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BS: An amusing little problem |
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Subject: RE: BS: An amusing little problem From: GUEST,Grishka Date: 10 Feb 13 - 02:52 PM My feeling (not knowledge) is that if you know nothing about the probability of any particular n or K being chosen, you cannot say anything about the probability of the value of the other check. If however this probability is known (or you can make a reasonable guess judging by the issuer's generosity), it cannot be equal for all those infinitly many possible n. From your K, you can then calculate the probability for the other check being of double value, which will rarely be 50%. If my K is high, I would keep that check. If it is very low, I may take the other one. BK, do you know the correct answer? Do we have mathematicians here? |
Subject: RE: BS: An amusing little problem From: SINSULL Date: 10 Feb 13 - 09:58 AM I'm from NYC. I'd take both checks and leeave. SINS |
Subject: RE: BS: An amusing little problem From: kendall Date: 10 Feb 13 - 08:20 AM I wouldn't place any value on either check from a stranger. |
Subject: RE: BS: An amusing little problem From: DMcG Date: 10 Feb 13 - 06:21 AM Sorry for the typos! |
Subject: RE: BS: An amusing little problem From: DMcG Date: 10 Feb 13 - 06:20 AM Its an interesting to which the answer is be no means too obvious. It is, I hope, clear that if you played the game sufficient times the average return per game would be the same whether you always switched or never switched. Equally it is clear that you could write two cheques like that and make the offer. If is also true that on an individual game by choosing the face-down check instead of the one you've revealed, you stand to gain K dollars at the risk of losing only K/2. So the flaw must be in the assertion that it is therefore sensible to switch. And it is, since we agreed that overall switching brings no benefit. SO we have a mismatch in our understanding of potential benefit for a single game and the impact that has on out our probable benefit. |
Subject: RE: BS: An amusing little problem From: SPB-Cooperator Date: 10 Feb 13 - 05:59 AM I haven't read up on game theory since te early 80s |
Subject: BS: An amusing little problem From: BK Lick Date: 10 Feb 13 - 04:11 AM Suppose I present you with two personal checks made out to you and offer to gift you with whichever one of them you choose. I place the checks face down before you, labeled A and B on their backs, and stipulate that their values are 2n and 2n+1 dollars for some integer value of n. I invite you to turn one of them face up and then choose one of them to keep as a gift from me. Suppose that the check you turn face up has value K. Then the other check is worth either 2K or K/2 and therefore by choosing the face-down check instead of the one you've revealed, you stand to gain K dollars at the risk of losing only K/2. Thus it appears that whatever the value of the check you turn over, it is to your advantage to choose the other. Suppose now that the game is changed and you must make your choice without seeing the value of either check. Say you choose check A. Whatever its value, by the reasoning above it's to your advantage to change your mind and choose check B. But then, of course, you should change back to check A, and so forth -- but this is surely absurd.What's going on here? Why should the act of revealing the value of one check make it advisable to choose the other? —BK |