In: Math
Alfraed and Broetschen have each put $500 into a pool and bet on the winner of the 2057 Stanley cup which goes to the first team to win 4 games out of seven matches. All other teams having been disbanded due to dental injuries, the contest is between the Waterloo Weirdos and the Kitchener Klutzes and after one game, Kitchener is ahead one game to zero in the best of 7 final. Alfraed, who cleverly bet on Kitchener, wants out of the bet, since he needs money immediately to cover a poker debt to a sadistic biker in Accounting.
a. Assuming the teams are evenly matched, what is the probability that Alfraed would win the total stake ($ 1000) if he continued?
b. What would be a fair division of the stakes (the total amount at stake is $1000) if the bet is terminated? By how much does Alfraed profit from the bet in this case?