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Current Bitcoin PoW algorithm leads to a block time distribution like this bitcoin block mining time distribution

with is quite sparse. If instead it requires a chain of lower-difficulty hashes (e.g. instead of one hash of difficulty 12 it would be enough to provide chain of 4 hashes of difficulty 10), the distribution would be more dense

bitcoin block mining time distribution with chain of 4 hashes bitcoin block mining time distribution with chain of 32 hashes

This way block mining time (and therefore transaction finalization time) will be more predictable. Is this simply a historical occasion that is difficult to alter, or are there significant drawbacks in this mining algorithm?

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That would violate the progress-free property of mining, which is very desirable.

If miners have to construct multiple PoWs per block, that means they (private) accumulate points, and the first one to reach enough points wins the block. In the extreme, with a long enough chain, this will imply that the fastest miner always wins, which is very anti-competitive. Even with just a few PoWs per block, there is a strong benefit to larger miners. In contrast, a single PoW per block functions as a lottery, and miner win probabilities scale proportional to hashrate, and thus to investment.

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As is usually the case in Bitcoin, the reason the PoW algorithm works the way it does is because it was the best Satoshi could come up with, and now we're stuck with it unless we do a hard fork.

However, I can see many potential problems with a proof of work algorithm that relies on a chain of hashes for a single block. As Pieter notes in his answer, we want mining to be progress-free, so having miners each work on their own chain of hashes is off the table. We can instead have miners work only on the next hash in the chain for a share of the block reward, which comes with its own set of problems:

  • The whole point of proving work with a block hash is that the hash commits to the list of transactions in the block. If we instead have a chain of hashes, we need to figure out when, how and by whom the transactions are selected and committed, including coinbase transactions for each of the block's miners.
    • While we're at transaction selection, I'm sure there might be potential problems with one party selecting transactions in a way that hurts other miners who will be working to confirm the block. For example, they could intentionally select low-fee transactions whose fees were paid out of band, disproportionately profiting from the block because they don't have to share the fees with other miners.
  • Increasing the frequency at which miners have to exchange information and switch to mining on top of a new hash would create many of the same centralization issues as increasing the block frequency itself. See: How would faster blocks cause mining centralization?
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