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 the, the game, 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)
“Every fact is related on one side to sensation, and, on the other, to morals. The game of thought is, on the appearance of one of these two sides, to find the other: given the upper, to find the under side.”
—Ralph Waldo Emerson (1803–1882)
“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)
“In mathematics he was greater
Than Tycho Brahe, or Erra Pater:
For he, by geometric scale,
Could take the size of pots of ale;
Resolve, by sines and tangents straight,
If bread and butter wanted weight;
And wisely tell what hour o’ th’ day
The clock doth strike, by algebra.”
—Samuel Butler (1612–1680)
“Vanessa wanted to be a ballerina. Dad had such hopes for her.... Corin was the academically brilliant one, and a fencer of Olympic standard. Everything was expected of them, and they fulfilled all expectations. But I was the one of whom nothing was expected. I remember a game the three of us played. Vanessa was the President of the United States, Corin was the British Prime Minister—and I was the royal dog.”
—Lynn Redgrave (b. 1943)