Lighter

Does it still work without seeing a goat? (Right now I think it does.)

No it doesn't. The contestant can change his mind as many times as he likes on his first choice. The odds will still say 1/3. He may have changed his mind several times in his head before declaring his choice. Why should changing his mind publicly make any difference?

It is only Monty opening a door to reveal a goat that gives you extra information to recalculate the odds.

I will leave gnu to more patient souls.