General Betting
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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?
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?
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But for a large sample size, if you always take the option to change, in the long term your return will be £1250.
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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 |