You should earn .05% of the total coins generated over a given time period. (2,628,000/year * .05% = 1,314coins/year)

While I appreciate your response, it seems like you may have misunderstood my question.

If you're mining solo, you don't get .05% of the total coins generated over a given period of time. Bitcoin is a discrete system, and you are only rewarded if you generate a block, at which point you get 50 BTC (or less, in the future). On top of that, the probabilities change every 2016 blocks because of difficulty changes.

So imagine this example scenario: The difficulty

*just* changed to 434883, which means that each time one of your miners performs a Bitcoin hash (sha256[sha256[data]]), you have a 5.4e-14% chance of it meeting the Target and rewarding you with a tasty 50 BTC prize.

Now, for 2016 blocks after that, you end up being very unlucky, and generate no blocks at all. 2016 blocks having passed, the difficulty rises to 500000. Now your probability changes to 4.7e-14%. Just because you spent all that work in the past 2016 blocks doesn't make it more likely that you'll generate a block. It's all independent. So what does that mean? It means all your work was wasted, and now it's more difficulty to generate a block. You could have left your machine off for two weeks, and gotten the same results.

Contrast that with having been in a pool for 2016 blocks. You would have gotten paid for your work during that difficulty period.

Now, again, I was terrible at statistics in college, so someone more versed in it will have to correct my (probably obvious) mistakes. It's the discontinuities that difficulty changes introduce that throws me off, really.