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?

Frederico had asked to show why the payoffs are illogical without knowing anything about football, the teams involved, or the actual probabilities.
I do not think this can be accomplished without knowing the rules of the game and the probabilities involved. For instance, suppose the rules of the game resulted in 99% of any all games played to
end in a tie, to include those games that proceeded into overtime. What is the probability a bettor could win any money with placing any combination of the bets offered?
Even knowing in realityt that ties have a small probability of occurrance, they do exist. Thus - contrary to the explaination in the problem's solution - no actual bet limited to those that are offered is ascertained to have a positive return. 

Posted by Dej Mar on 2013-04-11 05:15:04