An English soccer team plays a series of matches again different opponents, of varying ability. A bookmaker offers odds for each match as to whether it will be a home win, away win, or draw. Part-way through the season, the team has played n matches, and has drawn k of them, which is more than might be expected from the odds. What is the probability that the bookmaker is mis-pricing the odds on these matches, rather than just being unlucky? If the bookmaker continues to price the team's remaining matches in a similar way, and I bet $1 that each one will be a draw, what is my expected return?
As an added bonus I will email the name of the team to the author of the best answer :-)