snakes_histogram, a MATLAB code which produces histograms of the count, PDF and CDF estimates for the length of a one-player game of Snakes and Ladders, produced by simulating N games.
Snakes and Ladders is a children's game played on a 10x10 numbered board. A player's turn consists of rolling a single die, and moving the indicated number of squares. If the final square is the foot of a ladder, the player moves up to a higher numbered square. If the final square is the mouth of a snake, the player moves downward.
For the one-player version of the game, it is interesting to pose the question of the probability that a particular game will take a certain number of moves.
By adding a square 0, where the player begins, the game board can be modeled as a vector of length 101, and the transitions from one square to another can be modeled by a transition matrix. Most commonly, the entries in row I will be zero except that columns I+1 through I+6 will have the value 1/6. However, rows which correspond to a snake or ladder, and rows for which I+6 is greater than 100, must be handled specially.
This program allows the user to specify the number N of games to simulate. It then creates histograms showing the count, PDF and CDF based on the observed data.
The computer code and data files made available on this web page are distributed under the GNU LGPL license.
snakes_histogram is available in a MATLAB version.
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