It is sorta pointless to farm for keys if you are awarded a key after completing prison of elders to use on the chest, unless you need multiple keys to unlock each of the 3 chests.
English
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You are only awarded one key a week. Once you complete your first poe game of the week you will get a key. You will not get another until the weekly reset and you complete another game.
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You're not awarded a key after completing poe each time.