After dozens of mindless games of Chutes and Ladders to appease my kids, and seemingly countless times moving up and down the board, I started to wonder: "How many average turns do I take in this tortuous (and torturous) game?"
This is in the same vein as the equally important question: "How many licks does it take to get the center of a tootsie pop?" but that's not game related, so not worth our time.
After mulling it over every game, I finally decided to find it out via a program that ran a simulation 1,000,000 times. Yes, these stats are worthless, but I'll share them in the off chance that others are in the same boat in an attempt to validate my efforts.
Our family plays on the "standard board," as seen here. The pictures on our board are different, but the chutes and ladders are in the same place...
Given this board, and playing with standard rules (must land exactly on the final space) here are the stats I determined, which are per player...
Average turns: 40
Average ladders: 3.5
Average slides: 4.4
Minimum moves possible: 7
The maximum moves, in theory, could be infinite, so it's hardly worth mentioning that the max in my simulation was ~300. (Yet I still mentioned it, in continuing with the worthless info theme). But we can determine your chances of finishing a game within so many moves. Again, these are per player.
7 (minimum) moves: 0.05%
10 moves: 2.5%
20 moves: 22.3%
30 moves: 44.5%
40 (average) moves: 63.4%
50 moves: 75.2%
60 moves: 83.4%
70 moves: 88.6%
80 moves: 92.3%
90 moves: 94.7%
100 moves: 96.5%
So what have we learned?
If you play Chutes and Ladders solo, not only is it pathetic (as, say, someone hypothetically writing a program to figure out worthless stats) but there is a remote chance you could be playing for a very long time.
If you play with others, chances are better that someone will finish sooner, but then you have to contend with the total number of player moves and passing around the spinner. And that's not even taking into account the necessary potty breaks, but little Johnny and grandma can't help it.
Conclusion: When playing Chutes and Ladders, it will usually feel like it takes longer than it should. Of course, we already knew that, but now we understand why.
- Last edited Fri Mar 21, 2014 5:25 pm (Total Number of Edits: 1)
- Posted Fri Mar 21, 2014 5:13 pm
I love projects like this.
See also: http://datagenetics.com/blog/november12011/
Turns out when you remove the "land by exact count" requirement for the 100 space, it cuts the average turn count down to around 20.