The answer to the riddle is counter-intuitive. Let's see if I can help it make more sense to you.

First, let's say we do the Let's Make a Deal exercise 99 times. Now we can talk meaningfully about odds. Let's walk through it slowly in a non-math, intuitive way.

Out of 99 tries, yow many times will you have picked the correct door with your first pick? Answer: 33. 66 times, the gold will be behind one of the other two doors.

But here's the problem: even though you know that there is a 2/3 chance the gold is behind one of the other two doors, YOU DON'T KNOW WHICH ONE OF THE OTHER TWO IT'S LIKELY TO BE BEHIND. So if I'm about to pick door number 1, I can't improve my odds by saying "my first choice is wrong 2/3 of the time, so I'll just bypass that and go straight to door number 2."

So let's change the rules a bit. You have chosen a door, which you know has only a 1/3 chance of being right. Monty Hall then says the following to you: "Okay, CougarBoard member, he're's the deal of the century. You can either keep the door you have, or you can have BOTH of the other doors." What would you do? Of course, you would take both of the other doors. Why? Because there's a 2/3 chance the gold is behind one of them, and only a 1/3 chance the gold is behind your first pick. That's an easy call.

So let's change the rules a bit more. You have chosen a door, with a 1/3 chance you are right and a 2/3 chance you are wrong. Monty says: "Okay, CougarBoard member, here's the deal of the centry. You can keep the door you have, with a 1/3 chance of being right. OR, you can switch. IF YOU SWITCH, and if it turns out switching was the right move (because your first choice was wrong), I'll help you out by telling you which one of the other two doors the gold is behind." What do you do? Of course, you switch. Monty is doing you a favor by giving you a hint about which one of the other doors has the gold IF the gold is behind one of them (which is still 2/3 likely). By switching, you would improve your odds from 1/3 to 2/3.

Now let's change the rules again. This time, after your initial pick, Monty says: "Here's the deal. You can keep your pick, or you can switch. If you switch, I'll point out one of the other doors that the gold is definitely NOT behind, so that will eliminate one wrong door if you decide to switch. I'm not promising the gold will be behind the other one, but I'll eliminate one wrong choice for you if you switch." Do you switch? Of course. Why? Because your initial choice still has a 2/3 chance of being wrong, and Monty is simply offering to give you a hint about which of the other two doors to pick if you switch. If you were to switch without any hints from Monty, your odds wouldn't change, but since switching gives you the benefit of Monty's help, you improve your odds.

The real "Let's Make a Deal" game is just like this last example, except that Monty gives you his hint before you switch rather than after. The timing of Monty's help doesn't change the odds. Put a different way: By showing you a door with a goat behind it, Monty isn't changing the odds that your initial choice was wrong; he's simply arming you with better information about which of the other doors you should go with if you switch (which will be the right move 2/3 times). The odds of the gold being behind one of the doors you didn't pick is still 2/3; Monty has simply given you better information about which of the other two doors is more likely to have the gold if your original pick turns out to be wrong.

And that's the key to the "Let's Make a Deal" hypothetical. As another poster noted, none of this works if Monty is just randomly picking a door to show you; it only works because MONTY KNOWS what door the gold is (and isn't) behind, and you benefit from that knowledge if you switch. The odds of your initial choice being wrong haven't changed, you just have better information about which of the other doors to go with if you change.

Hope this helps.