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Blockchain miners calculate the hash of (block data + nonce value). They actually guess (are looking for) nonce in order to get hash staring with a defined number zeroes. (The number of required starting zeros in hash value define the difficulty of finding a nonce that fits - proof of work).

My question is do all miners guess/try nonces from the same pool or range (this way they actually non-efficiently test the same guesses many times) or they somehow split the pool of possible nonces among themselves in order not to try the same nonces multiple times?

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The nonce value is indeed "guessed" by the miner.

The miner can also choose a part of the coinbase transaction (what the stratum protocol calls the ExtraNonce2). Another part of the coinbase transaction is imposed by the pool: this is the ExtraNonce1, in terms of the stratum protocol.

Pools are supposed to assign distinct ExtraNonce1 to all miners, to prevent duplication of work.

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