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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)

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 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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