I may have an even simpler explanation than your "Who needs Monty". It involves no simulation, just a different perspective.

I believe a professional gambler would have had an easier time with this. Let's hypothesize the gambler will win something if he guesses correctly, but will loose something if he is wrong. Thus, he is more highly motivated than, for example, I. Consider the gambler's reasoning. "I'm being forced to pick one of three doors and only one is the right door. So, I'm probably picking the wrong door. Ah, now Monty is giving me a chance to change my pick and he's shown me that one of the other doors is not the one I want. Since I was thinking that one of the other two doors was likely the correct one, and Monty has eliminated one of them, I'll choose the other. For my money, that's almost like certainty."

I find many of the other ideas for reasoning to the correct result quite enlightening, but I wonder how much effort went into them. I know my first response upon reading about this problem was that vos Savant was wrong. I had to think about the problem quite a bit to admit she was right. It took even longer to come up with the "gambler presentation". Perhaps Ms vos Savant and some others immediately saw the correct answer. They have my admiration. However, it seems unfair for some to berate latecomers to this problem for not immediately seeing the correct answer, as well as the "proper way" of getting to that answer.

When I originally thought about the controversy relating to this problem, I began to wonder how many times someone may have given a proof that seemed obviously correct only to find later that it was totally wrong. My original "proof" was like many others - we know one of the other two doors is a wrong guess. When Monty exposes it, we gain no new information. Therefore, there is no reason to change our guess. Equally, there is no reason not to. The flaw, of course, is the assumption we gain no new information. Once we know the correct answer(!), we can easily state and solve the problem using conditional probabilities. Why not use probabability theory in the first place? Because, it was clear we already knew the "correct" answer. Why go through all that formality? Now we know.

I enjoy your web site.

Mike