You are on a game show. You are shown three closed doors. A prize is hidden behind one, and the game show host knows where it is. You are asked to select a door. You do. Before you open it, the host opens one of the other doors, showing that it is empty, then asks you if you'd like to change your guess. Should you, should you not, or doesn't it matter?

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that would just improve your chances of having chosen the correct one. They went from 33% to 50%. At this point, it really makes no difference if you switch doors or not, so long as you don't choose the one you know is empty haha

You shouln't. Now that she showed you which one was empty. You went from 33% chance to 50%. I usually stick with my gut anyways.

Changing your guess would be the smart move. You had a 2/3 chance of picking incorrectly the first time, and he revealed one of the doors that was definitely wrong. Since your first guess was more than likely wrong, the other option is more than likely correct.

Change! You are twice as likely to have the right door if you change your answer.

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