sodawater
Joined: May 14, 2012
• Posts: 3321
January 15th, 2015 at 4:23:55 PM permalink
There is an online game of capture-the-flag where players are assigned randomly to a team of four: red or blue.

After 493495 decisive games, red has won 250545 and blue has won 242950.

The probability of the red teams doing this well or better by pure chance is 1.5383258×10^-27 -- so basically, impossible.

This seems to prove that the players of this game play better when on the red team than on the blue team. Possibly because red is considered the more aggressive color?

Game stats from: http://tagpro.me
Wizard
Joined: Oct 14, 2009
• Posts: 23732
January 15th, 2015 at 5:34:28 PM permalink
I just checked and the totals, not counting ties, are:

Red 250629
Blue 244693
Total 495322

I show that red is 8.43 standard deviations ahead of expectations. The probability of luck that good, or better, in a fair game is 1 in 60,035,983,156,335,600.

It's not whether you win or lose; it's whether or not you had a good bet.
sodawater
Joined: May 14, 2012
• Posts: 3321
January 15th, 2015 at 5:54:23 PM permalink
Thanks, Wizard.

What did I do wrong in my math that we got such different numbers? I used this link to come up with my probability -- http://www.wolframalpha.com/input/?i=chances+of+250545+heads+in+493495+flips -- since the chances of winning a fair game not counting ties is 0.5