tag:blogger.com,1999:blog-32371144.post5117258504480827003..comments2024-03-22T19:23:04.610-04:00Comments on Room for Doubt: Two EnvelopesLev Reyzinhttp://www.blogger.com/profile/09629175455869565423noreply@blogger.comBlogger5125tag:blogger.com,1999:blog-32371144.post-47533181495507784782010-05-17T15:04:19.753-04:002010-05-17T15:04:19.753-04:00You have to identify the random events first.
I h...You have to identify the random events first.<br /><br />I have two envelopes: red and blue and I randomly pick one envelope to put the higher amount in. This is the random event that happens first. (Let's say I picked blue.)<br /><br />Secondly, you pick one envelope at random, say, red. This is the second and *final* random event.<br /><br />There are *no more random events*. No matter how much you'd like to believe that "the other envelope has X% chance", it does not since money doesn't teleport between envelopes while you keep changing your mind. Everything's been already decided.Anonymousnoreply@blogger.comtag:blogger.com,1999:blog-32371144.post-65884792241006568942010-05-15T15:54:17.407-04:002010-05-15T15:54:17.407-04:00I'm sorry, Bernard Kirzner, M.D, but I do not ...I'm sorry, Bernard Kirzner, M.D, but I do not understand your argument at all -- especially 1) when you say the difference in the amount of money in the envelopes has nothing to do with which has more and 2) when you say "270-30 = $150."<br /><br />Also, as I've noted, the $30 and $270 example isn't well defined. You should read to the bottom of my post, or to my next post.<br /><br />One last thought -- in my view, doing math formally is never a bait and switch. In fact, when you think about the problem sufficiently formally (see my next post), the paradox resolves.Lev Reyzinhttps://www.blogger.com/profile/09629175455869565423noreply@blogger.comtag:blogger.com,1999:blog-32371144.post-22043242307476165132010-05-15T14:51:22.477-04:002010-05-15T14:51:22.477-04:00Wrong. Wrong. Wrong.
I love you and your site, bu...Wrong. Wrong. Wrong.<br /><br />I love you and your site, but on this one you are mixing up calculations about the difference between the two envelopes in absolute terms (270-30=240), in relative terms, and on average. <br /><br />If I switch every time or if I stay every time, my long term odds stay the same. <br /><br />On average over time I will hit somewhere near 30 half the time and 270 somewhere near half the time. On average I will make 270-30=$150...BUT THIS IS SO WHETHER I SWITCH OR STAY. BOTH CHOICES HAVE THE SAME LIKELIHOOD OF 1/3X OR 3X, I.E. 50%. <br /><br />The fatal flaw in this mathematics excercise is that figuring out the differences and averages mathematically HAS NOTHING TO DO WITH WHICH ENVELOPE HAS THE BIGGER OR SMALLER AMOUNT OF MONEY IN IT. <br /><br />It's a bait and switch, seemingly about the choice of envelopes, but really just a mathematical distraction with mathematical formulae from the equal choices of envelope switching (or holding.) <br /><br />Falsifiability means looking at what information would disprove the hypothesis. Having the same odds of succes by staying, disproves the wisdom, really the advantage, of switching. QEDBernard Kirzner, M.D.noreply@blogger.comtag:blogger.com,1999:blog-32371144.post-43478439738482917312010-05-05T09:03:18.072-04:002010-05-05T09:03:18.072-04:00I think you're right, but it still seems parad...I think you're right, but it still seems paradoxical. You choose the envelope *randomly* between the two, but gain by switching.<br /><br />A new post on this problem coming soon...Lev Reyzinhttps://www.blogger.com/profile/09629175455869565423noreply@blogger.comtag:blogger.com,1999:blog-32371144.post-8656187030938856492010-05-05T01:39:24.581-04:002010-05-05T01:39:24.581-04:00Only intuition I think
The reason here I think is...Only intuition I think<br /><br />The reason here I think is the multiplicative difference in the payoff for switching. The expected value of the payoff is skewed by the fact that if you switch and win, you increase the payoff by 200%, but if you switch and lose, your payoff is reduced only 67%. This means that in the long run over many trials, you would expect to make more money by always switching than by not.<br /><br />If instead of a factor of 3x there were instead an absolute difference of, say, $30, there would be no benefit in the mean from switching.Mollyhttps://www.blogger.com/profile/16260226674012334618noreply@blogger.com