The game “Rock, Paper, Scissors” does not need a special introduction. Disputants of all ages on all continents vigorously shake their fists, repeating in different languages the words of this simple rhyme. For centuries, this game has been one of the most versatile ways to draw lots in a variety of life situations – from children’s games and sports to making important decisions in business, technology and politics.
The rules are simple
The players in chorus pronounce the text of the rhyme, shaking their fists to the beat.
On the last word of the rhyme, the players simultaneously show one of the conditional gestures with their hands. Each gesture symbolizes one of the subjects of the rhyme text.
The winner is determined according to pre-known rules for the relationship of objects. The player with the item “stronger” than the others wins. If several players have won and shown the same item, then a draw is declared and the game is replayed.
Absolutely fair game
The main property of this game is non-transitivity. In it:
every item can be defeated by some other item;
all items are strictly equivalent.
There is no strongest item here, they all “defeat” each other in a circle:
Stone dulls scissors.
Scissors cut paper.
Paper covers stone.
The game is symmetrical: the same strategies are available to both players. And the coincidence of figures always gives a draw. From a game theory point of view, this is a zero-sum game.
History and variants
The game Rock, Paper, Scissors is believed to have been invented in China during the Han Dynasty. Its ancient name is shoshilin. This name can be translated as “hand commands”. Today, in different countries it is called differently: “rochambeau”, “ik-ek-ok”, “jan-ken-pon”. The lists of items also change. For example, in the Malay version it is: “Bird, water, stone.” But the principle of the game remains the same – any item from the list can win.
Over the long time of its existence, this game has become part of the culture and gradually acquired many options and modifications. For example, one of the intellectual entertainments was the invention of their own versions of the game. Fans of non-transitive leisure quickly got bored with inventing versions with three objects and began to gradually increase their number.
In order for the game to be balanced and all items to remain equivalent, their number must necessarily be odd. Most often there are versions with five items. The most popular five-piece version was Sheldon Cooper’s version of The Big Bang Theory:
Rock, paper, scissors, lizard, Spock.
Stone dulls scissors.
Scissors cut paper.
Paper covers stone.
The lizard poisons Spock.
The stone crushes the lizard.
The scissors cut off the head of the lizard.
The evidence against Spock is written on the paper.
The lizard eats paper.
Spock vaporizes the stone.
Spock breaks the scissors.
Actually this option invented programmer Sam Kass and usability analyst Karen Brila. By the way, Sam Kass writes on his website that he increased the number of items in order to reduce the likelihood of a predictable game, and therefore draw rounds.
There are options for seven, nine and more items. There is even a monstrous version with 101 items, which was invented by artist Dave Lovelace. There is: a power saw, a cockroach, Medusa Gorgon and beer. The list of relationships between objects consists of 5050 lines.
Dave Zobel, in The Big Bang Theory: Science in the Series, gives interesting examples of the relationship between objects from different versions of the game:
Mom’s nagging makes the leader regret that he drove the tiger away.
The guinea pig disarms the dynamite by chewing on the wick.
Playing all these game options with a large number of items is almost unrealistic – you need to at least remember all the gestures, and not everyone can do it. These options are interesting, but completely inapplicable in practice. But the option with five items is quite realistic to come up with and put into practice. This is what we’ll do.
Preparing a diagram
To invent a new version of the game, we need to solve three problems:
Come up with names for things.
Come up with an unambiguous and understandable gesture for each item.
Think of relationships between objects according to a given scheme.
Just like that, coming up with five objects and linking them with relationships in a ring will not work. We also need to consider cross-relationships between them, so that each item is connected to all the others. And it is important to do it right so as not to accidentally make any of the items stronger than others.
This is where the relationship diagram comes in handy. In order to build it, we use the following algorithm:
Arrange five vertices in a circle.
Draw connections between all the objects – without arrows yet.
Place the arrows on the links correctly – from the winning item to the losing item.
To correctly arrange the arrows, you can use the following algorithm:
Divide the chart into two equal vertical sections.
On the connections that are entirely on the left side, draw arrows – from top to bottom.
Rotate the diagram so that the new vertex is on top.
Repeat steps 1-3 until all arrows in the diagram are filled.
For true connoisseurs, I will also give an unfilled diagram for 7 items.
We come up with a habraversion
Now you need to fit objects into the vertices. The difficulty lies in the fact that you need not only to come up with five original items, but also to provide for their relationship according to the arrows in the diagram. There will be ten relationships in total.
To simplify your task a bit, you can use this life hack: start by making a looped set of three items – come up with plausible relationships for them. Then take one item from the resulting list and add two more to it. For the second list, you also need to come up with connections. After that, you can try to compose all the missing relationships between objects. Of course, this must be done in strict accordance with the arrows on our diagram. If it doesn’t work out the first time, then you can “play” with the order of the items or replace one or more of them.
It is also necessary not to forget that the names of the objects will have to be listed in the rhyme. The words should go well with each other. Connections are not important here – in the rhyme, you can list items in any order.
I got this version of the game of five objects:
Mouse, server, developer, cookie, cat.
The mouse is eating a cookie.
The cookie beckons the developer.
The developer carries a mouse.
The server is warming the cat.
The cat catches the mouse.
The mouse gnaws through the wires of the server.
Cookie bombards the server with crumbs.
The server stores developer files.
The developer strokes the cat.
The cat throws a cookie off the table.
It remains only to come up with gestures for each item. Here, too, you can show your imagination and have fun from the heart.
Considering a strategy
In theory, our game is absolutely fair:
Each player acts randomly.
The players act independently of each other.
There are no strong and weak items in the game.
In theory, the best strategy in this game is to be spontaneous, try to show completely random items. But in real life, the gameplay is influenced by many factors that have nothing to do with the rules. The outcome of the game is random only in theory.
Here are a few strategies you can use to turn the odds in your favor:
In the game of a particular opponent, non-random patterns and habits can be recognized. Many people have favorites and dislikes. You can try to calculate them. For example, Sheldon Cooper always showed his favorite Spock.
An interesting psychological feature can be used: in the second round, the player often subconsciously shows the item that could defeat him in the previous round. For example, if in the first round the player showed a stone, then in the next round he would show paper. To win, you need to choose scissors.
Sometimes it helps to use the so-called “Sicilian logic” – to act contrary to the most likely expectations of the enemy. For example, Sheldon can take advantage of the fact that opponents expect him to show Spock.
You can try to quickly react to the figure that the opponent began to form.
This, of course, is the purest “cheating”, but it is not prohibited by the rules. In card games, too, not everything depends on the rules. By the way, the fourth strategy is successfully used by a robot designed at the University of Tokyo in 2013. He defeats a man with a 100% result. To do this, the robot analyzes the movements of the human hand using a high-speed camera. A person is just beginning to form his figure from his fingers, and the robot already knows what the enemy will show.
It is these small imperfections of human nature that can be successfully used to develop your unique winning strategy. Many do just that. By the way, the game “Rock, Paper, Scissors” holds world championships with a solid prize fund. There is an international federation for the game and official rules for the competition.
So, the game “rock, scissors, paper” is not so simple and uncomplicated as it might seem at first glance. There is something to think about here. And have fun at the same time.