Solution to the Three-Door Problem

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Below is a picture of the results of the 1001 trials with each of the three strategies. As you can see from the table in the bottom right-hand corner, the Switch strategy wins about two-thirds of the time. The Stick strategy wins about one-third of the time. The Flip strategy wins about half the time. Why?

Consider this. The probability that you will pick an incorrect door on your first guess is 2/3. When this happens, Monty is forced to open the one remaining GOAT door. By switching, you will then get the winning door on the 2 out of 3 times that you were incorrect on the first guess. Thus by switching, you turn the odds in your favor.

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