I'm going to set up this game, but instead of a car as a prize, as I'm obviously not that wealthy, I'll give away free cubes. We'll do this in San Francisco during the break and we'll just call up random members of the audience who are there spectating the competition. If I have enough cubes, I'll do it 10 times.
Tyson Mao MSC #631 California Institute of Technology On Dec 28, 2005, at 12:46 PM, Rune Wesström wrote: > "Good thinking Stefan!" ? He is contradicting himself when saying: > "you can gain some knowledge this way and be more sure that changing > would be better...but... the probability stays at 2/3". But if we had > a probability of 2/3 whithout this knowledge and then bettered it, how > can we still stay at 2/3? He is discussing the a priori probabilities > before the first choise, *I* am discussing the probabilities before > the second choice, that is, when the host has opened one door. There > is some concensus here that the probabilities are 1/3 or 2/3. But if > we accept the theoretical assumtion (Pochmann apparently does) that > the host has an "easy" door and a "difficult" door and he chooses the > first with a probability of 1/2 + epsilon and the second with a > probability 1/2 - epsilon (epsilon not 0), the result will be another. > Ask mister Pochmann to calculate the probabilities for you. Mister > Bayes may help him. > R > ----- Original Message ----- > From: "pjgat09" <[EMAIL PROTECTED]> > To: <[email protected]> > Sent: Wednesday, December 28, 2005 5:41 PM > Subject: [Speed cubing group] Re: (Off topic)3 doors... > > > Thats the best way I have heard it put for this entire dicussion. Good > thinking Stefan! > > Peter Greenwood > > --- In [email protected], "Stefan Pochmann" > <[EMAIL PROTECTED]> wrote: >> >> This doesn't make the argument wrong. Yes, you can gain some knowledge >> this way and be more sure that changing would be better. But it >> doesn't make you win more often when changing. The probability for >> that stays at 2/3. >> >> I knew a similar case as yours, but here's a really extreme one: After >> you pick your first door, the host opens *all* three doors and let's >> you stay or change. Even with this 100% knowledge (because you see the >> car), changing is successful exactly 2/3 of the time, namely in those >> cases where you were initially wrong. >> >> Cheers! >> Stefan >> >> >> --- In [email protected], Rune Wesström <rune. >> [EMAIL PROTECTED]> wrote: >>> >>> A lot of intuition! >>> You guess on door #1. The host is staying in front of door #3. Door >> #2 is 2 meters away from him, nevertheless he opens that door. What >> would you expect to find behind door #3? A goat?! (Let us exclude >> double-crossing!). >>> ----- Original Message ----- >>> From: "Stefan Pochmann" <[EMAIL PROTECTED]> >>> To: <[email protected]> >>> Sent: Wednesday, December 28, 2005 3:47 PM >>> Subject: [Speed cubing group] Re: (Off topic)3 doors... >>> >>> >>> Changing wins if and only if you initially chose the wrong door, i. >> e. >>> two times of three. >>> >>> Can you explain why your suggestion makes this wrong? >>> >>> Cheers! >>> Stefan >>> >>> --- In [email protected], Rune Wesström <rune. >>> [EMAIL PROTECTED]> wrote: >>>> >>>> In real life the host is Not staying totally symmetrically in >>> relation to the doors. (He is right-handed Or left-handed. Maybe he >>> has to take a halfstep to open a certain door etc.). If he now opens >>> the "easiest" door, Not changing wins more often than one time of >>> three. If he opens the other door, changing will win more often than >>> two times of three. >>> >>> >>> >>> >>> >>> >>> >>> >>> Yahoo! Groups Links >>> >> > > > > > > > > > > Yahoo! Groups Links > > > > > > > > > > > Yahoo! Groups Links > > > > > > ------------------------ Yahoo! Groups Sponsor --------------------~--> Get fast access to your favorite Yahoo! Groups. Make Yahoo! your home page http://us.click.yahoo.com/dpRU5A/wUILAA/yQLSAA/MXMplB/TM --------------------------------------------------------------------~-> Yahoo! Groups Links <*> To visit your group on the web, go to: http://groups.yahoo.com/group/speedsolvingrubikscube/ <*> To unsubscribe from this group, send an email to: [EMAIL PROTECTED] <*> Your use of Yahoo! Groups is subject to: http://docs.yahoo.com/info/terms/
