When a pool gets a job that job is then distributed to the miners that are connected to the pool.
So in my mind it would stand to reason then the more hashpower a pool has the better off or luckier a miner would potentially be at hitting a block if they were to be mining there. Solo or otherwise.
I just don't see how that wouldn't be the case.
The pool doesn't get a job from the network, the pool creates jobs for its miners, I think I understand where the confusion comes from, you need to understand how mining actually works, and to do so, let's just forget about pools, and pretend that there are just 10 miners mining bitcoin, so Satoshi mined the first block with a difficulty of 1 (does not matter how he did it) and now the 10 miners are trying to mine the second block.
The first block has a "block hash" and let's just pretend it's "2222" in this case, now every miner will take that number 2222, add a random number to it, then hash it into the sha256 function to hopefully produce a "hash" that has a certain amount of zeros in front which is the "difficulty", now for the sake of simplicity we will pretend the current difficulty is 1, or in other words, the hash needs to have 1 single zero in front to be taken as a successful block.
So now I take that hash of 2222 and put it into the hash function it gives me
edee29f882543b956620b26d0ee0e7e950399b1c4222f5de05e06425b4c995e9
Any leading zeros? nop, ok then I need a random number to it, and that random number is called NONCE.
let me try to add 1 after 2222, so I hash 22221
it gives me
59dad30654dd2ea8f8b27ef495a801969db3df45c2c27eaa7cdecbc6792b6ba8
no luck, let me add 2 after 2222 and hash 22222
it gives me
cc399d73903f06ee694032ab0538f05634ff7e1ce5e8e50ac330a871484f34cf
note: those hashes are real hashes, taking 2222 and adding all the numbers from 1 to 57 did not give me a zero, but then the number/nonce 58 gave me that, so if you hash 222258 you get this hash
0789d652274665285d3a581e584c2114790d335dbc95f107bfaf4b7c10de524d
You can confirm this or do a similar practice using this website > https://emn178.github.io/online-tools/sha256.html
So now when I hit this, I will broadcast to the network, and tell them, hey I found a block, it's hash is
0789d652274665285d3a581e584c2114790d335dbc95f107bfaf4b7c10de524d
The nonce I used was 58
everyone knows the previous block's hash was 2222, so they will hash 222258, if it really does start with 0, they will accept the block, and then use the new found hash to try and get another hash that starts with 0, until the difficulty changes and then they need to find a hash that starts with 00 or 000.
I think now everything about the basic mining process is clear right?
now imagine every one of these 10 people became a mining pool and has thousands of miners mining with him, it doesn't make any sense for everyone to start adding 1 and then 2 and then 3 to get to that 58 number which solved the block, everyone will be doing the same work, redoing the work the someone else did is pretty useless, as a pool operator I want the miners to try a different set of nonce/random number
I want to tell miner A, to start trying from 1 to 1000 , miner B to start from 1001 to 2000 and so on and so forth, but then I don't know if miner A will finish his 1000 tries in 1 second, it will also take a lot of recourses to allocated certain limits to every miner so what I do is, I don't send them the same work/hash
I send miner A 2222A I send miner B 2222B, this way I know even if they both start hashing 1,2,3,4 their results will be different and no duplicate work will happen.
So now, if miner B buys a large farm and I send him 2222B the total number of "digits" he can hash is limited, let's say it's only 5 digits so 2222B-----, he will do 2222B10000 and then 2222B10002, very soon he will reach to 2222B99999 and he has no more digits to change, the miner in this situation will need to change one of the parameters to open a new door of possibilities, so maybe he will do 2222BB----.
Miner B now has more chances than before because he can try more hashes, which means the pool as a whole has more chances, but miner A's chances are still limited.
The short version of this whole thing is that every individual miner has his own "job", in fact, every hash board of your miner or even every chip has its own work/job, mining to a pool does not change that, mining to a pool is like mining solo but with a promise/obligation to pay the other miners a % based on their hashrate contribution, and are also are under the same obligation, in the end, it's only 1 miner that finds the block, the pool system simply devices the profit between all miners based the hashrate.
In a solo pool like CK, the pool gives all the profit - fees only to the mine which found the block.
Please note:
** Changing a single digit in the input of the hash will give you a completely different hash, so hashing 2222B0000 will not be the same as 2222b0000
** Not only 58 solves the 2222 block, but there are dozen of other numbers that do so, it's all random, for an example 22221234 also has a hash with 0
** Miner B has more hashrate and can try more numbers in the same period of time compared to miner A, but that does not mean miner A can't beat him to the race, it's just that based on probability miner B is more likely to find a good hash
Finally, please keep in mind the above explanation of how the pool specifies different jobs to miners or how miners submit a block or what value do they hash and how they hash it, is an extreme oversimplification of the real process, there are many more parameters involved but by the understanding the above you will at least haveve a good clue and clear some (if not all ) of the confusion.