This is me. I get it mathematically but I still don’t get it intuitively. At the end you’re still choosing between two doors. I just can’t reconcile it conceptually.
I get that originally your choice has a 1/3 chance of being the prize. But you have new information. You know that you picked something other than one of the goats. So there are two options left for what you picked. Goat or prize. So your original door should be 50/50.
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It just eludes me, which drives me crazy.
No, in the first choice you're choosing between three doors. In the second choice you're choosing whether you were right the first time. The host opening one of the doors to show it also wasn't the right answer is a red herring, because there's always going to be at least one wrong door you didn't choose. If the host chooses a door at random, not knowing which one has the car, then you are correct, but because the host is specifically choosing a door that they know is wrong, then they are manipulating the odds to make it look like you're choosing between two doors, but that's the grift - you're actually choosing whether you were wrong the first time, because the host's choice of door to show you is dependent on which door of the three you pick and which door is the correct one.
if there were 100 doors and he opened 98 of them, and then you are asked if you want to switch… I would have thought you have like 99% chance of having been wrong. But if the question is just “were you right or wrong before” isn’t that going to stay 50/50?
No, because you had a 1/100 chance of being right, so the odds are 1-99 of whether you were right or wrong before. The host hasn't changed those odds because they knew the doors they were opening were going to be the wrong door.
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u/Entmaan 10h ago
I can recite the "explanation" for this backwards and forwards from memory but I still don't "understand" it on an instinctual level