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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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 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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