Gnu--

You speak of Random Chance in playing the Hall game as being the same as a coin toss. A coin toss is a single event. The Hall game is a dual event. The first event, your choosing a door, is also random, but the exposition of that event is not random. As I pointed out before, Hall will neither show you your choice nor the car at that time.

Now you have a second related event, another choice. If you treat that second choice as a coin toss, heads change-tails stay, you have, indeed, reduced the game to a 50/50 proposition. But the math and the bottom part of the grid at TheSnail - Date: 30 Oct 12 - 04:53 PM [or at Wikipedia] show a switch door choice increases the probability (not a guarantee) of winning to 67%. That is a better chance than the pure chance of a coin toss, is it not? Of course you can deny the accuracy of the grid, but that would just be bull-headedness, gnu.
(Hmmm, is that sort of a pun?)