For the PerplexusBowl match between the Pascal Probabilities and the Random Results, a bookie was offering the following payoffs:
PP to win in normal time, 3 to 2
RR to win in normal time, 2 to 1
PP to win in overtime, 7 to 1
RR to win in overtime, 9 to 1
(The first line means that if you bet $2 on PP to win in normal time, and it does, you get your money back plus $3.)
Without knowing anything about football or the involved teams or the actual probabilities, can you show why these payoffs are illogical?
In bookie terms: the market has been framed with a negative percentage A very clever gambler (or mathematician) could make a nice profit no matter what the result by betting as follows
PP to win in normal time, $308.87 at 3 to 2 (wins $772.17) RR to win in normal time, $257.39 at 2 to 1 (wins $772.17) PP to win in overtime, $96.52 at 7 to 1 (wins $772.17) RR to win in overtime, $77.22 at 9 to 1 (wins $772.20)
So for an outlay of $740 dollars you are guaranteed a return of at least $772.17.
Increasing the bets in the same ratio would increase the profit.