100 prisoners, 100 drawers, each may open 50. all must find their own number or all die.
this game
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cycle strategy
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random strategy
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each drawer holds a random permutation of 1..100. a prisoner who uses the cycle strategy opens their own-number drawer first, then follows whatever number they find, up to 50 times. everyone survives iff the permutation has no cycle longer than 50 — which happens about 31% of the time. the random strategy (open 50 drawers at random) succeeds with probability (1/2)^100, i.e. never.