Chutes & Ladders

Chutes & Ladders is a game by Hasbro for children. There are 100 squares on the board and the child advances the number of spaces that is determined by a spinner numbered 1 through 6. If the child lands at the bottom of a ladder, they immediately climb to the top. If the child lands at the top of a chute, they immediately slide to the bottom. The game is over when the child lands exactly on square 100.

The Problem

For purposes of entertainment, we wish to know how long it takes to play a Chutes & Ladders game. Is it something that is over very quickly or something that takes a long time to play? The problem is that this is another of those games like craps that theoretically could go on forever. In actual practice, of course, it doesn't, eventually someone ends up at square 100 and the game is over.

Type of Simulation

We're looking for the average number of times it takes to play a game. That means that we need to simulate the game and record the number of moves that it takes. We will repeat this process several times (the more the better) and then find the average of all the values.

This problem is not asking us to find a probability, so we don't simply record the results as success or failure. In fact, that would make little sense here since ultimately, the game is finished and the success rate is 100%.

The Simulation

This game is a prime candidate for computer simulation because of the length of the time it takes to play a game. Unfortunately when a computer is simulating a complex game like Chutes & Ladders, someone has to write the program to do that. Fortunately, Macromedia has written a program called Flash and I have written a version of Chutes & Ladders called Ups & Downs.

Play the game several times and record the number of moves it takes to finish each game. Then, when you're done, find the mean of those values you've recorded.

Return to Simulation Page