| Kantor said: It makes logical sense, the 2/3 probability, if you consider the whole thing as one problem. But I'm not really convinced. The way I see it is as follows: Three doors; a car and two goats. You choose a door. Doesn't matter which. Host reveals a goat. END OF PROBLEM A. Two doors; a car and a goat (what I'm saying is that this is an entirely different puzzle. By opening a door and revealing a goat, the host has changed the situation, and the choices you can make). You are now choosing between the car and the goat. It's a 50:50 chance. |
Ending problem A would mean no information from it is carried forward. But knowing what door is "yours" is information. If you completely forgot which door you chose first and were now faced with two doors, you be 50-50.
You can apply this situation over different points of view and get the same result: Let's say you forget all about "problem A" and have to choose between the two doors. If someone watching it all still knows about "problem A" and hopes you'll win, he'll hope you'll select the "other" door, for that, given the information HE has is got 2/3 of chances of winning. Now, he knows you don't know anything about either door, so he knows it's 50-50 that you'll choose any door. Thus 1/2 * 1/3 1/2 * 2/3 = 1/2, making it 50-50. You can reach the same resut trhough presenter's eyes.
But you DO carry information from "problem A" onward. You know which door you chose and you know how the game works. So you can't just pretend that never happened.
