Author: Uri Blass
Date: 08:02:59 09/27/02
Go up one level in this thread
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 Not seeing a car is important in the 999998 doors is an important information that changes the probability. Uri
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