Steven StrogatzDec 24, 2022
Why do so many people get Monty Hall problem (also known the three doors problem) wrong? Steven Tijms explores both the math and the psychology in this illuminating article: https://chance.amstat.org/2022/11/monty-hall
Monty Hall and the ‘Leibniz Illusion’ | CHANCE

Steven Tijms Seeing Is Believing Throughout the history of mathematics, quite a few mathematical problems have achieved celebrity status outside the circle of mathematicians. Famous problems such as squaring the circle or proving Fermat’s last theorem have intrigued thousands of people over the centuries. But almost no mathematical problem has been as fiercely and widely […]

Show threadJeroen van Dorp
@stevenstrogatz I always wondered what “probability” means when you only have one observation. I always thought probability to be defined as the quotient of the number of times you observe an outcome and a large number of observations. The probability of succes actually here doubles. De Vos Savant was right there, but was she right with her conclusion that changing doors helps? What does probability mean with only one observation? Do you get 2/3 of the prize? Or only for 2/3 of the time?
Dec 24, 2022 at 6:27pmWeb
Show threadryk047Dec 24, 2022
@jeroenvandorp @stevenstrogatz It's more about misdirection than probability. If Monty didn't open a door but instead offered you whatever's behind the two doors you didn't pick, you'd switch because you'd believe you're going from 1/3 -> 2/3 odds. The misdirection, opening a door with no car behind it, changes nothing: the doors you didn't pick always have one that's without a car. But it does misdirect you and make it seem you're in a 1/2:1/2 world.
Show threadJeroen van DorpDec 24, 2022
@ryk047 @stevenstrogatz Absolutely true. But for me the point is that De Vos Savant claimed that because the probability doubles from 1/3 to 2/3 you should switch doors. The first observation is true, no doubt, but I never understood why the second conclusion should be true.
Show threadryk047Dec 24, 2022
@jeroenvandorp @stevenstrogatz I think her explanation carries the misdirection over. If she'd said the probability of the door Monty opened, zero, plus the probability of the one he offered you to switch to, it might have helped. Still, you start with the notion the probabilities are 1/3:1/3:1/3, then are fooled by the reveal of the open door to believe they change. De Vos Savant's explanation is wrong in the sense that if you switch you're getting what's behind two doors.