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The explanation that best helped me 'intuitively' understand things is to rephrase the game as being two separate games: choosing one of three doors, and after
by mercer 5y ago
The explanation that best helped me 'intuitively' understand things is to rephrase the game as being two separate games: choosing one of three doors, and after that having the option to go for a coin toss instead. Obviously you'd go for the coin toss.
Now I understand that the reason why that worked for me is precisely because it becomes much more clear that it's really about new information, and what tripped me up was trying to maintain a kind of 'narrative', I suppose?
- graderjs 5y agoI still don't think I really "get" it, but this explanation makes the most sense to me. Thanks! Like of course I would switch and go for the coin toss, but I don't know how to convert that certainty into actually probabilities, tho I'm sure that the odds of my choices are not 1/3 versus 1/2, because there's probably some interplay. If I think about it more I start to get confused again, along the lines of: does the first choice even matter then? and what if I reverse my first and second choices (as in I pick 1, then switch to 3, but what if I picked 3 then switched to 1), how can I still have better odds by switching, since there's only 1 right answer? But sticking with the coin toss, I feel, "OK this makes sense."
- mercer 5y agothe first choice matters insofar that you can choose to stick with it, so while the coin toss in isolation is 50/50, for the game as a whole you need to consider the option of sticking with that initial 1 in 3 chance along side the 1 in 2 chance.