You're wrong...but don't feel bad. Lots of people make this mistake. Assuming the 'host' always opens one of the remaining doors and the remaining door never has a prize behind it, you should always switch. Why? On your first pick you have a 1 in 3 chance of getting the prize. If you always switch, your chance of getting the prize becomes 2 in 3. Prize -> Goat Goat1 -> Prize Goat2 -> Prize Thus, you win. or, to put it another way... Imagine there are 1000 doors and after picking a single door (1/1000 chance of getting the prize) the host opens all but 1 door. Would you switch? Of course! At that point there's a 9999/1000 chance you will win!
Where are you getting this from? He must be wrong just because you believe differently? Think about this:
You pick door A. Then the host opens door C. You say: "always switch to door B." Ok, well how about this: assume, at the same time, there was a guy who had started out by picking door B. Should he switch to door A now? By your logic, he should. But that means that both A AND B are "better" choices than each other, at the same time . . . doesn't make sense, does it. By your logic that's how things are, and they don't make sense. Maybe your logic is wrong . . .
Personally, I would have thought that the end result was winning 50% of the time, since one of the two is open. That's what seems to make sense to me. Two doors remaining, one with a prize behind it. (The parent post about having a 9999/1000 (though he means 999/1000) chance after 998 doors have been opened is ridiculous; the logic is incredibly flawed.)
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Where are you getting this from? He must be wrong just because you believe differently? Think about this:
You pick door A. Then the host opens door C. You say: "always switch to door B." Ok, well how about this: assume, at the same time, there was a guy who had started out by picking door B. Should he switch to door A now? By your logic, he should. But that means that both A AND B are "better" choices than each other, at the same time . . . doesn't make sense, does it. By your logic that's how things are, and they don't make sense. Maybe your logic is wrong . . .
Personally, I would have thought that the end result was winning 50% of the time, since one of the two is open. That's what seems to make sense to me. Two doors remaining, one with a prize behind it. (The parent post about having a 9999/1000 (though he means 999/1000) chance after 998 doors have been opened is ridiculous; the logic is incredibly flawed.)
Anyways, that's what I think.