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?

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