The rationalist in me wishes we would just have competitive coin flipping and get it over with.
That would be awesome. However, it would not have the results you expect at all. I can bias a coin that I flip to about 60%; some professional magicians can do 95%+.
Do you have any sources for this?
http://blogs.scientificamerican.com/guest-blog/2011/09/22/cognitive-biases-in-sports-the-irrationality-of-coaches-commentators-and-fans/