Another good one from Scott Ogawa.  It’s the Creampuff Dilemma.  A college football coach has to set its pre-season non-conference schedule, thinking ahead to the end-of-season polling that decides Bowl Bids.  A schedule stocked with creampuffs means lots of easy wins.  But holding fixed the number of wins, a tough schedule will bolster your ranking.

Here’s Scott’s model.  Each coach picks a number p between 0 and 1.  He is successful (s=1) with probability p and unsuccessful (s=0) with probability 1-p.  These probabilities are independent across players.  (Think of these as the top teams in separate conferences.  They will not be playing against each other.)

Highest s-p wins.