# Optimized dart throwing and other games

Posted to Statistical Visualization  |  Tags: ,  |  Nathan Yau

If you play darts just trying to hit the bullseye, you aren’t playing for maximum output. Don’t fret though. DataGenetics is here to help with mathematical advice on how to play the game based on your skill level (Update: This is very similar to the dart work by Ryan Tibshirani, et al.):

The optimal strategy for aiming depends on your skill as darts player. A very skillful player should aim for the middle of the triple 20; Much of the time he will hit his target, and the times he misses will be few enough that his average score will still be high.

A very poor player should aim close to the bullseye, as just hitting the board will be an achievement (and a scoring one at that!). Aiming for the center maximizes the chances of hitting something.

But what happens between these two extreme?

I was a kid the last time I threw darts, and I was more interested in throwing them as high as I could in the air watching them stick into the grass. Maybe it’s time to try it the right way.

• T.Wijbenga

Interesting stuff. On the non-visualization side of darts, I always wondered how they came to the particular sequence of numbers of a dartboard. Around 10 years ago, I stumbled on this article, which tries to find a explanation: http://www.mathpages.com/home/kmath025.htm.

• I am shocked that they did not reference the work by
Ryan Tibshirani, Andrew Price, and Jonathan Taylor. Their original work is here:
http://www.stat.cmu.edu/~ryantibs/papers/darts.pdf
The research received a lot of press because it appeared in Wired magazine (http://www.wired.com/magazine/2009/11/st_darts/) and was picked up by some other press outlets. The Wired article is titled “Darts for Geeks” and the blog you reference is titled “A Geek Plays Darts.”

A simplified version also appeared recently in Significance magazine, which is published by the Royal Statistical Society.

• tushar rao

Thanks for the Paper link. Its good that you pointed out their referencing mis-gauge.

• Andrew Pariser

Thanks for pointing this out so quickly, Rick!

Ryan is a friend of mine from graduate school. He’s even written a user-friendly website regarding his research:
http://www.stat.cmu.edu/~ryantibs/darts/

Nathan – maybe you can change the link on your post to give credit to the original researchers?

• Excellent, and in their paper (page 7) they allow for covaried / asymmetrical Gaussian errors *and* tell you how to estimate your own errors.

• Kevin Carlson

This sounds dangerously close to Operations Research.
More of the same please! :)

• Hmm. Not sure it helps for cricket (darts game) which I play mostly and so do most people I know.

• So they’re assuming Gaussian errors. I’m almost certain my errors are asymmetrical. In particular I think right-handed and left-handed players have different error distributions.

As a right-handed player, I have the hardest time hitting the bottom-left of the board, and it’s relatively easier along the same diagonal as my arm’s motion.

My errors are autocorrelated but that’s more of a mental-game.

Anyway, I thought they were going to use actual data about real player errors, rather than assume a theoretical distribution.

• This is neither the original nor the full solution, but someone has figured out how to optimally play Monopoly based on Markov transition matrices.

http://www.math.yorku.ca/Who/Faculty/Steprans/Courses/2042/Monopoly/Stewart4.html