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Rock paper scissors

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The game of Rock, Paper, Scissors (sometimes with its elements permuted and/or Rock replaced with Stone or Paper with Cloth, but also known as Roshambo, Rochambeau, Janken, Mora,or JanKenPon) is a whimsical hand game most often played by children. It is often used in a similar way to coin flipping, throwing dice or drawing straws to randomly select a person for some purpose, though unlike truly random selections it can be played with skill if the game extends over many sessions, because one can often recognize and exploit the non-random behavior of an opponent. It is also often used as a method for creating appropriately biased random results in live action role-playing games, as it requires no equipment.

Game play

     
       
       
       

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


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

  • Rock (or "stone"): a clenched fist.
  • Paper: all fingers extended, palm facing downwards, upwards, or sideways(thumb pointing to the sky).
  • Scissors: forefinger and middle finger extended and separated into a "V" shape.

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

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

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

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

Strategies

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

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

Cheating

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

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

Variations

There are multiple variations on Rock, Paper, Scissors of varying popularity and humor content. These roughly fall into three types: number of players, names of symbols (weapons), and number of symbols.

Number of players

The game is easily adaptable to more than just two players. This variant works remarkably well, even for large groups. The rules are the same, with the following exceptions:

  • If all three weapon types are played, the round is considered to be a draw. A new round begins.
  • If there are only two different weapon types showing between all of the players, then all of the players showing the losing weapon are eliminated.

Names of symbols

Another variation involves changing the names of the symbols. Each symbol has its own gesture associated with it.

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

Hunter, Gun, Lion has the hunter beating the gun, gun beats lion, and Lion beats Hunter.

In Ninja, Cowboy, Lion, Ninja beats Cowboy, Cowboy beats Lion, and Lion beats Ninja.

Number of symbols

The number of symbols and win conditions used in the game may be varied with most of the original strategy remaining intact. The number of symbols can be decreased to two, increased above three, or "trump" weapons can be added.

Odd or Even (2)

In Odd or Even, one player selects odd or even. The only choice in weapons are "one" (a fist with outstretched thumb) or "two" (a fist with outstretched thumb and forefinger). The values signified by the players are added, with the first player winning on a correct prediction about the result. With a choice between two values (it does not matter that they are 1 and 2, only that they are not both odd or even) the game is balanced, and there is no benefit from making the call. Should you allow three (or any odd number) values to choose from, either odd or even would be a more probable outcome with both players acting randomly. (That is because n choices make n2 possible outcomes. Squares of even numbers are even, squares of odd numbers odd.)

Rock Paper Scissors Spock Lizard (5)

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

Trumps (3+)

Players often add other "weapons" to the game on a ad-hoc basis, but it is very likely that this will result in an unbalanced game. In particular, four (or any even number) of weapons cannot be made balanced, unless some pairs of weapons result in a draw; there will always be some weapons that will be superior to others. It also loses some of the aesthetic simplicity of the game, which is otherwise one of the simplest possible games of skill.

Dynamite is an example of a trump play. It is expressed as the extended index finger, defeats only rock, but is defeated by either scissors or paper. Therefore, anything dynamite will beat, paper will beat; and anything dynamite will tie, paper will tie or beat. Given that paper performs better by tying against another paper, it is always better to use paper than to use dynamite, and dynamite is useless. In game theory, it is said that paper has weak dominance over dynamite.

Fire and water are also potential "trumps," and have been used in ultimate frisbee tournaments. Fire will beat any of the standard weapons (rock, paper, scissors), but because of the power its play is restricted to a single use in the player's entire lifetime. Water may be played as many times as one wishes, but will lose to anything except fire.

Tournaments

There are Roshambo tournaments held occasionally. The 2003 Molson Canadian Rock Paper Scissors International World Championships [1] held in Toronto, Ontario were widely reported. Some of the Roshambo websites spoof comparable sites for other games. Real Roshambo tournaments are an interesting psychological exercise. Obviously, the strategy dictated by game theory is to pick each choice 1/3 of the time randomly. However, a human cannot be truly random, and the skill in the tournament would involve exploiting your opponent's nonrandom throws.

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

Other games reduce to Rock, Paper, Scissors

  • In many real-time strategy games, there are three types of troops, with each troop type beating one and losing to another. For example, cavalry beat archers, archers beat pikemen, and pikemen beat cavalry. There are also some turn-based strategy games with a similar dominace structure; however, sometimes the troops are replaced with weapons regarding what dominates what.
  • In Magic: The Gathering, the deckbuilding strategies tend to break down into a few major types. Though only an approximation, usually paper-rock-scissors is compared to aggro-control-combo. Since there is a random element, a matchup is not usually a 100% chance of victory for the dominant deck. The optimal strategy can be found using probability, and depends on what you expect other players to do.
  • In Ambition, Rochambeau scenarios can occur, the variable being a player's strategy in a given round. Each player will select the strategy based upon his/her hand (for example, a player might wish, on a given hand, to play aggressive spades early on, clear diamonds early, and dump the King of Clubs as early as possible) that s/he thinks is most likely to produce a profitable round. The interaction of these strategies creates the game.
  • Various sports, including ultimate frisbee, 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 a quick Rochambeau.
  • Pokémon is sometimes compared to a very complex variant of paper-rock-scissors, particularly the trio of starting Pokémon available in all the games, except Pokémon Yellow. Although the overall type chart is likely unbalanced (which in practice doesn't usually matter too much), the three starting Pokémon's types are very balanced, with Grass (drys up Water), Fire (burns Grass), and Water (douses Fire). However, there are similar trios of Pokémon that do not have balanced type relations - Eevee's three stone-evolved forms, Vaporeon, Jolteon and Flareon; the three legendary birds, Articuno, Zapdos and Moltres; and the legendary trio from Gold, Silver and Sapphire, which are Suicune, Raikou and Entei. In each case, the Electric-type Pokémon (Jolteon, Zapdos and Raikou) is superior. Note, however, that just as with Magic: The Gathering, a type advantage does not provide a 100% chance of beating your opponent, only an increased chance.
  • In Uru Live, the short-lived online component of the computer game Uru: Ages Beyond Myst, explorers could play a D'ni game called "Ahyoheek," which is a sophisticated Rock, Paper, Scissors implementation. It is played on a special pentagonal table with electronic scorekeeping and holographic display built in. (These tables exist only in Uru Live, of course.) The three "throws" are Pen, Book, and Beetle; Pen writes in Book, Book crushes Beetle, Beetle provides ink to Pen. It is played by 2 to 5 people simultaneously, each person sitting at one side of the table. Each side of the table has a concealed panel of three buttons, each corresponding to a throw. A game of Ahyoheek consists of multiple rounds; the goal is to win three rounds with the same throw. A round begins with one person choosing his throw; other players must follow suit before a timer displayed in the center of the table reaches zero. At the end of a round, each player's throw is compared with each of the other players'. A player earns one round-point for each opponent he beats, and loses one for each opponent who beats him. The player(s) with the most round-points win(s) the round, and a panel of small lights indicates the throw with which they won. When at least one person has won three rounds with the same throw, and the winners are declared. Uru Live also had a ranking system based on the number of Ahyoheek games won and the skill of beaten opponents, but it is beyond the scope of this article.
  • Many other RPGs also have an elemental system (usually involved with the magic system) which, while usually less complex, also provides superiority to certain types when used against other types.

Non-transitivity

Rochambeau is also often used as an example of the mathematical concept of non-transitivity. A transitive relation R is one for which a R b and b R c implies a R c. A reflexive, antisymmetric, and transitive relation on a set is known as a partial ordering, from which notions of "greater" and "less" follow. A game option which is "greater" than another is closer to being optimal, but such a notion does not exist in Rochambeau: The relation used to determine which throws defeat which is non-transitive. Rock defeats Scissors, and Scissors defeat Paper, but Rock loses to Paper. (In fact, Rochambeau could be called "antitransitive" because if A strictly defeats B, and B strictly defeats C, A necessarily loses against C.)

History

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


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