So my 4 year old daughter was sick yesterday and I spent part of the afternoon playing chutes and ladders with her.  (She won every game because there is apparently a law in my house that the sick child always wins the game).

So I got to thinking about how many turns is the typical game of chutes and ladders.  And also what’s the least amount of spins you need to finish the game.

So like every good father, I wrote a simulation!

So first, I wanted to know the distribution of the number of turns it takes a single player to complete the game.  I simulated the game 10000 times and found a median of 30 spins with an average of 35.84 spins.  In the 10000 simulations I performed the largest number of spins was 243 (I would have quit at about 50 spins) and the lowest number was 7 spins, which happened 21 times in the 10000 simulations.

You can see a histogram of the distribution of the the number of turns it would take a single player to complete the game.

And for fun, here is one way to win the game in 7 moves.  The spins in the game below are 1, 6, 6, 1, 1, 6, 6.  (Some other ways to do it include: (4, 6, 2, 6, 6, 6, >3) and (4, 6, 3, 5, 6, 5, 6), with this second one actually including the player hitting a slide!)

But most people don’t play chutes and ladders by themselves.  So how long will the game take before anyone you are playing with wins the game? If you have two people the average number of turns is 24.1 with a median of 21 turns.  Three players will last an average of 19.9 turns with a median of 18. and four players will average 17.66 turns with a median of 54.

So, that it’s.  Really important summer stuff that I’ve been doing.

If you are interested, here is another article about chutes and ladders and here is a link to my code is here on github.

Cheers.