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Each prisoner can open 50, so the first has a 50% chance of killing everyone. Can the first leave the envelopes sorted in some way? Can the prisoners decide the order in which they go?
First sentence: correct. Not permitted to sort the envelopes, as that would be considered communication. The prisoners can decide which order they go in, sure, but it doesn't really help.
Change the problem to open 10 envelopes then put envelopes in groups of 10. 1/10 chance for each one. Second observes a group with 9 remaining. each in that group has a 1/9*1/10 chance of being right. better than other group
No, that's communication between prisoners again... The envelopes are presented in the exact same initial state by each prisoner.
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