Bayes Pays Off.

In our stats class today, to make it fun, our professor actually did the experiment described in the last post, "Bayes Breaks Down", and I was lucky enough to be the one chosen to make the decision. I opened the envelope and it contained £12 - a tenner and a two-pound coin. I reasoned that if the other contained twice as much, it would require at least two coins (since there are no £4 coins, and no bills smaller than £5), whereas if it contained £6, it could also be done with a single note and single coin. Since he would have chosen the amounts in the envelopes to be as indistinguishable as possibly before being opened, it's unlikely that he would have put two coins in one and not in the other. So I chose to keep the first envelope.

It happens I was right. Sometimes priors pay off.