> It doesn't matter if it was at random or deliberate. It matters that a non-prize (goat in most versions) is revealed. The question is about one very specific

> It doesn't matter if it was at random or deliberate. It matters that a non-prize (goat in most versions) is revealed. The question is about one very specific scenario, even in what antris was originally given: The goat is revealed. In that scenario, you switch. You can just go back to the simulation numbers and check. If you eliminate the games where Monty "wins" (i.e., reveals the prize), you are in the specific scenario you described. You have chosen a door and Monty has revealed a goat, and you win 3309 times by staying and 3307 times by switching. If you rewrite the simulation to follow the correct problem statement (that Monty knows and always picks a goat), you will see that switching is in fact the correct strategy.