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Snakes and ladders

Snakes and ladders

Overview
Snakes and Ladders is an ancient Indian board game
Board game
A board game is a game which involves counters or pieces being moved on a pre-marked surface or "board", according to a set of rules. Games may be based on pure strategy, chance or a mixture of the two, and usually have a goal which a player aims to achieve...

 regarded today as a worldwide classic. It is played between two or more player
Player (game)
A player of a game is a participant therein. The term 'player' is used with this same meaning both in game theory and in ordinary recreational games....

s on a game board having numbered, gridded squares. A number of "ladders" and "snakes" (or "chutes") are pictured on the board, each connecting two specific board squares. The object of the game is to navigate one's game piece from the start (bottom square) to the finish (top square), helped or hindered by ladders and snakes, respectively.
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Encyclopedia
Snakes and Ladders is an ancient Indian board game
Board game
A board game is a game which involves counters or pieces being moved on a pre-marked surface or "board", according to a set of rules. Games may be based on pure strategy, chance or a mixture of the two, and usually have a goal which a player aims to achieve...

 regarded today as a worldwide classic. It is played between two or more player
Player (game)
A player of a game is a participant therein. The term 'player' is used with this same meaning both in game theory and in ordinary recreational games....

s on a game board having numbered, gridded squares. A number of "ladders" and "snakes" (or "chutes") are pictured on the board, each connecting two specific board squares. The object of the game is to navigate one's game piece from the start (bottom square) to the finish (top square), helped or hindered by ladders and snakes, respectively. The historic version had root in morality lessons, where a player's progression up the board represented a life journey complicated by virtues (ladders) and vices (snakes).

The simplicity and seesawing nature of the contest make the game popular with younger children, but the lack of any skill component makes the game less appealing for older players.

Board geometry


The size of the grid (most commonly 8×8, 10×10, or 12×12) varies from board to board, as does the exact arrangement of the snakes and ladders, with both factors affecting the duration of play. As a result, the game can be represented as an absorbing Markov chain
Absorbing Markov chain
In the mathematical theory of probability, an absorbing Markov chain is a Markov chain in which every state can reach an absorbing state. An absorbing state is a state that, once entered, cannot be left....

. Random dice rolls determine game piece movement in the traditional form of the game.

History


Snakes and Ladders originated in India as part of a family of dice board games, including pachisi
Pachisi
Pachisi is a cross and circle board game that originated in ancient India which has been described as the "national game of India". It is played on a board shaped like a symmetrical cross...

 (modern day Ludo). It was known as moksha pAtam or vaikunthapaali or paramapada sopaanam (the ladder to salvation). The game made its way to England and was sold as Snakes and Ladders, then the basic concept was introduced in the United States as Chutes and Ladders (an "improved new version of England's famous indoor sport") by game pioneer Milton Bradley
Milton Bradley
Milton Bradley , an American game pioneer, was credited by many with launching the board game industry in North America with Milton Bradley Company....

 in 1943.

The game as popularly played in ancient India was known as Moksha Patam, and emphasized the role of fate or karma
Karma
Karma in Indian religions is the concept of "action" or "deed", understood as that which causes the entire cycle of cause and effect originating in ancient India and treated in Hindu, Jain, Buddhist and Sikh philosophies....

. A Jain version, Gyanbazi, dates to the 16th century. The game was called Leela
Leela (game)
Leela is a board game with origins in ancient India. The original game was created by Hindu scholars with the intention of teaching moral values, and was a precursor to the modern game Snakes and Ladders....

 and reflected the Hinduism
Hinduism
Hinduism is the predominant and indigenous religious tradition of the Indian Subcontinent. Hinduism is known to its followers as , amongst many other expressions...

 consciousness surrounding everyday life. Impressed by the underlying ideals of the game, a newer version was introduced in Victorian England in 1892.

Moksha Patam was associated with traditional Hindu philosophy contrasting karma and kama, or destiny and desire. It emphasized destiny, as opposed to games such as pachisi, which focused on life as a mixture of skill (free will) and luck. The game has also been interpreted and used as a tool for teaching the effects of good deeds versus bad. The ladders represented virtues such as generosity, faith, and humility, while the snakes represented vices such as lust, anger, murder, and theft. The morality lesson of the game was that a person can attain salvation (Moksha
Moksha
Within Indian religions, moksha or mukti , literally "release" , is the liberation from samsara and the concomitant suffering involved in being subject to the cycle of repeated death and reincarnation or rebirth.-Origins:It is highly probable that the concept of moksha was first developed in...

) through doing good, whereas by doing evil one will inherit rebirth
Reincarnation
Reincarnation best describes the concept where the soul or spirit, after the death of the body, is believed to return to live in a new human body, or, in some traditions, either as a human being, animal or plant...

 to lower forms of life. The number of ladders was less than the number of snakes as a reminder that a path of good is much more difficult to tread than a path of sins. Presumably the number "100" represented Moksha (salvation). In Andhra Pradesh
Andhra Pradesh
Andhra Pradesh , is one of the 28 states of India, situated on the southeastern coast of India. It is India's fourth largest state by area and fifth largest by population. Its capital and largest city by population is Hyderabad.The total GDP of Andhra Pradesh is $100 billion and is ranked third...

, snakes and ladders is played in the name of Vaikuntapali.

In the original game the squares of virtue are: Faith (12), Reliability (51), Generosity (57), Knowledge (76), and Asceticism (78). The squares of vice or evil are: Disobedience (41), Vanity (44), Vulgarity (49), Theft (52), Lying (58), Drunkenness (62), Debt (69), Rage (84), Greed (92), Pride (95), Murder (73), and Lust (99).

Playing


Each player starts with a token on the starting square (usually the "1" grid square in the bottom left corner, or simply, the imaginary space beside the "1" grid square) and takes turns to roll a single die
Dice
A die is a small throwable object with multiple resting positions, used for generating random numbers...

 to move the token by the number of squares indicated by the die roll. Tokens follow a fixed route marked on the gameboard which usually follows a boustrophedon
Boustrophedon
Boustrophedon , is a type of bi-directional text, mostly seen in ancient manuscripts and other inscriptions. Every other line of writing is flipped or reversed, with reversed letters. Rather than going left-to-right as in modern English, or right-to-left as in Arabic and Hebrew, alternate lines in...

 (ox-plow) track from the bottom to the top of the playing area, passing once through every square. If, on completion of a move, a player's token lands on the lower-numbered end of a "ladder", the player moves his token up to the ladder's higher-numbered square. If he lands on the higher-numbered square of a "snake" (or chute), he must move his token down to the snake's lower-numbered square.

If a player rolls a 6, he may, after moving, immediately take another turn; otherwise play passes to the next player in turn. If a player rolls three consecutive 6s, he must return to the starting square (grid "1") and may not move again until rolling another 6. The player who is first to bring his token to the last square of the track is the winner.

A variation exists where a player must roll the exact number to reach the final square (hence winning). Depending on the particular variation, if the roll of the die is too large the token remains in place.

Specific editions


The most widely known edition of Snakes and Ladders in the United States is Chutes and Ladders from Milton Bradley
Milton Bradley Company
The Milton Bradley Company is an American game company established by Milton Bradley in Springfield, Massachusetts, in 1860. In 1920, it absorbed the game production of McLoughlin Brothers, formerly the largest game manufacturer in the United States, and in 1987, it purchased Selchow and Righter,...

 (which was purchased by the game's current distributor Hasbro
Hasbro
Hasbro is a multinational toy and boardgame company from the United States of America. It is one of the largest toy makers in the world. The corporate headquarters is located in Pawtucket, Rhode Island, United States...

). It is played on a 10×10 board, and players advance their pieces according to a spinner rather than a die. The theme of the board design is playground
Playground
A playground or play area is a place with a specific design for children be able to play there. It may be indoors but is typically outdoors...

 equipment—children climb ladders to go down chutes. The artwork on the board teaches a morality
Morality
Morality is the differentiation among intentions, decisions, and actions between those that are good and bad . A moral code is a system of morality and a moral is any one practice or teaching within a moral code...

 lesson, the squares on the bottom of the ladders show a child doing a good or sensible deed and at the top of the ladder there is an image of the child enjoying the reward. At the top of the chutes, there are pictures of children engaging in mischievous or foolish behaviour and the images on the bottom show the child suffering the consequences. There have also been many pop culture versions of the game produced in recent years, with graphics featuring such characters as Dora the Explorer
Dora the Explorer
Dora the Explorer is an American animated television series created by Chris Gifford, Valerie Walsh, and Eric Weiner. Dora the Explorer became a regular series in 2000. The show is carried on the Nickelodeon cable television network, including the associated Nick Jr. channel. It aired on CBS until...

 and SpongeBob SquarePants
SpongeBob SquarePants
SpongeBob SquarePants is an American animated television series, created by marine biologist and animator Stephen Hillenburg. Much of the series centers on the exploits and adventures of the title character and his various friends in the underwater city of "Bikini Bottom"...

.

In Canada the game has been traditionally sold as Snakes and Ladders, and produced by the Canada Games Company
Canada Games Company
Canada Games was a Canadian games manufacturing company, originally based in Brampton, Ontario, before moving to nearby Concord. Its slogan was "The Best in Fun from Canada Games."...

. Several Canadian specific versions have been produced over the years, including version substituting Toboggan
Toboggan
A toboggan is a simple sled which is a traditional form of transport used by the Innu and Cree of northern Canada. In modern times, it is used on snow to carry one or more people down a hill or other slope for recreation. Designs vary from simple, traditional models to modern engineered composites...

 runs for the snakes. With the demise of the Canada Games Company, Chutes and Ladders produced by Milton Bradley/Hasbro has been gaining in popularity.

The most common in the United Kingdom is Spear's Games'
J. W. Spear & Sons
J. W. Spear and Sons was a significant manufacturer of board games during the 20th century. The company was founded by Jacob Wolf Spier in Fürth, near Nuremberg, Germany in 1879, producing goods such as table mats, photo frames, and waste-paper baskets.By the turn of the century, games had become...

 edition of Snakes and Ladders, played on a 10×10 board where a single die is used.

During the early 1990s in South Africa, Chutes and Ladders games made from cardboard were distributed on the back of egg boxes as part of a promotion.

Mathematics of the game



Any version of Snakes and Ladders can be represented exactly as an absorbing Markov chain
Absorbing Markov chain
In the mathematical theory of probability, an absorbing Markov chain is a Markov chain in which every state can reach an absorbing state. An absorbing state is a state that, once entered, cannot be left....

, since from any square the odds of moving to any other square are fixed and independent of any previous game history. The Milton Bradley version of Chutes and Ladders has 100 squares, with 19 chutes and ladders. A player will need an average of 39.6 spins to move from the starting point, which is off the board, to square 100.

In the book Winning Ways the authors show how to treat Snakes and Ladders as an impartial game
Impartial game
In combinatorial game theory, an impartial game is a game in which the allowable moves depend only on the position and not on which of the two players is currently moving, and where the payoffs are symmetric...

 in combinatorial game theory
Combinatorial game theory
Combinatorial game theory is a branch of applied mathematics and theoretical computer science that studies sequential games with perfect information, that is, two-player games which have a position in which the players take turns changing in defined ways or moves to achieve a defined winning...

 even though it is very far from a natural fit to this category. To this end they make a few rule changes such as allowing players to move any counter any number of spaces, and declaring the winner as the player who gets the last counter home. This version, which they call Adders-and-Ladders, involves more skill than the original game.

In culture


The game is a central metaphor of Salman Rushdie's Midnight's Children
Midnight's Children
Midnight's Children is a 1981 book by Salman Rushdie about India's transition from British colonialism to independence and the partition of India. It is considered an example of postcolonial literature and magical realism...

. The narrator describes the game thusly:


All games have morals; and the game of Snakes and Ladders captures, as no other activity can hope to do, the eternal truth that for every ladder you hope to climb, a snake is waiting just around the corner, and for every snake a ladder will compensate. But it's more than that; no mere carrot-and-stick affair; because implicit in the game is unchanging twoness of things, the duality of up against down, good against evil; the solid rationality of ladders balances the occult sinuosities of the serpent; in the opposition of staircase and cobra we can see, metaphorically, all conceivable oppositions, Alpha against Omega, father against mother.

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