- Snakes and ladders
title = Snakes and ladders
players = 2+
ages = 3+
setup_time = negligible
playing_time = 15-45 minutes
complexity = simple
strategy = none
random_chance = total
skills = counting
Snakes and ladders, or Chutes and ladders, is a classic children's
board game. [ [http://boardgames.about.com/od/gamehistories/p/chutes_ladders.htm About.com - Chutes and Ladders] ] 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.cite journal | author = S. C. Althoen, L. King, K. Schilling | year = 1993 | month = March | title = How Long Is a Game of Snakes and Ladders? | journal = The Mathematical Gazette | volume = 78 | issue = 478 | pages = 71–76 | doi = 10.2307/3619261 | accessdate = 2007-09-19]
The game was sold as "Snakes and ladders" in
Englandbefore Milton Bradleyintroduced the basic concept in the United Statesas "Chutes and ladders", an "improved new version of ... England's famous indoor sport." 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.
Snakes and ladders originated in India as a game based on morality called Vaikuntapaali or Paramapada Sopanam (the ladder to salvation). Augustyn, pages 27-28] This game made its way to
England, and was eventually introduced in the United States of Americaby game- pioneer Milton Bradleyin 1943.
The game was played widely in ancient
Indiaby the name of Moksha Patamu, the earliest known Jain version Gyanbazidating back to 16th century. The game was called "Leela" - and reflected the Hinduismconsciousness around everyday life. Impressed by the ideals behind the game, a newer version was introduced in Victorian Englandin 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).
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
boustrophedontrack 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 where it is, or the token may proceed to the final square and then go backwards until it has transversed the same number of squares as the die shows. In some variations, there is one space with a ladder that leads directly to the final space.
The most widely known edition of Snakes and Ladders in the USA is "Chutes and Ladders", produced by 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 rather than a die. The theme of the board design is playgroundequipment--children climb ladders to go down chutes. The artwork on the board teaches a moralitylesson, 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 Explorerand 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 Tobogganruns for the snakes. [ [http://www.gamesmuseum.uwaterloo.ca/VirtualExhibits/Whitehill/snakes/index.html ELLIOTT AVEDON MUSEUM & ARCHIVE OF GAMES - Snakes and Ladders] ] With the demise of the Canada Games Company "Chutes and Ladders" produced by Milton Bradley/Hasbro has been gaining in popularity.
A version sold as "Snakes & Ladders" is available from
Cardinal Gamesin both Canada and the United States. [ [http://www.cardinalgames.com/ Cardinal No.58318] ]
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
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. In the book " Winning Ways" the authors show how to treat Snakes and Ladders as a (loopy) impartial gamein combinatorial game theoryeven though it is very far from a natural fit to this category. To this end they make a few "minor" 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. It is hard to deny that this version, which they call "Adders-and-Ladders", involves more skill than does the original game.
* Augustyn, Frederick J. (2004). "Dictionary of toys and games in American popular culture". Haworth Press. ISBN 0789015048.
* [http://www.tradgames.org.uk/games/Moksha-Patamu.htm History of Snakes and Ladders] at tradgames.org
Sufi[http://ourworld.compuserve.com/homepages/ABewley/chessboard.html Game of the Gnostics]
*Shatranj Irfani [http://www.untiredwithloving.org/snakes_ladders.html Indian Sufi version XIX century]
Indian version of [http://www.hinduonnet.com/thehindu/thscrip/print.pl?file=2004030600170300.htm&date=2004/03/06/&prd=yw& Snakes and Ladders]
*Hasbro's official [http://www.hasbro.com/default.cfm?page=ps_results&product_id=8626 Chutes and Ladders] page
* [http://www.math.niu.edu/~rusin/uses-math/games/chutes/ Mathematical analysis] of Chutes and Ladders
* [http://www.amazon.com/gp/product/0892814195 Leela: The Game of Self-Knowledge] by Harish Johari
* cite web |publisher=
Victoria and Albert Museum
title= Online game of snakes and ladders based closely on a Jain board game
Wikimedia Foundation. 2010.