissors!"), or a version where they shake their hands three times before "throwing".

History

Origins

The first known mention of the game was in the book Wuzazu by the Chinese Ming-dynasty writer Xie Zhaozhi (fl. c. 1600), who wrote that the game dated back to the time of the Chinese Han dynasty (206 BCE – 220 CE).[7] In the book, the game was called shoushiling. Li Rihua's book Note of Liuyanzhai also mentions this game, calling it shoushiling (t. 手勢令; s. 手势令), huozhitou (t. 豁指頭; s. 豁指头), or huaquan (划拳).

Mushi-ken, the earliest Japanese sansukumi-ken game (1809). From left to right: slug (namekuji), frog (kawazu) and snake (hebi).

Throughout Japanese history there are frequent references to sansukumi-ken, meaning ken (fist) games where "the three who are afraid of one another" (i.e. A beats B, B beats C, and C beats A).[8] This type of game originated in China before being imported to Japan and subsequently also becoming popular among the Japanese.[8]

The earliest Japanese sansukumi-ken game was known as mushi-ken (虫拳), which was imported directly from China.[8][9] In mushi-ken the "frog" (represented by the thumb) triumphs over the "slug" (represented by the little finger), which, in turn prevails over the "snake" (represented by the index finger), which triumphs over the "frog".[8] Although this game was imported from China the Japanese version differs in the animals represented. In adopting the game, the original Chinese characters for the poisonous centipede (蜈蜙) were apparently confused with the characters for the slug (蛞蝓).[9] The most popular sansukumi-ken game in Japan was kitsune-ken (狐拳). In the game, a supernatural fox called a kitsune (狐) defeats the village head, the village head (庄屋) defeats the hunter, and the hunter (猟師) defeats the fox. Kitsune-ken, unlike mushi-ken or rock–paper–scissors, is played by making gestures with both hands.[10]

Kitsune-ken was a popular Japanese rock paper scissors variant. From left to right: The hunter (ryōshi), village head (shōya) and fox (kitsune).

Today, the best-known sansukumi-ken is called jan-ken (じゃんけん),[9] which is a variation of the Chinese games introduced in the 17th century.[11] Jan-ken uses the rock, paper, and scissors signs[8] and is the game that the modern version of rock paper scissors derives from directly.[9] Hand-games using gestures to represent the three conflicting elements of rock, paper, and scissors have been most common since the modern version of the game was created in the late 19th century, between the Edo and Meiji periods.[12]

Spread beyond East Asia

By the early 20th century, rock paper scissors had spread beyond East Asia, especially through increased Japanese contact with the west.[13] Its English-language name is therefore taken from a translation of the names of the three Japanese hand-gestures for rock, paper and scissors:[14] elsewhere in East Asia the open-palm gesture represents "cloth" rather than "paper".[15] The shape of the scissors is also adopted from the Japanese style.[14]

A 1921 article about cricket in the Sydney Morning Herald described "stone, scissors, and paper" as a "Teutonic method of drawing lots", which the writer "came across when travelling on the Continent once".[16] Another article, from the same year, in the Washington Herald described it as a method of "Chinese gambling".[17] In Britain in 1924 it was described in a letter to The Times as a hand game, possibly of Mediterranean origin, called "zhot".[18] A reader then wrote in to say that the game "zhot" referred to was evidently Jan-ken-pon, which she had often seen played throughout Japan.[19] Although at this date the game appears to have been new enough to British readers to need explaining, the appearance by 1927 of a popular thriller with the title Scissors Cut Paper,[20] followed by Stone Blunts Scissors (1929), suggests it quickly became popular.

In 1927 La Vie au patronage, a children's magazine in France, described it in detail,[21] referring to it as a "jeu japonais" ("Japanese game"). Its French name, "Chi-fou-mi", is based on the Old Japanese words for "one, two, three" ("hi, fu, mi").

A 1932 New York Times article on the Tokyo rush hour describes the rules of the game for the benefit of American readers, suggesting it was not at that time widely known in the U.S.[22] The 1933 edition of the Compton's Pictured Encyclopedia described it as a common method of settling disputes between children in its article on Japan; the name was given as "John Kem Po" and the article pointedly asserted, "This is such a good way of deciding an argument that American boys and girls might like to practice it too."[23]

Strategies
Children in Laos playing rock paper scissors
Children in Myanmar playing rock paper scissors

It is impossible to gain an advantage over a truly random opponent. However, by exploiting the psychological weaknesses of inherently non-random opponents, it is possible to gain a significant advantage.[24][25] Indeed, human players tend to be non-random.[25][26] As a result, there have been programming competitions for algorithms that play rock paper scissors.[24][27][28]

During tournaments, players often prepare their sequence of three gestures prior to the tournament's commencement.[29][30] Some tournament players employ tactics to confuse or trick the other player into making an illegal move, resulting in a loss. One such tactic is to shout the name of one move before throwing another, in order to misdirect and confuse their opponent.

The "rock" move, in particular, is notable in that it is typically represented by a closed fist—often identical to the fist made by players during the initial countdown. If a player is attempting to beat their opponent based on quickly reading their hand gesture as the players are making their moves, it is possible to determine if the opponent is about to throw "rock" based on their lack of hand movement, as both "scissors" and "paper" require the player to reposition their hand. This can likewise be used to deceive an anticipating opponent by keeping one's fist closed until the last possible moment, leading them to believe that you are about to throw "rock".

Algorithms

As a consequence of rock paper scissors programming contests, many strong algorithms have emerged.[24][27][28] For example, Iocaine Powder, which won the First International RoShamBo Programming Competition in 1999,[27] uses a heuristically designed compilation of strategies.[31] For each strategy it employs, it also has six metastrategies which defeat second-guessing, triple-guessing, as well as second-guessing the opponent, and so on. The optimal strategy or metastrategy is chosen based on past performance. The main strategies it employs are history matching, frequency analysis, and random guessing. Its strongest strategy, history matching, searches for a sequence in the past that matches the last few moves in order to predict the next move of the algorithm. In frequency analysis, the program simply identifies the most frequently played move. The random guess is a fallback method that is used to prevent a devastating loss in the event that the other strategies fail. More than ten years later, the top performing strategies on an ongoing rock–paper–scissors programming competition similarly use metastrategies. However, there have been some innovations, such as using multiple history matching schemes that each match a different aspect of the history – for example, the opponent's moves, the program's own moves, or a combination of both.[32] There have also been other algorithms based on Markov chains.[33]

In 2012, researchers from the Ishikawa Watanabe Laboratory at the University of Tokyo created a robot hand that can play rock paper scissors with a 100% win rate against a human opponent. Using a high-speed camera the robot recognizes within one millisecond which shape the human hand is making, then produces the corresponding winning shape.[34][35]

Instances of use in real-life scenarios

American court case

In 2006, American 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.[36][37] 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 11–12 July 2006.[38]

Auction house selection
Cézanne's Large Trees Under the Jas de Bouffan sold for $11,776,000 at Christie's in 2005.[39]

In 2005, when Takashi Hashiyama, CEO of Japanese television equipment manufacturer Maspro Denkoh, decided to auction off the collection of Impressionist paintings owned by his corporation, including works by Paul Cézanne, Pablo Picasso, and Vincent van Gogh, he contacted two leading 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 earn Hashiyama's approval. Unwilling to split up the collection into separate auctions, Hashiyama asked the firms to decide between themselves who would hold the auction, which included 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 rock paper scissors 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 the international director of Christie's Impressionist and Modern Art Department Nicholas Maclean, 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".[40] Christie's won the match and sold the $20 million collection, earning millions of dollars of commission for the auction house.

FA Women's Super League match

Prior to a 26 October 2018 match in the FA Women's Super League, the referee, upon being without a coin for the pregame coin toss, had the team captains play rock paper scissors to determine which team would kick-off. The referee was subsequently suspended for three weeks by The Football Association.[41]

Play by chimpanzees

In Japan, researchers have taught chimpanzees the rules of rock paper scissors.[42]

Analogues in game design

In many games, it is common for a group of possible choices to interact in a rock paper scissors style, where each selection is strong against a particular choice, but weak against another. For instance cavalry–artillery–infantry. Such mechanics can make a game somewhat self-balancing, prevent gameplay from being overwhelmed by a single dominant strategy and single dominant type of unit.[43]

Many card-based video games in Japan use the rock paper scissors system as their core fighting system, with the winner of each round being able to carry out their designated attack. In Alex Kidd in Miracle World, the player has to win games of rock paper scissors against each boss to proceed. Others use simple variants of rock paper scissors as subgames.

Many Nintendo role-playing games prominently feature a rock paper scissors gameplay element. In Pokémon, there is a rock paper scissors element in the type effectiveness system. For example, a Grass-type Pokémon is weak to Fire, Fire is weak to Water, and Water is weak to Grass.[44] In the 3DS remake of Mario & Luigi: Superstar Saga and Mario & Luigi: Bowser's Inside Story, the battles in the second mode (Minion Quest: The Search for Bowser / Bowser Jr.'s Journey) use a “Power Triangle” system based on the game's three attack types: Melee, Ranged, and Flying. In the Fire Emblem series of strategy role-playing games, the Weapon Triangle and Trinity of Magic influence the hit and damage rates of weapon types based on whether they are at an advantage or a disadvantage in their respective rock paper scissors system. In Super Smash Bros., the three basic actions used during the match are described in their respective rock paper scissors system: attack, defense, and grab.

Analogues in nature

Lizard mating strategies
Main article: Common side-blotched lizard § Mating

The common side-blotched lizard (Uta stansburiana) exhibits a rock paper scissors 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.[45][46]

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.[47] Additional in vitro results demonstrate rock paper scissors dynamics in additional species of bacteria.[48] Biologist Benjamin C. Kirkup, Jr. demonstrated that these antibiotics, bacterioicins, were active as Escherichia 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.[49]

Rock paper scissors is the subject of continued research in bacterial ecology and evolution. It is considered one of the basic applications of game theory and non-linear dynamics to bacteriology.[50] Models of evolution demonstrate how intragenomic competition can lead to rock paper scissors dynamics from a relatively general evolutionary model.[51] The general nature of this basic non-transitive model is widely applied in theoretical biology to explore bacterial ecology and evolution.[52][53]

Analogues in mechanical devices and geometrical constructions

In the televised robot combat competition BattleBots, relations between "lifters, which had wedged sides and could use forklift-like prongs to flip pure wedges", "spinners, which were smooth, circular wedges with blades on their bottom side for disabling and breaking lifters", and "pure wedges, which could still flip spinners" are analogical to relations in rock paper scissors games and called "robot Darwinism".[54] Also specially designed rock paper scissors game" mechanical devices can demonstrate intransitivity of relations such as "to rotate faster than", "to lift and not be lifted", "to be stronger than" in some geometrical constructions.[55]

Tournaments
Two players at the 4th UK Rock Paper Scissors Championships, 2010

Various competitive rock paper scissors tournaments have been organised by different groups.

World Rock Paper Scissors Society

Starting in 2002, the World Rock Paper Scissors Society standardized a set of rules for international play[56] 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.[57][58][59][60][61] WRPS events are noted for their large cash prizes, elaborate staging, and colorful competitors.[62] In 2004, the championships were broadcast on the U.S. television network Fox Sports Net, with the winner being Lee Rammage, who went on to compete in at least one subsequent championship.[63][64] The 2007 tournament was won by Andrea Farina.[65] The last tournament hosted by the World RPS Society was in Toronto, Canada, on November 14, 2009.[66]

UK championships

Several RPS events have been organised in the United Kingdom by Wacky Nation. The 1st UK Championship took place on 13 July 2007, and were then held annually. The 2019 event was won by Ellie Mac who went on to pick up the cash prize of £20,000 but was unable to double her earnings in 2020 due to the coronavirus outbreak.[67]

USARPS tournaments

USA Rock Paper Scissors League is sponsored by Bud Light. Leo Bryan Pacis was the first commissioner of the USARPS. Cody Louis Brown was elected as the second commissioner of the USARPS in 2014.

In April 2006, the inaugural USARPS Championship was held in Las Vegas. 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 12 June 2006.

The $50,000 2007 USARPS Tournament took place at the Las Vegas Mandalay Bay in May 2007.

In 2008, Sean "Wicked Fingers" Sears beat 300 other contestants and walked out of the Mandalay Bay Hotel and Casino with $50,000 after defeating Julie "Bulldog" Crossley in the finals.

The inaugural Budweiser International Rock, Paper, Scissors Federation Championship was held in Beijing, China after the close of the 2008 Summer Olympics at Club Bud. A Belfast man won the competition.[68]

Team Olimpik Championships 2012

The international tournament was held in London 2012. UK Champions Team GB (Andrew Bladon, Jamie Burland, Tom Wilkinson and Stephen Preston) went in as overwhelming favorites, but after a "domestic incident" team captain and UK Team Champion Joe Kenny was forced to pull out, allowing Stephen Preston to take his place. Great Britain came a respectable third to achieve the Bronze Medal, while the crowd favorite Vatican City got the Silver and Lapland A took the prestigious Gold Medal. British team captain Tom Wilkinson commented "after a 4-0 whitewash of hot favorites Vatican City we thought we had it. A simple lapse of concentration lost it for us, but we are happy with our bronze medal. We'll come back from this and look to take the title back again next year. The support was immense, and we are thankful of everyone who came out to support us".[69]

National XtremeRPS Competition 2007–2008

The XtremeRPS National Competition is a US nationwide RPS competition with Preliminary Qualifying contests that started in January 2007 and ended in May 2008, followed by regional finals in June and July 2008. The national finals were to be held in Des Moines, Iowa in August 2008, with a chance to win up to $5,000.

Guinness Book of World Records

The largest Rock Paper Scissors tournament is 2,950 and was achieved by Oomba, Inc. (USA) at Gen Con 2014 in Indianapolis, Indiana, United States, on 17 August 2014.[70]

World Series

Former Celebrity Poker Showdown host and USARPS Head Referee[71] Phil Gordon has hosted an annual $500 World Series of Rock Paper Scissors event in conjunction with the World Series of Poker since 2005.[72] The winner of the WSORPS receives an entry into the WSOP Main Event. The event is an annual fundraiser for the "Cancer Research and Prevention Foundation" via Gordon's charity Bad Beat on Cancer. Poker player Annie Duke won the Second Annual World Series of Rock Paper Scissors.[73] The tournament is taped by ESPN and highlights are covered during "The Nuts" section of ESPN's annual WSOP broadcast.[74][75][76] 2009 was the fifth year of the tournament.

Jackpot En Poy of Eat Bulaga!

Jackpot En Poy is a game segment on the Philippines' longest running midday show, Eat Bulaga!. The game is based on the classic children's game rock paper scissors where four players are paired to compete in the three-round segment. In the first round, the first pair plays against each other until one player wins three times. The next pair then plays against each other in the second round. The winners from the first two rounds then compete against each other to finally determine the ultimate winner. The winner of the game then moves on to the final round. In the final round, the player is presented with several Dabarkads, each holding different amounts of cash prize. The player will then pick three Dabarkads who he or she will play rock paper scissors against. The player plays against them one at a time. If the player wins against any of the Eat Bulaga! hosts, he or she will win the cash prize.[77][78][79]

Variations
A print by Kikukawa Eizan that shows geisha playing kitsune-ken, a Japanese rock paper scissors variant (1820)

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 and rules, to giving their own name to the game in their national language.

Adapted rules

In Korea, a two-player upgraded version exists by the name muk-jji-ppa.[80] After showing their hands, the player with the winning throw shouts "muk-jji-ppa!" upon which both players throw again. If they throw differently (for example, rock and paper, or paper and scissors), whoever wins this second round shouts "muk-jji-ppa!" and thus the play continues until both players throw the same item (for example, rock and rock), at which point whoever was the last winner becomes the actual winner.

In Japan, a "strip-poker" variant of rock paper scissors is known as 野球拳 (Yakyuken). The loser of each round removes an article of clothing. The game is a minor part of porn culture in Japan and other Asian countries after the influence of TV variety shows and Soft On Demand.

In the Philippines, the game is called jak-en-poy, from one of the Japanese names of the game, transliterated as jan-ken-pon. In a longer version of the game, a four-line song is sung, with hand gestures displayed at the end of each (or the final) line: "Jack-en-poy! / Hali-hali-hoy! / Sino'ng matalo, / siya'ng unggoy!" ("Jack-en-poy! / Hali-hali-hoy! / Whoever loses is the monkey!") In the former case, the person with the most wins at the end of the song, wins the game. A shorter version of the game uses the chant "Bato-bato-pick" ("Rock-rock-pick [i.e. choose]") instead.

A multiple player variation can be played: Players stand in a circle and all throw at once. If rock, paper, and scissors are all thrown, it is a stalemate, and they rethrow. If only two throws are present, all players with the losing throw are eliminated. Play continues until only the winner remains.[81]

Different weapons

In the Malaysian version of the game, "scissors" is replaced by "bird," represented with the finger tips of five fingers brought together to form a beak. The open palm represents "water". Bird beats water (by drinking it); stone beats bird (by hitting it); and stone loses to water (because it sinks in it).

Singapore also has a related hand-game called "ji gu pa", where "ji" refers to the bird gesture, "gu" refers to the stone gesture, and "pa" refers to the water gesture. The game is played by two players using both hands. At the same time, they both say, "ji gu pa!" At "pa!" they both show two open-palmed hands. One player then changes his hand gestures while calling his new combination out (e.g., "pa gu!"). At the same time, the other player changes his hand gestures as well. If one of his hand gestures is the same as the other one, that hand is "out" and he puts it behind his back; he is no longer able to play that hand for the rest of the round. The players take turns in this fashion, until one player loses by having both hands sent "out". "Ji gu pa" is most likely a transcription of the Japanese names for the different hand gestures in the original jan-ken game, "choki" (scissors), "guu" (rock) and "paa" (paper).

Using the same tripartite division, there is a full-body variation in lieu of the hand signs called "Bear, Hunter, Ninja".[82] In this iteration the participants stand back-to-back and at the count of three (or ro-sham-bo as is traditional) turn around facing each other using their arms evoking one of the totems.[83] The players' choices break down as: Hunter shoots bear; Bear eats ninja; Ninja kills hunter.[84] The game was popularized with a FedEx commercial[85] where warehouse employees had too much free time on their hands.

Additional weapons

As long as the number of moves is an odd number and each move defeats exactly half of the other moves while being defeated by the other half, any combination of moves will function as a game. For example, 5-, 7-, 9-, 11-, 15-, 25-, and 101-weapon versions exist.[86] Adding new gestures has the effect of reducing the odds of a tie, while increasing the complexity of the game. The probability of a tie in an odd-number-of-weapons game can be calculated based on the number of weapons n as 1/n, so the probability of a tie is 1/3 in standard rock paper scissors, but 1/5 in a version that offered five moves instead of three.[87]

Similarly, the French game "pierre, papier, ciseaux, puits" (stone, paper, scissors, well) is unbalanced; both the stone and scissors fall in the well and lose to it, while paper covers both stone and well. This means two "weapons", well and paper, can defeat two moves, while the other two weapons each defeat only one of the other three choices. The rock has no advantage to well, so optimal strategy is to play each of the other objects (paper, scissors and well) one third of the time.[88]

Rock Paper Scissors Lizard Spock gestures

One popular five-weapon expansion is "rock paper scissors Spock lizard", invented by Sam Kass and Karen Bryla,[89] which adds "Spock" and "lizard" to the standard three choices. "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 mentioned in a 2005 article in The Times of London[90] and was later the subject of an episode of the American sitcom The Big Bang Theory in 2008 (as rock-paper-scissors-lizard-Spock).[91]

The majority of such proposed generalizations are isomorphic to a simple game of modular arithmetic, where half the differences are wins for player one. For instance, Rock-Paper-Scissors-Spock-Lizard may be modeled as a game in which each player picks a number from one to five. Subtract the number chosen by player two from the number chosen by player one, and then take the remainder modulo 5 of the result. Player one is the victor if the difference is one or three, and player two is the victor if the difference is two or four. If the difference is zero, the game is a tie.

Alternatively, the rankings may be modeled by a comparison of the parity of the two choices. If it is the same (two odd-numbered moves or two even-numbered ones) then the lower number wins, while if they are different (one odd and one even) the higher wins. Using this algorithm, additional moves can easily be added two at a time while keeping the game balanced:

  1. Declare a move N+1 (where N is the original total of moves) that beats all existing odd-numbered moves and loses to the others (for example, the rock (#1), scissors (#3), and lizard (#5) could fall into the German well (#6), while the paper (#2) covers it and Spock (#4) manipulates it).
  2. Declare another move N+2 with the reverse property (such as a plant (#7) that grows through the paper (#2), poisons Spock (#4), and grows through the well (#6), while being damaged by the rock (#1), scissors (#3), and lizard (#5)).

Game-theoretic variations
Oriented graph of Paper Rock Scissors Fire Water

Any variation of Rock Paper Scissors is an oriented graph. According to theoretical calculations, the number of distiguishable oriented graphs, every of which is a potentially playable Rock Paper Scissors game, grows with the number of weapons = 3, 4, 5, … as follow:[92]

7; 42; 582; 21,480; 2,142,288; 575,016,219; 415,939,243,032; … (sequence A001174 in the OEIS).

A game-theoretic analysis showed that 4 variants of 582 possible variations using 5 different weapons have non-trivial mixed strategy equilibria.[93] The most representative game of these 4 is Rock Paper Scissors Fire Water. Rock beats Scissors, Paper beats Rock, Scissors beats Paper, Fire beats everything except Water, and Water is beaten by everything except it beats Fire. The perfect game-theoretic strategy is to use Rock, Paper, and Scissors of the time and of the time for Fire and Water. Nevertheless, experiments show that people underuse Water and overuse Rock, Paper, and Scissors in this game.[94]

gollark: Well, I have an infinite amount more than that.
gollark: My faith in humanity is stored as a floating point, so if it goes too low it'll just be -Infinity or NaN or something.
gollark: I wouldn't trust Trump to actually do any of the things he's said he would.
gollark: Radioactive decay? That's pretty random.
gollark: So it would *basically* make everyone happy.

See also

References

Notes

  1. Fisher, Len (2008). Rock, Paper, Scissors: Game Theory in Everyday Life. Basic Books. p. 92. ISBN 9780786726936.
  2. "Game Basics". Archived from the original on 2019-03-22. Retrieved 2009-12-05.
  3. St. John, Kelly (2003-03-19). "Ready, set ... Roshambo! Contestants vie for $1,000 purse in Rock, Scissors, Paper contest". San Francisco Chronicle. Retrieved 2007-11-20.
  4. Wells, Steven (2006-11-24). "It's not your dad's ick-ack-ock". The Guardian. Retrieved 2013-08-13.
  5. Fisher, Len (2008). Rock, paper, scissors: game theory in everyday life. Basic Books. p. 94. ISBN 9780786726936.
  6. "How to win at rock-paper-scissors". BBC News. Retrieved 2 May 2015.
  7. Moore, Michael E.; Sward, Jennifer (2006). Introduction to the game industry. Upper Saddle River, NJ: Pearson Prentice Hall. p. 535. ISBN 978-0-13-168743-1.
  8. Linhart, Sepp (1995). "Some Thoughts on the Ken Game in Japan: From the Viewpoint of Comparative Civilization Studies". Senri Ethnological Studies. 40: 101–124. hdl:10502/750.
  9. Linhart, Sepp (1995). "Rituality in the ken game". Ceremony and Ritual in Japan. London: Routledge. pp. 38–41. ISBN 9780415116633.
  10. Linhart, Sepp (1998). "From Kendo to Jan-ken: The Deterioration of a Game from Exoticism to Ordinariness". The Culture of Japan as Seen through Its Leisure. New York: SUNY Press. pp. 325–326. ISBN 9780791437919.
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