Okay, I think we're dealing with a different problem, here.
Here's an interesting way of looking at it:
You make a choice (boxes represent chance of winning):
Your choice = [33%]
What's left = [66%]
Now, they're going to reveal one WRONG box, and it wont be yours. 66% of the time, the right answer is NOT your box.
For that 66% of the time
They reveal one box [wrong], the other box left is automatically right. [100%]
So, you'll win 100% of 66% of the time.
The other 33%:
They reveal one of the other boxes [both of which are wrong], and the other is automatically wrong. If you switch, you have a 0% of winning, that 33% of the time.
The whole snag to the equation, my friends, is the fact that they NEVER reveal your INITIAL choice. So if we are to assume truly random distribution, switching will cause you to win 2/3 of the time. It is important to note that the door being opened is not random; it will always be a) WRONG, and b) NOT YOURS.
The interesting thing is that it's not actually a game of three choices of 33% each, or two choices of 50%. It's a game (by its "rules") where you have two choices, one is [33%], the other is [66%]
The reason for this is that revelation is NOT random in this game - whatever you pick, they wont reveal it. If they randomly revealed any wrong box (including yours), your odds would be 50/50, thus:
Your choice [33%]
What's left [66%]
If the correct answer is in "What's Left" [66%]:
50% of the time they reveal your box [wrong], and so you have a [50%] chance of getting the right other box.
The other 50% of the time they reveal one of the other boxes [wrong], which leaves you with a [100%] chance that it's the one you pick.
If the correct answer is in "Your Box" [33%]:
They reveal one of the other boxes [wrong]. Switching would leave you a [0%] chance of winning.
So, if you always keep your box, you're going to win 33% [your box] + 16% [50% of 50% of 66%] of the time. = 50%
If you always switch, you're going to win 33% [50% of 66%] + 16% [50% of 50% of 66%]
If you always want to switch, you're automatically wrong a third of the time, and it's completely random another third (whenever they reveal your box).
If you never want to switch, you're automatically right a third of the time, and it's completely random another third (whenever they reveal your box).
What the rules of this game do, by never revealing your box, is that they take that last random third out, so it's now you have a 33% chance of winning if you keep your box, and a 33% chance of losing if you don't.
Phew. I hope that clears things up. Remember, they NEVER reveal the
answer. If they did, you'd win 66% of the time.