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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 Another way | Comment 6 of 8 |
    I solved this in an easier way by first changing the payoffs to straight dividends: the first match pays 2.5 times your bet (if you win), the second 3 times, the third 8 times, and the last 10 times.

    Suppose I want to be paid $240 (a multiple of 2.5, 3, 8, and 10). I would have to bet $96 on the first option, $80 on the second, $30 on the third, and $24 on the last; I would have bet $230, and would get $240 no matter what.

    So, these payoffs would allow me a little bit over a 4% sure income... not very good from the bookie's point of view!

      Posted by e.g. on 2005-11-27 22:00:56
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