Of course you stick -- Monte obviously opened the other doors just to trick you into switching because he knows you got the right answer. Of course he can do

Of course you stick -- Monte obviously opened the other doors just to trick you into switching because he knows you got the right answer. Of course he can do this; you already know that 999 doors have goats, so whether or not you picked correctly he can open 998 doors to reveal goats. If you had picked a goat door, he would have just opened the door you picked or opened the door that has the money to show you that you got the wrong answer. The assumption that Monty Hall will always offer you a chance to switch is what is broken in the problem statement and the reason why so many people think that the correct answer is unintuitive.