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 clever gambler (or mathematician) could make a profit no matter what the result by betting as follows
PP to win in normal time, $300 at 3 to 2 (wins $750)
RR to win in normal time, $260 at 2 to 1 (wins $780)
PP to win in overtime, $100 at 7 to 1 (wins $800)
RR to win in overtime, $80 at 9 to 1 (wins $800)
So for an outlay of $740 dollars you are guarenteed a return of at least $750.
Increasing the bets in the same ratio would increase the profit.