> But if you avail yourself of the chance to switch, you have then chosen 2 out of the 3 doors that were available at the beginning of the game, thereby increasing your chances to snag a car to 2/3!!

This is another counter-intuitive aspect for the following reason. If I hold two lottery tickets out of a total of three, my chances of winning are likewise 2 in 3. In that case, however, I have physical control over both tickets at once. I can see with my own eyes that I have two of the three chances. In Monty's game, by way of contrast, I am *giving up* my claim on the first door I select when I switch to another. It feels the same as tearing up a ticket.

Giving up a claim on the first door would thus seem by everyday reasoning to make a difference in the final calculation; but in fact it does not.