A similar conundrum is the problem of the two envelopes on a quiz show. The winner of a quiz chooses one of two envelopes, and looks at the value of the cheque therein. Say that it is £1,000. He knows that the larger prize is twice the smaller prize, so the other envelope must contain £500 or £2,000. He is given the option to change or keep the cheque he has. Most would change, as they gain £1000 or lose £500. But it does not matter, and this is because one gains the logarithm of 2 or loses the logarithm of a half, so one is risking 0.30103 to gain 0.30103.
And yes, mathematically, it would be make no difference if, after opening an envelope with £100, the other one had one penny or £1,000,000. There he would be lose -4 (the log of the ratio) to gain +4 (the log of the ratio, again). And I am surprised that anbody would think otherwise. I thought smart minds use Betfair.
Does any of the above make sense to any of you? Here are some similar questions and answers from an old thread I fondly remember..http://archives2.twoplustwo.com/showflat.php?Cat=0&Number=153855&page=0&fpart=1&vc=1