3 ms·
One thing that intrigued me about this puzzle is wondering what mental model for probability would make solving it intuitive? The one that works for me was thin
by aszs 7y ago
One thing that intrigued me about this puzzle is wondering what mental model for probability would make solving it intuitive? The one that works for me was thinking about it in terms of information:
Because Monty can never choose the door you first picked he can't give you any new information about that door.
So when he reveals which of the remaining doors has a goat, he is only giving us new information about those remaining doors. That information reduces the odds on the remaining doors and that is why you should always switch.
- dhimes 7y agoThis puzzle has stayed with me for a decades for two reasons. #1 is it was the first time I was embarrassed in public discourse on Usenet. Guy shot me down pretty hard, but when he was done there was no uncertainty- he was right and I was wrong. #2 is I finally realized the importance of that postulate of Quantum Mechanics: The wavefunction contains everything you can know about the system. This problem pointed out for me that probability is not an unvariable thing. Different people will calculate different probabilities for different events (think if we're playing cards and I have three aces and you have none- you will calculate a different probability of drawing a ace that I will) and we will both be correct. This without this postulate the probabilities of QM would be meaningless.
- kortex 7y agoIf you switch "you" get to "open" two doors in fact, not one. It's just that Monty picks which one for you. And since your choice is random, you might as well let an RNG do it for you. If you consider it two independent rounds instead of stay/switch, Stay: you get to roll 1d3, "1" wins Switch: you get to roll 1d3, "1" loses, "2" or "3" wins