two

actually the number two IRL

Thanks for playing, everyone. I'll see you around.


funny story. a friend of mine read that post about the monty hall problem and DMed me to say that surely I was mistaken: it can't possibly matter if the host selects a door at random, the probability of winning if you switch must still be 2/3. this is what we eventually termed "the terrifying second order monty hall problem effect paradox": it's possible that once you understand the solution to the monty hall problem, your intuition reverses and suddenly you think that the solution can be applied to situations where it can't be, and it's very hard to actually convince yourself of what was once obvious. this almost happened to me in that while i was writing that post i had a few moments where i thought, "but surely it can't actually be 50%..." before retracing my steps and realising where i was going wrong.

dunno what conclusion to draw from this really. guess probability really is hard. understanding the problem is step one, patiently working through it is step two. my friend eventually drew up a (pretty and inscrutable) table that compactly shows every outcome of both normal monty hall and the version where the host selects at random, and was conviced after this (rather than by any of my own terrible attempts to explain the situation). so maybe math is best when you're doing it instead of being shown it.

that said that's probably enough about math from me for a while...


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