Author: Peter Berger
Date: 09:27:38 09/27/02
Go up one level in this thread
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
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