>Al,
>
>>I'm amazed that both you and Jim Booth have it all wrong! :-) You've both fallen into the trap of making something more complicated than it is. Consider these incontrovertible facts:
>
>Actually they are right.
>
>>1. There are 2 remaining doors.
>>2. Exactly one of them has a goat, the other a boat.
>
>Imagine there are 1000 doors, 999 goats one boat. The host let you choose one. The propability you choose a goat is .999 . The trick sits in the fact that host HAS (in .999 of the cases) to open to 998 remaining goat doors (IOW in 99,8% he's got no choice of choosing which door to open) So now you faced with 2 doors. One you choose, and one remained. The chances you were right is .001 the chances that the boat is after the remaining door is .999
>
>Note that using 3 or 1000 doors make no difference. In the cases of 3 doors the host has a propability of 2/3 that he must open the remaining goat (as you initially choose the other) leaving a 2/3 propability that the boat is after the other remaining door.
>
>Walter,

Sorry Walter,

You need to show me where my 2 facts are wrong. If you can't, then you are wrong. Make your theories fit the facts, not vice versa :-)

How many doors are left? Two. We are fortunate to "own" one of them. What lies behind the doors? Exactly one goat, and exactly one boat. Therefore, what is the chance that we "own" the boat already? 0.5, or 50%. The other door has an exactly equal chance to contain the boat; therefore there is no advantage (or disadvantage) in changing your selection.