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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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 better betting spree (with apologies to Vernon) | Comment 3 of 8 |

In bookie terms: the market has been framed with a negative percentage A very clever gambler (or mathematician) could make a nice profit no matter what the result by betting as follows

PP to win in normal time, \$308.87 at 3 to 2 (wins \$772.17) RR to win in normal time, \$257.39 at 2 to 1 (wins \$772.17) PP to win in overtime, \$96.52 at 7 to 1 (wins \$772.17) RR to win in overtime, \$77.22 at 9 to 1 (wins \$772.20)

So for an outlay of \$740 dollars you are guaranteed a return of at least \$772.17.

Increasing the bets in the same ratio would increase the profit.

 Posted by Mindy Rodriguez on 2005-11-26 21:25:16

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