Mathematics of The Game
Any version of Snakes and Ladders can be represented exactly as an absorbing 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 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 players to move any counter any number of spaces, and declaring the winner as the player who gets the last counter home. Unlike the original game, this version, which they call Adders-and-Ladders, involves skill.
Read more about this topic: Snakes And Ladders
Famous quotes containing the words mathematics of, mathematics and/or game:
“Why does man freeze to death trying to reach the North Pole? Why does man drive himself to suffer the steam and heat of the Amazon? Why does he stagger his mind with the mathematics of the sky? Once the question mark has arisen in the human brain the answer must be found, if it takes a hundred years. A thousand years.”
—Walter Reisch (1903–1963)
“Why does man freeze to death trying to reach the North Pole? Why does man drive himself to suffer the steam and heat of the Amazon? Why does he stagger his mind with the mathematics of the sky? Once the question mark has arisen in the human brain the answer must be found, if it takes a hundred years. A thousand years.”
—Walter Reisch (1903–1963)
“Neighboring farmers and visitors at White Sulphur drove out occasionally to watch ‘those funny Scotchmen’ with amused superiority; when one member imported clubs from Scotland, they were held for three weeks by customs officials who could not believe that any game could be played with ‘such elongated blackjacks or implements of murder.’”
—For the State of West Virginia, U.S. public relief program (1935-1943)