Rock paper scissors

Genres	Hand game
Players	2 (or more)
Setup time	None
Playing time	seconds
Chance	None to some, depending on the skill level of those playing

Rock paper scissors (also known by several other names and word orders, see § Names) is an intransitive 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). The earliest form of "rock paper scissors"-style game originated in China and was subsequently imported into Japan, where it reached its modern standardized form, before being spread throughout the world in the early 20th century.

A simultaneous, zero-sum game, it has three possible outcomes: a draw, a win, or a loss. A player who decides to play rock will beat another player who chooses scissors ("rock crushes scissors" or "breaks 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 replayed to break the tie.

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 some degree of skill by recognizing and exploiting non-random behavior in opponents.^[2][3]

Etymology

The name "rock paper scissors" is simply a translation of the Japanese words for the three gestures involved in the game,^[4] though the Japanese name for the game is different.

The name Roshambo or Rochambeau has been claimed to refer to Count Rochambeau, who allegedly played the game during the American Revolutionary War. The legend that he played the game is apocryphal, as all evidence points to the game being brought to the United States later than 1910; if this name has anything to do with him it is for some other reason.^[5][6] It is unclear why this name became associated with the game, with hypotheses ranging from a slight phonetic similarity with the Japanese name jan-ken-pon,^[5] to the presence of a statue of Rochambeau in a neighborhood of Washington, D.C.^[6]

Names

The modern game is known by several other names such as Rochambeau, Roshambo, Ro-sham-bo, Bato Bato Pik, and Jak-en-poy.^[7][8][9] While the game's name is a list of three items, different countries often have the list in a different order.

In North America and the United Kingdom, it is known as "rock, paper, scissors" or "scissors, paper, stone".^[10][11] If this name is chanted while actually playing the game, it might be followed by an exclamation of "shoot" at the moment when the players are to reveal their choice (i.e. "Rock, paper, scissors, shoot!").^[12]

In Australia, the most common name is "scissors, paper, rock" (the reverse of the American format).^[13] There have been claims that there are regional variations of the name in Australia; the video claimed that it was referred to as "scissors, paper, rock" in New South Wales, "rock, paper, scissors" in Victoria, South Australia and Western Australia and "paper, scissors, rock" in Queensland, though this has been disputed.^[14]

In New Zealand, the most common name in English is "paper, scissors, rock".^[15] In Māori, it is known as pēpa, kutikuti, kōhatu (lit. 'paper, scissors, rock').^[16]

Gameplay

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

The players may start by counting to three aloud, or by speaking the name of the game (e.g. "Rock! Paper! Scissors!"), raising one hand in a fist and swinging it down with each syllable onto their other hand (or in a less common variant, holding it behind their back). They then "throw" or "shoot" by extending their selected sign towards their opponent on what would have been the fourth count, often saying the word "shoot" while doing so. Variations include a version where players throw immediately on the third count (thus throwing on the count of "Scissors!"), a version including five counts rather than four ("Rock! Paper! Scissors! Says! Shoot!", almost exclusively localized in the United States to Long Island and some parts of New York City), and a version where players shake their hands three times before "throwing".^{[citation needed]}

History

Origins

The first known mention of the game was in the book Wuzazu [zh] by the Ming-dynasty writer Xie Zhaozhe [zh] (fl. c. 1600), who wrote that the game dated back to the time of the Han dynasty (206 BCE – 220 CE).^[17] 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).

From China the game was brought to Japan.^[18] Throughout Japanese history there are frequent references to sansukumi-ken, meaning ken (fist) games "of the three who are afraid of one another" (i.e. A beats B, B beats C, and C beats A).^[18]

The earliest sansukumi-ken in Japan was apparently mushi-ken (虫拳), a version imported directly from China.^[18][19] 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".^[18][19] (The Chinese and Japanese versions differ in the animals represented; in adopting the game, the Chinese characters for the venomous centipede (蜈蜙) were apparently confused with the characters for the slug (蛞蝓)).^[19]

The most popular sansukumi-ken game in Japan^[when?] was kitsune-ken (狐拳). In this 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, requires gestures with both hands.^[20]

Today, the best-known sansukumi-ken is called jan-ken (じゃんけん),^[19] which is a variation of the Chinese games introduced in the 17th century.^[21] Jan-ken uses the rock, paper, and scissors signs^[18] and is the direct source of the modern version of rock paper scissors.^[19] 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.^[22]

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.^[23] Its English-language name is therefore taken from a translation of the names of the three Japanese hand-gestures for rock, paper and scissors;^[4] elsewhere in East Asia the open-palm gesture represents "cloth" rather than "paper".^[24] The shape of the scissors is also adopted from the Japanese style.^[4]

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".^[25] Another article, from the same year, the Washington Herald described it as a method of "Chinese gambling".^[26] In Britain in 1924 it was described in a letter to The Times as a hand game, possibly of Mediterranean origin, called "zhot".^[27] 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.^[28] 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,^[29] followed by Stone Blunts Scissors (1929), suggests it quickly became popular.

The game is referred to in two of Hildegard G. Frey's novels in the Campfire Girls series: The Campfire Girls Go Motoring (1916) ^[30] and The Campfire Girls Larks and Pranks (1917),^[31] which suggests that it was known in America at least that early. The first passage where it appears says "In order that no feelings might be involved in any way over which car we other girls traveled in, Nyoda, Solomon-like, proposed that she and Gladys play 'John Kempo' for us. (That isn't spelled right, but no matter.)" There is no explanation in any of the places where it is referenced of what the game actually is. This suggests that the author at least believed that the game was well known enough in America that her readers would understand the reference.

In 1927 La Vie au patronage, a children's magazine in France, described it in detail,^[32] 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.^[33] Likewise, the trick-taking card game “Jan-Ken-Po”, first published in 1934, describes the rules of the hand-game without mentioning any American game along the lines of “rock paper scissors”. 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."^[34]

Strategies

It is impossible to gain an advantage over an opponent that chooses their move uniformly at random. However, it is possible to gain a significant advantage over a non-random player by predicting their move, which can be done by exploiting psychological effects or by analyzing statistical patterns of their past behavior.^[35][36][37] As a result, there have been programming competitions for algorithms that play rock paper scissors.^[35][38][39]

During tournaments, players often prepare their sequence of three gestures prior to the tournament's commencement.^[40][41] 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.^{[citation needed]}

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".^{[citation needed]}

Algorithms

As a consequence of rock paper scissors programming contests, many strong algorithms have emerged.^[35][38][39] For example, Iocaine Powder, which won the First International RoShamBo Programming Competition in 1999,^[38] uses a heuristically designed compilation of strategies.^[42] 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. There have since 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.^[43] There have also been other algorithms based on Markov chains.^[44]

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.^[45][46]

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

Adapted rules

In Korea, where the standard version of the game is called gawi-bawi-bo, a two-player upgraded version exists by the name muk-jji-ppa.^[47] 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 another popular two-handed variant, one player will shout "minus one" after the initial play. Each player removes one hand, and the winner is decided by the remaining hands in play.^[48]

In Japan, a strip game 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 the Japanese jankenpon). 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 ") instead.^{[citation needed]}

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.^[49]

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), "gū" (rock) and "pā" (paper).

In Indonesia, the game is called suten, suit or just sut, and the three signs are elephant (slightly raised thumb), human (outstreched index finger) and ant (outstreched pinky finger).^[50] Elephant is stronger than human, human is stronger than ant, but elephant is afraid of the ant.

Using the same tripartite division, there is a full-body variation in lieu of the hand signs called "Bear, Hunter, Ninja".^[51] 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.^[52] The players' choices break down as: Hunter shoots bear; Bear eats ninja; Ninja kills hunter.^[53] The game was popularized with a FedEx commercial^[54] where warehouse employees had too much free time on their hands.

Additional weapons

Generalized rock-paper-scissors games where the players have a choice of more than three weapons have been studied.^[55] Any variation of rock paper scissors is an oriented graph, where the nodes represent the symbols (weapons) choosable by the players, and an edge from A to B means that A defeats B. Each oriented graph is a potentially playable rock paper scissors game. According to theoretical calculations, the number of distinguishable (i.e. not isomorphic) oriented graphs grows with the number of weapons = 3, 4, 5, ... as follows:^[56][57]

7, 42, 582, 21480, 2142288, 575016219, 415939243032, … (sequence A001174 in the OEIS).

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 stone 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.^[58]

"pierre, papier, ciseaux, puits";
+ means that the row player "beats", - means "is beaten" and O means tie

Opponent Row player	stone	paper	scissors	well	Optimal strategy for the row player[58]
stone	O	-	+	-	${\displaystyle 0}$
paper	+	O	-	+	${\displaystyle {\frac {1}{3}}}$
scissors	-	+	O	-	${\displaystyle {\frac {1}{3}}}$
well	+	-	+	O	${\displaystyle {\frac {1}{3}}}$

Variants in which 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 are typically considered. Variations with up to 101 different moves have been published.^[59] 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.^[60]

One popular five-weapon expansion is "rock paper scissors Spock lizard", invented by Sam Kass and Karen Bryla,^[61] 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^[62] and was later the subject of an episode of the American sitcom The Big Bang Theory in 2008 (as rock-paper-scissors-lizard-Spock).^[63]

Rock-Paper-Scissors-Spock-Lizard;
+ means that the row player "beats", - means "is beaten" and O means tie

Opponent Row player	rock	paper	scissors	Spock	lizard	Optimal strategy for row player
rock	O	-	+	-	+	${\displaystyle {\frac {1}{5}}}$
paper	+	O	-	+	-	${\displaystyle {\frac {1}{5}}}$
scissors	-	+	O	-	+	${\displaystyle {\frac {1}{5}}}$
Spock	+	-	+	O	-	${\displaystyle {\frac {1}{5}}}$
lizard	-	+	-	+	O	${\displaystyle {\frac {1}{5}}}$

A game-theoretic analysis showed that 4 variants of 582 possible variations using 5 different weapons have non-trivial mixed strategy equilibria.^[57] 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 ${\displaystyle {\frac {1}{9}}}$ of the time and ${\displaystyle {\frac {1}{3}}}$ of the time for fire and water. Nevertheless, experiments show that people underuse water and overuse rock, paper, and scissors in this game.^[64]

Rock-Paper-Scissors-Fire-Water;
+ means that the row player "beats", - means "is beaten" and O means tie

Opponent Row player	rock	paper	scissors	fire	water	Optimal strategy for row player[57]
rock	O	-	+	-	+	${\displaystyle {\frac {1}{9}}}$
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