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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.)
    Solution betting spree | Comment 1 of 8

    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.

     


      Posted by Vernon Lewis on 2005-11-26 08:02:57
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