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If I have two identical ASICs sitting in a room, pointed to the same pool, and using the same connectivity - will they be following the same sequence of input parameters? If not, who and how makes them different?
Each miner receives share from the pool typically at a rate of 18 per-min and each share is unique work.
ref
https://kano.is/index.php?k=minedet for how mining works.
From that link:
So for stratum we put a bunch of other 'nonces' in the coinbase "sig", that includes a unique number for each miner, and run the others from 0 up to some specified limit to generate a different coinbase transaction each time, that will generate a unique Merkle Root, to be put in a block header, to be hashed over the full Nonce range.
Thus with a unique number for each miner, and the miner itself following the stratum rules for creating coinbase transactions, the miner can keep generating a large amount of work that isn't expected to run out before the pool sends it new work.