TaeKahn
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While the overall probabilities for the game will never change, the contestant’s perception of the current state of the game will cause them to affect their win rate. To elaborate on what I was saying, imagine the following internal monologue of a contestant:
I’ve eliminated one goat. Two doors left. One is a goat, one is a car. No way to tell which is which, so I’ll just randomly pick one.
IMO, this is probably what most contestants believe when faced with the final choice. Obviously, there is a way to have a greater success rate, but this person is evaluating in a vacuum. If contestants were aware of the actual probabilities involved, I think... (read more)
I have a small issue with the way you presented the Monty python problem. In my opinion, the setup could be a little clearer. The Bayesian model you presented holds true iff you make an assumption about the door you picked; either goat (better) or car (less wrong). If you pick a door at random with no presuppositions (I believe this is the state most people are in), then you have no basis to decide to switch or not switch, and have a truly 50% chance either way. If instead you introduce the assumption of goat, when the host opens up the other goat, you know you had a 2/3 chance to pick a goat. With both goats known or presumed, the last door must be the car with an error rate of 1/3.
You are making perfect sense; it’s me that is not. I had thought to clarify the issue for people that might still not “get it” after reading the article. Instead, I’ve only muddied the waters.