Take this lightly until confirmed, but here's my understanding...
There is no variation in the problem itself - every node is intended to work on the same block at the same time (accounting for latencies and such). The luck factor is really the random number generated at the beginning of each node's attempt to solve a new block. When a new block needs to be solved, each node generates a random value (nonce), which is used to hash the block. If that hash isn't the right one, the nonce is incremented, and the new incremented value is used to hash the block again.
Say my clunker manages 1,000 khash/s (which it really does...
), and you have a cluster that cranks out 100,000 khash/s, there's still a reasonable chance that my clunker will randomly (and very luckily) land on the value that solves the block within a very small number of hashes... say my nonce is a winner after only 10 hashes. I'm working out 1,000,000 hashes per second, so it only took me 1/100,000 of a second to solve the block. You cluster would have to (again, luckily) generate the right nonce in less than 0.00001 seconds to beat my lucky guess... which means your cluster would have guess correctly in less than 100,000,000 (hash/s) / 100,000 (s) = 1,000 hashes. Given the huge number of hashes possible, the likelihood of you hitting it in under 1,000 is remarkably low...
Granted, my chances of hitting it in under 10 hashes was even more insanely low, but you get the idea I think. So yes, the cluster will, overall, solve more blocks than my clunker, but it won't win out every single time.
Now that I've gone through all that... I'm sure someone will point out a flaw in my reasoning!
I'm fine with that though, I want to make sure I understand it all correctly!
Edit - Laszlo said it much more conscisely, but I think we made the same point...? Hopefully!
There is no variation in the problem itself - every node is intended to work on the same block at the same time (accounting for latencies and such). The luck factor is really the random number generated at the beginning of each node's attempt to solve a new block. When a new block needs to be solved, each node generates a random value (nonce), which is used to hash the block. If that hash isn't the right one, the nonce is incremented, and the new incremented value is used to hash the block again.
Say my clunker manages 1,000 khash/s (which it really does...
), and you have a cluster that cranks out 100,000 khash/s, there's still a reasonable chance that my clunker will randomly (and very luckily) land on the value that solves the block within a very small number of hashes... say my nonce is a winner after only 10 hashes. I'm working out 1,000,000 hashes per second, so it only took me 1/100,000 of a second to solve the block. You cluster would have to (again, luckily) generate the right nonce in less than 0.00001 seconds to beat my lucky guess... which means your cluster would have guess correctly in less than 100,000,000 (hash/s) / 100,000 (s) = 1,000 hashes. Given the huge number of hashes possible, the likelihood of you hitting it in under 1,000 is remarkably low...Granted, my chances of hitting it in under 10 hashes was even more insanely low, but you get the idea I think. So yes, the cluster will, overall, solve more blocks than my clunker, but it won't win out every single time.
Now that I've gone through all that... I'm sure someone will point out a flaw in my reasoning!
I'm fine with that though, I want to make sure I understand it all correctly!Edit - Laszlo said it much more conscisely, but I think we made the same point...? Hopefully!