Author: Rolf Tueschen
Date: 09:31:25 09/27/02
Go up one level in this thread
On September 27, 2002 at 12:27:38, Peter Berger wrote: >On September 27, 2002 at 12:18:17, Uri Blass wrote: > >>On September 27, 2002 at 11:36:44, Gerrit Reubold wrote: >> >>>On September 27, 2002 at 11:15:27, Uri Blass wrote: >>> >>>>On September 27, 2002 at 11:09:41, Gerrit Reubold wrote: >>>> >>>>>On September 27, 2002 at 11:02:59, Uri Blass wrote: >>>>> >>>>>>On September 27, 2002 at 10:32:18, Gerrit Reubold wrote: >>>>>> >>>>>>>On September 27, 2002 at 10:18:19, Uri Blass wrote: >>>>>>> >>>>>>>>On September 27, 2002 at 10:04:42, Gerrit Reubold wrote: >>>>>>>> >>>>>>>>>On September 27, 2002 at 09:45:47, Uri Blass wrote: >>>>>>>>> >>>>>>>>>I discuss this situation: >>>>>>>>>- The candidate chooses door 1 >>>>>>>>>- The host chooses (say) door 3, and is lucky, there is a goat in door 3 >>>>>>>>> >>>>>>>>>So there _is_ a game! >>>>>>>>> >>>>>>>>>Now the candidate should switch and double its winning chances. >>>>>>>>> >>>>>>>>>Do you agree? >>>>>>>> >>>>>>>>No >>>>>>>>> >>>>>>>>>If you don't agree: Consider the game with 1.000.000 doors, the candidate >>>>>>>>>chooses door 1. The host opens 999.998 doors, without knowing where the car is. >>>>>>>>>By incredible luck all those doors have goats behind them. There is now door 1 >>>>>>>>>and door 432.102 closed. So again there is a game! Do you agree that the >>>>>>>>>candidate should switch? >>>>>>>> >>>>>>>>No >>>>>>>> >>>>>>>>in 100000 cases you are going to have 999998 cases when there >>>>>>>>is no game >>>>>>>>1 case when there is a game when it is a good idea to switch and >>>>>>>>1 case when there is a game when it is a bad idea to switch >>>>>>>> >>>>>>> >>>>>>>I discuss only the situation when there is a game. The two cases when there is a >>>>>>>game are _NOT_ equally likely. >>>>>>> >>>>>>>When the game starts: >>>>>>>The car is with 999999/1000000 probability behind one of the doors 2..1000000. >>>>>>> >>>>>>>Do you agree? >>>>>> >>>>>>Yes >>>>>>> >>>>>>>Now 999998 doors are opened, the 999999/1000000 probability is still correct. >>>>>> >>>>>>Before I see the result of opening the doors I agree. >>>>>> >>>>>>>The car is with 1/1000000 behind door 1 and with 999999/1000000 behind door >>>>>>>432.102 >>>>>>> >>>>>>>Do you agree? >>>>>> >>>>>>No >>>>>> >>>>> >>>>>Why not? The car is not moving. It is not more likely that it is behind door 1 >>>>>than before the doors were opened. >>>> >>>>The car is not moving but my knowledge is changed. >>>>The fact that there is a game changes the probability. >>>> >>>>Let play 100000 games when the car is behind door i in game i. >>>> >>>>Wehn the car is behind door 1 you lose by switching. >>>>When the car is behind door 432102 you win by switching >>>>In other cases there is no game. >>> >>>>The number of wins equal to the number of losses and it mean that the >>>>probability is 1/2. >>>> >>>>Uri >>> >>>I disagree, why should the odds for door 1 change when door 999999 is opened? >>> >>>Gerrit >> >>What do you disagree about? >> >>Suppose we play 1000000 games when I always choose door 1 >>and the host always open the other doors except door 432102. >> >>Suppose that the car is in door i in game i. >>Do you agree that 999998 games are canceled? >> >>Do you agree that in the games that are not canceled you >>can win 1 of 2 if you do not switch? >> >>Do you agree that it means that the probability to win is 1/2 after you >>know that the game is not canceled? >> >>I did not understand the second reply of Rolf so I did not answer >>about it. >> >>Uri > >The better assumption is to say that the car is in j where j is anthing between >2 and 999999. Now the unlikely thing happened: the not-knowing Monty managed to >take away all other no-car-doors. > >The probability for your initial choice to be right isn't 1/2 at all. Because >the door that survived the Monty-opening-procedure still represents its 999998 >brothers perfectly well. > >Write a little simulation and you'll see you are wrong. In fact Bruce Moreland >even posted some code in CTF already. > >Peter Yes, writing code is easy, as someone said, but answering if the code could be applied seems to a bit more difficult... Have you read my post with the candidate going to the toilette in between? Rolf Tueschen
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