user54585: In pool mining, it's my understanding that miners solve a reduced difficulty hash which proves that work is being done and also simultaneously helps solve a block.
How is this computationally possible? and how can the pool difficulty be different from the Bitcoin block?
I guess I don't understand how work on blocks is computationally divided among pool miners.  

user54606: From what I understand basically if the entire blockchain requires a very high hash rate (for example result should end with 100 zeros) in pool mining your shares will be based on the number of times you are able to solve a simpler problem requiring a medium hash rate (should end with 50 zeros). So you are still solving the same problem but attempts where you get the simpler answer is used to calculate the shares that you are given.

user48884: Contrary to popular belief, mining is not something where there is progress. Each hash has the same probability of being a valid block hash. You could get lucky and find a valid hash with your next hash, or you could not. There is no progress that is made. When you mine on a lower difficulty, the target that your hash must be under is much higher than that of the networks. With enough hashes, someone will eventually find a hash that is lower than the network target, and that hash would also be lower than their pool target. The higher target (thus lower difficulty) is only for tracking who is actually doing work and how much work they are doing so that they can be paid appropriately.

54585: <p>In pool mining, it's my understanding that miners solve a reduced difficulty hash which proves that work is being done and also simultaneously helps solve a block.</p>

<p>How is this computationally possible? and how can the pool difficulty be different from the Bitcoin block?
I guess I don't understand how work on blocks is computationally divided among pool miners.  </p>
 54606: <p>From what I understand basically if the entire blockchain requires a very high hash rate (for example result should end with 100 zeros) in pool mining your shares will be based on the number of times you are able to solve a simpler problem requiring a medium hash rate (should end with 50 zeros). So you are still solving the same problem but attempts where you get the simpler answer is used to calculate the shares that you are given.</p>
 48884: <p>Contrary to popular belief, mining is not something where there is progress. Each hash has the same probability of being a valid block hash. You could get lucky and find a valid hash with your next hash, or you could not. There is no progress that is made. When you mine on a lower difficulty, the target that your hash must be under is much higher than that of the networks. With enough hashes, someone will eventually find a hash that is lower than the network target, and that hash would also be lower than their pool target. The higher target (thus lower difficulty) is only for tracking who is actually doing work and how much work they are doing so that they can be paid appropriately.</p>
