Quote from: becoin on June 15, 2011, 09:27:37 PM

There is only one valid solution to a block, not many. Whatever small they are, shares are always part of a valid solution to a block.

That's incorrect. There are a large number of solutions to any given block. For a given difficulty, there is a target hash value and all hashes smaller than this target value are valid solutions to a block. If you look at the Bitcoin Calculator you can enter any difficulty and see the corresponding target value.

Notice that the lower the difficulty, the higher the target value. The higher the target value, the more numbers are smaller than the target and therefore the easier it is to find a solution. I encourage you to play with the calculator until you're sure you understand how this works, because it's key to understanding what is happening in your case.

Now, a share is the same thing as a difficulty 1 hash: it is a hash that would be a valid solution to a block if the difficulty was 1. In other words, it's a hash value smaller than 2.695953529101131e+67. Let's say your miner crunches some data and comes up with a hash of 1e+65. This would be a valid solution if the difficulty was 1 since it's smaller than that target. But it's not small enough to be a valid solution at the current difficulty of 877226, which has a target value of 3.073269009644151e+61. This hash is useless to you except as reassurance that your miner is working correctly.

Say you then come up with a hash of 1e+60. This is valid at difficulty 1 and also at difficulty 877226 and is a valid solution to the block. This earns you 50 bitcoins and a fanfare of trumpets.

From this example I hope you can see that a share/difficulty 1 hash is either a valid solution to a block, or it is utterly useless. Shares never "combine" to solve a block and no number of non-winning shares are of any value.

You may be wondering why pools even collect shares if most shares are worthless and cannot be combined in any way. The reason is simple: the fact that you are submitting shares to the pool is proof that you're really trying to solve the block and not just freeloading. A faster machine will generate more shares in a given period of time and therefore deserve more credit when one share actually happens to be valid.

I don't want to derail this topic discussing the technical details of mining, so if you're still confused let's move this to a separate topic