Yeah, that's what I thought. I was wrong.

If you think about it, whether or not it is good idea to switch depends on whether or not the contestant initially chose the door with the prize.

If the contestant initially chose the door with the prize, then he must stick with that choice in order to win the prize. That is a no-brainer.

If the contestant initially chose a door without the prize, then if he changes his selection, he is certain of winning the prize. Why? Because Monty has opened the only other door that does not conceal the prize.

What is the probability that the initial selection was the correct selection? 1/3, yes? And the probability the initial selection was incorrect? 2/3, yes?

If you work that through, you will come to the conclusion that the contestant does indeed double his chances of winning by changing his selection. That is backed up by possibly hundreds of experiments.