Trying to come up with an even simpler non-realistic toy example based on the classic Russian roulette example everybody uses. Imagine N people playing Russian roulette with six-shooter revolvers, repeatedly.https://twitter.com/vgr/status/1234555199307407365 …
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Though crucially, he empties the first 3 chambers by firing into the air, so the remaining three are in sequence, not randomly distributed. So when he randomizes by spinning the cylinder, there's only 1/6 chance of starting in a way that yields that particular outcome.
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Hmm... the first guy must estimate his survival chances at 1/2. After he survives, the second guy can actually estimate his survival chances at 2/3. After he survives too, the third guy will have estimate of 1/2 again. After all survive the first round, all 3 have 0% in 2nd.
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Ah thought of Monty Hall connection. In Sholay example, if he offers the first guy a chance to switch to second position, should he take it? Makes no difference *knowing what he knows then*. But if he offers it to 2nd guy after first one survives, he should *not* switch.
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So survival of 1st guy is non-trivial info. Survival of 2nd guy is as well, but in that case, makes no difference to the odds: value of information is balanced by increased closeness to the full sequence of barrels. So it's worth competing to be #2 *in the #1-survives scenario.*
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I bet there's a similar scene in an English-language movie. There's a whole bunch here https://en.wikipedia.org/wiki/Russian_roulette#Film …
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End of conversation
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