Are you serious? Are you buying this? Ok—let me make this easy: There NEVER WAS a 33% chance. Ever. The 1-in-3 choice is a ruse. No matter what door you choose, Monty has at least one door with a goat behind it, and he opens it. At that point, you are presented with a 1-in-2 choice. The prior choice is completely irrelevant at this point! You have a 50% chance of being right, just as you would expect. Your first choice did absolutely nothing to influence the outcome! This argument reminds me of the time I bet $100 on black at a roulette table because it had come up red for like 20 consecutive times, and of course it came up red again and I lost my $$. A guy at the table said to me “you really think the little ball remembers what it previously did and avoids the red slots??”. Don’t focus on the first choice, just look at the second—there’s two doors and you have to choose one (the one you already picked, or the other one). You got a 50% chance.
(by the way—sorry if I posted this twice?? Or in the wrong place?)
No, you don’t. Switching gives you the right door 2 out of 3 times. Long before reading this article, I was convinced by a program somebody wrote that actually simulates it by counting up how many times you would win or lose in that situation… and it comes out that you win by switching, 2 out of 3 times.
So, the interesting question at that point is, why does it work 2 out of 3 times?
And so now, you have an opportunity to learn another reason why your intuition about probabilities is wrong. It’s not just the lack of “memory” that makes probabilities weird. ;-)
Are you serious? Are you buying this? Ok—let me make this easy: There NEVER WAS a 33% chance. Ever. The 1-in-3 choice is a ruse. No matter what door you choose, Monty has at least one door with a goat behind it, and he opens it. At that point, you are presented with a 1-in-2 choice. The prior choice is completely irrelevant at this point! You have a 50% chance of being right, just as you would expect. Your first choice did absolutely nothing to influence the outcome! This argument reminds me of the time I bet $100 on black at a roulette table because it had come up red for like 20 consecutive times, and of course it came up red again and I lost my $$. A guy at the table said to me “you really think the little ball remembers what it previously did and avoids the red slots??”. Don’t focus on the first choice, just look at the second—there’s two doors and you have to choose one (the one you already picked, or the other one). You got a 50% chance. (by the way—sorry if I posted this twice?? Or in the wrong place?)
No, you don’t. Switching gives you the right door 2 out of 3 times. Long before reading this article, I was convinced by a program somebody wrote that actually simulates it by counting up how many times you would win or lose in that situation… and it comes out that you win by switching, 2 out of 3 times.
So, the interesting question at that point is, why does it work 2 out of 3 times?
And so now, you have an opportunity to learn another reason why your intuition about probabilities is wrong. It’s not just the lack of “memory” that makes probabilities weird. ;-)