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PaperclipPerfector  2mo ago (text post)   2235 thread views

Friday Fun Thread for September 6, 2024

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I got the right answer, but I always forget the simple way of thinking about it that you mentioned and do these problems the hard way.

There's a 1/3 chance of picking each box, one which has a 100% chance of giving you a gold on the first draw and the other has a 50% chance (ignoring the option with a zero percent chance of getting a first gold), so the chances of me being in each relevant box at the current state are 1/3 and 1/6. Renormalize, and you get a 2/3 chance of getting another gold. I think this renormalization reasoning works for these particular problems, but I'd probably have to sit with Bayes rule for a minute to convince myself that it does generalize. I've been doing game-theoretic information sets on extensive form games more recently, so I'm picturing a tree in my mind and an information set across states.

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