snakes_and_ladders_simulation, an Octave code which simulates a one-player game of Snakes and Ladders, to produce histograms of the count, PDF and CDF estimates for the length of a one-player game.

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 MIT license


snakes_and_ladders_simulation is available in a MATLAB version and an Octave version.

Related Data and Programs:


octave_simulation, an Octave code which uses simulation to study card games, contests, and other processes which have a random element. Usually, the purpose is to try to predict the average behavior of the system over many trials.


  1. Steve Althoen, Larry King, Kenneth Schilling,
    How long is a game of Snakes and Ladders?,
    The Mathematical Gazette,
    Volume 77, Number 478, March 1993, pages 71-76.
  2. Nick Berry,
    A Mathematical Analysis of Snakes and Ladders,

Source Code:

Last modified on 05 December 2022.