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.