[An.American.Expatriate]

You are correct as far as what my chances were prior to having any door opened (and allowing me, at every oppurtunity to select another).

However, once that first door is opened, my chance of picking the correct door (either remain with mine, or choosing a new one) is now 1 to @-1. This continues until we get down to the last two doors - mine and an unknown. Regardless of how many doors Monty has opened - my chance of choosing the correct door (either the one I have, or the one offered) is 1 in 2.

So, I agree that, before Monty starts opening his doors, my chance of having picked the correct on, is 1-@. I also agree that, once the game is over, my chance of having picked it right, from the beginning is 1-@. However, my chance, on the final decision (stay with Door #1, or take Curtain #3) is 1 in 2.

This is not that different than the old coin toss question ...

Or maybe I'm still missing a key piece of the puzzle?

I'm being honest - if I'm missing something I'd like to understand it!

[Nateman]

You are hung up on the idea that the odds for a choice already made change upon learning more information. What’s done is done. Suppose you pick an apple from a barrel of apples and that apple has a worm in it. Does that worm go away because you are now given the choice of much more reliable apples?