Just to argue a bit more in this thread (which is very silly) I have a couple of questions:
Are you suggesting that I still have 1/3, 2/3 (any way) when choosing at random or always alternating between staying/switching? If you did that should read 1/2, 1/2. /Gustav Stefan Pochmann skrev: >Ok, I'm done. With this idea of gaining extra information (i.e. not >like in the original pure probability riddle) I'm not sure we should >talk about *the* probability that changing or keeping your door wins a >certain fraction of all cases. > >That's because now it depends on your strategy. For simplicity, let's >consider my extreme hint example again where you *know* where the car >is before your second decision. The probability for something is >roughly speaking the good events divided by all events. Now if your >strategy is "keep if and only if I was right" then you always win. >That is, all your "change" decisions and all your "keep" decisions >will win. Instead of 2/3 and 1/3 we now have 3/3 and 3/3. However, if >your strategy is "keep if and only if I was wrong" then we drop to 0/3 >and 0/3. > >So it depends on your strategy and thus speaking about *the* >probability for keep/change doesn't make much sense, at least not >directly. I guess this term could make sense if you define it over >*all strategies*, and then it might be 2/3 and 1/3 again, but I won't >dare to claim that cause now it's getting too complicated :-) > >If we talk about keep/change as strategies, short for "I'll always >keep my door" (or "change"), then 2/3 and 1/3 is correct. It's also >correct if your choice is random. Or if you always alternate between >keep/change (unless the correct door alternates accordingly). Or other >constructions that keep the 2/3 vs 1/3 probabilities for keep vs >change. But inside other strategies, the probabilities can be very >very different. > >Cheers! >Stefan > > > >--- In [email protected], "Stefan Pochmann" ><[EMAIL PROTECTED]> wrote: > > >>--- In [email protected], Rune Wesström <rune. >>[EMAIL PROTECTED]> 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? >> >> >>Hehe, you better don't remove the important parts of the quote :-). >> >> >I > > >>was talking about two different things. I said: >> >> >> >>>>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. >>>> >>>> >>The probability that "change" wins the car stays at 2/3 and the >>probability for "keep" stays at 1/3. The extra knowledge doesn't >> >> >help > > >>to make these strategies any better, "keep" wins if and only if your >>initial choice was correct (1/3) and "change" wins if and only if it >>was wrong (2/3). >> >>What you *can* do with this extra knowledge is make up a *better >>strategy* than those two. In my extreme example where you get to see >>the car, a good strategy would be "keep my door if and only if it >>contains the car". This *new* strategy wins the car 100% of the >> >> >time. > > >>Now what about the situation you described? The game is the same but >>you get extra information from the behaviour of the host. Can you >> >> >use > > >>it to make up a new strategy? >> >>Hmmmmm.... actually I just noticed something. Gotta think about it, >>will be back when I'm done with that. But I'm gonna submit the above >>now anyway. >> >>Cheers! >>Stefan >> >> >> > > > > > > > > >Yahoo! Groups Links > > > > > > > > >__________ NOD32 1.1342 (20051228) Information __________ > >This message was checked by NOD32 antivirus system. >http://www.nod32.com > > > > > ------------------------ 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/
