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intrigued by how miners would have to compete to complete cryptographic task fast enough
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It's not a competition.
It's a simple random brute force hash to get leading zeros.
On average, every miner that hashes, they will find a 1 diff share for every 1 diff of hashes they do.
Network difficulty is currently 37590453655497.1 so,
on average, 1 in every 37590453655497.1 diff of hashes done will currently be a block.
When a block changes, you continue hashing with a different set of data.
On all good pools, you continue hashing with a different set of data every 30 seconds.
There's no competition or race involved in finding a block hash.
However, once you do find a block, you must get it out to the worldwide bitcoin network as fast as possible, so that someone else doesn't find the same height block before you tell them about yours and get them to switch to building on top of yours.
This is the most important part that people also misunderstand in their posts all over this forum.