Consider the model of betting markets discussed in lecture. The bookie charges a standard vig of 10% (or v = 0.1). The bookie chooses a spread to determine p, the probability that the spread is covered.

a) What is bettor's expected profit function when the spread is such that the bettor wins with probability p. (Think about the bettor's wins and losses.)

b) What is the value of p that makes the bettor's expected profit equal to zero? (In other words, find the bettor's break even point.)

c) Levitt (2004) notes: "It would be surprising to observe price distortions so large that simple strategies (e.g. always bet the underdog) could yield a positive profit." Out of a total of 100 games, what is the smallest number of games for which the bookie can allow the favorite to cover the spread such that always betting against the favorite does not yield positive profits for the bettor? Briefly explain.