Why is bitcoin mining difficult if hashing is easy?

Let's pretend you're rolling dice. Yes, a roll of the dice is very easy to do!

But to get snake eyes? That's trickier. You need to roll and roll and roll and roll again, and never quite sure when you'll get snake eyes.

Likewise, it is easy to hash, but to get exactly the right hash? That's much trickier.

So you've got to do lots and lots and lots of hashing, until with a bit of luck you get the right hash. (and obviously, the greater the hash power you have, the more "lucky" you'll be!)

This is also why there are mining pools. If you're rolling dice by yourself, it might take a long time until you get to be first in getting snake eyes. But if you're rolling dice with all your friends together (and you agree to split the prize, no matter who wins), then you improve your odds for each new block, and smooth out the variability in the long run.

What you're missing is the difficulty. This is the amount of zeros that must be at the beginning of the resulting hash in order for it to be valid for the block in question.

The previous block's hash and the new block are hashed together. If it doesn't meet the difficulty requirement, it increments and hashes it again. It does this millions or billions of times until it stumbles across a number that creates a hash of the required difficulty

The nonce is not known. The miner creates a block and has to find a nonce that, when put into the block and hashed, produces a result with a certain amount of leading zeros. Hashing the block with your guessed nonce is easy but you won’t likely produce a result that satisfies the leading-zero difficulty requirement. So you have to guess another nonce and try again.

The leading zero requirement actually is so difficult that yesterday it took all miners in the world combined 1,2*10^24 tries to find a nonce that satisfies the condition for one single block. That is a billion trillion tries. This is what makes it slow.

Mining efficiency is measured in TH/s and the global mining network currently produces roughly 200m TH/s (Tera hashes per second) to arrive at a nonce that produces a valid hash about every 10 minutes.

edit: 10^21 is the estimated amount of all the grains of sand on all of earths beaches by the swineburne center for astrophysics. So 10^24 is the grains of sand on a thousand earths

I still think this is the best video from 3Blue1Brown I’ve ever seen explaining the mechanics. Might help clarify for you.

https://www.youtube.com/watch?v=bBC-nXj3Ng4&vl=en

Edit: long story short I believe your last bold statement is the closest

The nonce can be anything the miner wants it to be. If the nonce is different, the resulting hash will be different (and completely random). If the difficulty is n zero bits in the hash, then 2^(-n) chance that a random nonce will work. There isn't a unique correct nonce. The first one that is found to satisfy the difficulty requirement gets accepted by the network.

It's kind of like playing the lottery. Tickets are cheap (calculating each hash is easy), but odds of success is slim. The more you calculate, higher the chances of success (the more tickets you buy, higher the chance of winning the jackpot).

You can only try to mine the next block when the previous block is known to you (and everyone), which would involve trying out many different nonces and hashing them until one works. If you are hashing at a rate of 100 hash/sec and everyone together is hashing at a rate of 1 million hash/sec, your chance of being first to guess is only 0.01%.

This creates an arms race where everyone is calculating hashes more and more quickly. At the moment everyone is calculating roughly 2*10^20 hashes / second for bitcoin mining https://www.blockchain.com/charts/hash-rate

Great answers so far! I think aside from difficulty, the other thing you must account for is how big a number a 256-bit binary number represents. Here's a good video that explains the scale and security of SHA 256: https://youtu.be/S9JGmA5_unY

So even though hashing is easy, the set of possible answers to the puzzle given the difficulty is really really large.

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The nuances involved in answering your question bring you to the greatest achievements of Satoshi's invention, keep digging.

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The short answer is that a pre-defined count of leading zero bits is a partial hash collision. Mining is a brute force competition. The size of the partial collision is calibrated to produce a result every 10 minutes (average)

As you stated, hashing is easy. There is a common misconception in many Bitcoin blogs and tutorials that "hard" is synonymous with "complex". It's not complex. Mining is hard in the number of guesses required by the entire mining network before one miner wins. From the white paper, "The average work required is exponential in the number of zero bits required"

More nuance below ...

guess a hash with a specific amount of zeroes in front of a hash

The Satoshi white paper has the words, "the hash begins with a number of zero bits". The actual implementation of Bitcoin does not follow this, because it only allows for adjustment in powers of two, which is too coarse

A Bitcoin miner wins the race if he has a block which has a header which has a hash smaller than the current target. Mathematically, this is similar to counting leading zero bits, but allows for finer adjustment

Miners take the blocks header, tx data, nonce

This is incorrect. Only the 80-byte header is hashed. It contains 6 fields. The tx data is represented by the Merkle root hash. The Merkle root hash and the nonce are 2 of these 6 fields
https://developer.bitcoin.org/reference/block_chain.html#block-headers

proof that work has been spent to get the hash to prove there was no cheating

The main reason for the work is to impose a 10-minute delay between blocks. The delay allows the distributed node network to stay synchronized. The work also has value in itself, to the extent that it prevents modifying transaction history by requiring the work to be repeated

open any command line, take any piece of data and apply a SHA-256 algorithm and you get a hash

And this is why verification of the work in a block is trivial, by executing a single hash (actually a single double-hash, but that's a minor detail). But a miner is operating a box with a few hundred special-purpose chips, brute forcing 100 trillion times per second. Our command line is much slower

is the nonce not known to the miner and along with the hash the miners have to also guess the correct nonce as well to achieve the necessary amount of zeroes?

Right (except for "amount of zeroes")

How can the nonce be unknown initially?

Its only purpose is to be unknown initially. Also, it's not very important

Zoom out a bit, far enough to see that the nonce is insignificant. One of the important attributes of a hashing algorithm is that changing as little as a single bit in the payload produces a completely different hash. By extension, the hashing algorithm has a random distribution of results (see above, brute force)

A static block has a header with 5 fields (76 bytes) unchanging, and the nonce (4 bytes) containing some value. Hash the header. If the hash is smaller than the current target, it's a winner. If not, increment the nonce, and hash again. Repeat, until the nonce rolls over to its starting value, or some other miner wins, or the hash is smaller than target

Extranonce: if the hash rolls over, the miner has to change one of the other 6 header fields. He does this indirectly, by changing a random number in the input scriptSig of the coinbase transaction. This small, inconsequential change to this transaction causes the coinbase txhash to change, which causes the Merkle root hash to change. Then the miner cycles through the approximately 4 billion nonce values again. A current generation mining devices hashes 100 trillion times per second. Therefore it exhausts the nonce range 25,000 times per second

Most miners will also modify a block's transaction list several times while mining it

The target is the upper bound of a range. The lower bound is zero. The winning condition is to have a block which has a header which has a hash less than the target. That is, within the target range

The average number of guesses required (all miners) for one miner to win the race is the total size of the 256-bit number range ( 2^256 ) divided by the size of the target range

Higher target -> easier mining
Lower target -> harder mining

The target is automatically adjusted every 2016 blocks, using a simple time ratio

New Target = Old Target * (Actual Time of Last 2016 Blocks / 20160 minutes)

https://github.com/bitcoinbook/bitcoinbook/blob/develop/ch10.asciidoc

Using this time ratio gives an accurate recalculation, without knowing the actual hash rate in the network

Difficulty: a calculated number, inversely proportional to target. Difficulty is not important in itself. It is mostly used as a convenience for humans who are unable to grok that smaller means harder

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