Snakes and ladders

Snakes and ladders, or chutes and ladders, is a classic children's board game.^[1] It is played between 2 or more players on a playing board with numbered grid squares. On certain squares on the grid are drawn a number of "ladders" connecting two squares together, and a number of "snakes" or "chutes" also connecting squares together. 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 chutes and the ladders: both of these may affect the duration of game play. As a result, the game can be represented as a state absorbing Markov chain.^[2]

The game was sold as Snakes and ladders in England before Milton Bradley introduced the basic concept in the United States as Chutes and ladders, an "improved new version of ... England's famous indoor sport."^[2] Its simplicity and the see-sawing nature of the contest make it popular with younger children, but the lack of any skill component in the game makes it less appealing for older players.

History

Snakes and Ladders originated in India as a game based on morality called Vaikuntapaali or Paramapada Sopanam (the ladder to salvation).^[3] This game made its way to England, and was eventually introduced in the United States of America by game pioneer Milton Bradley in 1943.^[3]

The game was played widely in ancient India by the name of Moksha Patamu, the earliest known Jain version Gyanbazi dating back to 16th century. The game was called Leela and reflected the Hinduism consciousness around everyday life. Impressed by the ideals behind the game, a newer version was introduced in Victorian England in 1892, possibly by John Jacques of Jacques of London.

Moksha Patamu was perhaps invented by Hindu spiritual teachers to teach children about the effects of good deeds as opposed to bad deeds. The ladders represented virtues such as generosity, faith, humility, etc., and the snakes represented vices such as lust, anger, murder, theft, etc. The moral of the game was that a person can attain salvation (Moksha) through performing good deeds whereas by doing evil one takes rebirth in lower forms of life (Patamu). The number of ladders was less than the number of snakes as a reminder that treading the path of good is very difficult compared to committing sins. Presumably the number "100" represented Moksha (Salvation). In Andhra Pradesh, snakes and ladders is played in the name of Vaikuntapali.

The squares of virtue on the original game are Faith (12), Reliability (51), Generosity (57), Knowledge (76), Asceticism (78); the squares of 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

Milton Bradley Chutes and Ladders game board c. 1952 showing good deeds and their rewards and bad deeds and their consequences.

Each player starts with a token in 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 to move the token by the number of squares indicated by the die roll, following a fixed route marked on the gameboard which usually follows a boustrophedon (ox-plow) track from the bottom to the top of the playing area, passing once through every square. If, on completion of this move, they land on the lower-numbered end of the squares with a "ladder", they can move their token up to the higher-numbered square. If they land on the higher-numbered square of a pair with a "snake" (or chute), they must move their token down to the lower-numbered square. A player who rolls a 6 with their die may, after moving, immediately take another turn; otherwise, the play passes to the next player in turn. If a player rolls three 6s on the die, they return to the beginning of the game and may not move until they roll another 6. The winner is the player whose token first reaches the last square of the track.

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 (which was purchased by the game's current distributor Hasbro). 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 equipment—children climb ladders to go down chutes. The artwork on the board teaches a morality 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 behavior 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 and SpongeBob SquarePants.

In Canada the game has been traditionally sold as Snakes and Ladders, and produced by the Canada Games Company. Several Canadian specific versions have been produced over the years, including version substituting Toboggan runs for the snakes.^[4] 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' edition of Snakes and Ladders, played on a 10x10 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

The cumulative probability of finishing a game of Chutes and Ladders by turn N.

Any version of Snakes and Ladders can be represented exactly as a Markov chain, 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. The game can be won in as few as 7 rolls.

In the book Winning Ways the authors show how to treat Snakes and Ladders as an impartial game in combinatorial game theory 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 any player to move any counter any number of spaces, and declaring the winner to be the one who gets the last counter home. This version, which they call Adders-and-Ladders, involves more skill than does the original game.

In culture

The game is a central metaphor of Salman Rushdie's Midnight's Children. 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.^[5]

Notes

References

• Augustyn, Frederick J. (2004). Dictionary of toys and games in American popular culture. Haworth Press. ISBN 0789015048.

External links

• Hasbro's official Chutes and Ladders page
• Mathematical analysis of Chutes and Ladders
• Perl software to generate statistics for Chutes and Ladders
• Snakes and ladders at BoardGameGeek
• Jain version of Snakes and Ladders explained in an interactive demonstration hosted by the Victoria and Albert Museum
• Leela, the Game of Knowledge, Hindu version
• Shatranj Irfani Indian Sufi version XIX century