Quote from: fpgaminer on June 01, 2011, 09:58:35 PM

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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.

Yes you do. Over time it will average out to your percentage of hash rate towards the global hash rate. You'll get nothing for a long time then get lucky and get 50. over a couple years time it will average out. The probability doesn't change. Difficulty is another way of saying global hash rate. As the global hash rate goes up the difficulty goes up to try to get 1 solution every 10 minutes. Global hash rate goes up your percentage goes down.

Quote from: fpgaminer on June 01, 2011, 09:58:35 PM

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.

Yeah you could have left your machine off for two weeks, or you could have been very luck and solved all 2016 blocks. It is all chance. Your machine is just rolling the dice a couple billion times a second and hoping your numbers come up. The rolls in the past have no bearing on the future rolls.

Quote from: fpgaminer on June 01, 2011, 09:58:35 PM

Contrast that with having been in a pool for 2016 blocks. You would have gotten paid foryour 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.

OVER TIME a solo miner will generate the same amount of coins as a pool miner that has a 0% charge. Pooling gives you a steady but small amount of coins and solo gives you nothing for a long time and then bam! 50.

Your chances of solving go down equally when the difficulty goes up whether you are pooling or solo.