tag:blogger.com,1999:blog-25562705.post1821961416069491156..comments2023-10-20T12:34:59.317-04:00Comments on Adventures in Computation: Alice, Bob, a Simple Game, a Surprise, and a ParadoxAaronhttp://www.blogger.com/profile/09952936358739421126noreply@blogger.comBlogger3125tag:blogger.com,1999:blog-25562705.post-88456689295732730422007-10-11T12:55:00.000-04:002007-10-11T12:55:00.000-04:00Hey Aaron, I think Jonathan might have a different...Hey Aaron, I think Jonathan might have a different solution that works and doesn't use the fact that the uniform prior is invalid. He defines Q as the value of the smaller envelope, not the value in the envelope that you see. Then with prob 0.5 you will get Q in your envelope and switching gives you +Q, and prob 0.5 you get 2Q and switching gives you -Q. So expected value of switching is 0.Sam Ganzfriedhttps://www.blogger.com/profile/01505796181499715913noreply@blogger.comtag:blogger.com,1999:blog-25562705.post-4808782177425460202007-10-08T00:23:00.000-04:002007-10-08T00:23:00.000-04:00Hi Jonathan. The standard two-envelopes problem (i...Hi Jonathan. The standard two-envelopes problem (in which one envelope contains twice as much as the other) can be "explained away" by pointing out that if the player is really calculating that 50% of the time, the other envelope is larger <I>whatever</I> he sees in the envelope he picks, then he is implicitely using as his prior distribution a uniform distribution over the integers, which is not a legal distribution. However, this variant shows that that isn't 'really' the problem. It is of course a problem, but the same paradox can be created without assuming an illegal distribution.Aaronhttps://www.blogger.com/profile/09952936358739421126noreply@blogger.comtag:blogger.com,1999:blog-25562705.post-66629892727427472022007-10-07T23:23:00.000-04:002007-10-07T23:23:00.000-04:00Printed that one out... It will take some reading....Printed that one out... It will take some reading. It's the awareness of each other's strategies that really is bothering me.<BR/><BR/>The two envelopes problem (which you mention at the end) doesn't have a nice solution on the wikipedia link you included.<BR/><BR/>I have claimed that 50% of the time you have Q, and will gain Q, and 50% of the time you have 2Q, and will lose Q, leaving me with no incentive to switch. <BR/><BR/>I use this puzzle/paradox to bother my (high school) students.Anonymousnoreply@blogger.com