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Boneheaded Bookie (Posted on 2005-11-26) Difficulty: 3 of 5
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?

    See The Solution Submitted by Federico Kereki    
    Rating: 4.0000 (5 votes)

    Comments: ( Back to comment list | You must be logged in to post comments.)
    Some Thoughts Some thoughts Comment 8 of 8 |
    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
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