how does switching make a difference?

Sorry I may be being think here, but:

Door 1 had 2/3 chance of being wrong.
Door 2 had 2/3 chance of being wrong.
Door 3 had 2/3 chance of being wrong.

We now know Door 3 *was* wrong.

Why do I switch from Door 1 (originally wrong 2 in 3 times) to Door 2 (originally wrong 2 in 3 times)?

The possibilities were:

1 2 3
C G G
G C G
G G C

We can disregard column 3 as we know the result, so that's not an option. The choice is between Columns 1 and 2.

1 2
C G
G C
G G

We can discount row 3 as we know (factually) that it is not possible for both doors to reveal a goat.

So that leaves
1 2
C G
G C

If I'd chosen Door 1 to start, I now have a 50:50 chance of that decision being correct, and if I switch doors I have a 50:50 chance of that decision being correct.

*I am missing something crucial here as Wikipedia tells me I am wrong*

Posted By: CWC, Nov 2, 17:51:25