Yes, good clarification and I think you're correct in a sense. Entropy would be a highly explanatory way to discuss hashing 'mattering'. There is still the question of 'mattering to what end'. Hashes 'matter to the end of building the chain' to the extent they successfully find a golden nonce. (e.g. THE successful hash submits a block to the chain to build upon.) Hashes that do not succeed to that end do not matter in that sense. BUT, from the perspective of entropy, yes, all hashes matter as a MORE descriptive illustration than the poisson example given above.... I'd have to look more into how entropy units function because I understand the idea of entropy units per satoshi, but would want to clarify entropy units as a function of searching the field and not entropy as a function of energy input into machines. Thank you!

You can't use entropy to directly model Bitcoin because hashing itself is stochastic.

statistically averaged, yes. direct, no

Difficulty adjusts only based on block time, not hash power. The mechanism is called CalculateGetNextWorkRequired.

Does EVERY hash from a Bitcoin miner matter? Pick the ‘wrong’ side on this debate and you’ll find yourself triggering computer scientists and cypherpunks, or enraging plebs and an army of lottery miners. Let's figure it out together. But first, a review. I wrote an article in March of this year disagreeing with the way Saylor and Lowery characterize bitcoin mining as a 'battery' or 'encrypted energy'. Here's the crux of that argument, bitcoin mining is neither because of the STATISTICAL nature of mining (you are guessing nonces before you hash a random output--it is non-deterministic). You can never create a directly causal MODEL that shows how energy or electricity translates to hashes and block wins. To illustrate this, I made the point that you are only, technically, contributing to the network IF you find a block. Finding blocks allows for issuance and settlement of bitcoin, and impacts network difficulty. In the code, this is CalculateGetNextWorkRequired. Technically, bitcoin was designed to explicitly never know (or need to know) how many people are hashing, how big they are, how much energy is being used, what kind of hardware they are using... This is a feature, not a bug. (IMO it's THE feature that Satoshi uses to solve the hard problem of monetary inflation... but that's for another day) In this technical sense, it is true that HASHES THAT DON'T FIND BLOCKS DON'T MATTER TO BITCOIN. Why? Hashes that don't find blocks DO NOT receive a reward of new bitcoin, settle transactions, or impact the chain or network difficulty. They don't matter (technically). In true Bitcoin fashion, this made many angry. Here is my visual interpretation of why: It comes down to the word 'matter'. If I say that hashes that do not find blocks do not technically matter, I am not saying: - lottery mining is stupid - don't mine - only big miners matter - just quit while you're ahead But a lot of people read my article that way! This is where I can be even clearer. 'To matter' in a technical sense means to interact with the chain, BUT there is another way 'to matter' that is entirely legitimate. This is the disagreement @penny_ether clarifies. It is worthwhile to mine (even if you don't find a block), for the simple reason that you cannot win a game you are not playing. We know this because even TRYING to win the game (by hashing) has a value associated with it that pools will pay you for--hashprice. OF COURSE all hashes matter in this sense. @Public_Pool_BTC makes the true assertion, that because mining is a Poisson process, all hashes are probabilistically relevant to the network. 100% true, but not directly relevant to my technical point (highly relevant to a different interpretation of 'matters') Otherwise there would not be a PRICE associated with them. Remember, a pool pays you for hashes, NOT just winning hashes. It's the expected value you get paid for. I love disagreements like this. They give us the opportunity to hash out (no pun intended) what we specifically mean when discussing bitcoin. That's what is so special about Bitcoin, everyone is open to learn and interpret it. So, in sum, "Do all hashes matter?" Both YES and NO. But, you have to specify what 'matter' means.

Still on the front range!

thank you!

I'd also be curious to see how the math changes given the original 32 byte nonce space miners search within is expanded in various ways (version, and extranonce1 and 2)

my first zap ever! TY!

statistically or directly? you can statistically model block time you cannot directly (causally) model block time

love your work!