Quote from: forrestv on January 17, 2014, 01:49:10 AM

Quote from: mdude77 on January 17, 2014, 01:19:39 AM

Quote from: mdude77 on January 16, 2014, 10:47:24 PM

Maybe my math is wrong. The resident math expert will likely chime in here correcting me if I'm off. It may just be a feeling. Regardless, it seems to me because of the endless drastic difficulty increases, when I come out behind in that difficulty period, I will never catch up in the next difficulty period. And there will be times when I come out behind... so therefore I'm better off in a standard pool.

I'll use some extreme numbers for an example. The numbers will scale either way, I'm using these for simplicity. I'm ignoring pool fees (lower on p2pool usually than conventional pools), share difficulty increases (doesn't increase on conventional pools), and high rejects on p2pool (doesn't increase on conventional pools).

Let's say for one given BTC difficulty period, according to average, I'm supposed to mine 1 BTC.

That period is awful luck wise. I only get 50% of what I'm supposed to. Instead of 1 BTC, I get 0.5 BTC.

The next period, my luck reverses. I make 50% more than I'm supposed to! But difficulty also increased 50%. I'm supposed to make 0.5BTC, on average, but instead I make 0.75BTC.

For those periods, I made a total of 1.25BTC.

On a conventional pool with low variance, I would have made 1.5BTC.

Let's try it with difficulty increasing 30%.

2nd period, my luck reverses. I'm supposed to make 0.7BTC, instead I make 1.05BTC.

For those two periods, I should have made 1.7BTC. Instead I made 1.55BTC. On a conventional pool with low variance, I would be a lot closer to 1.7BTC.

Granted, this is not specific to p2pool. The same logic applies to any pool with high variance. What's unique to p2pool is the high share difficulty (increases variance) and rejects (also increases variance).

Is there a flaw in my logic?

M

Yes. You're assuming that you'll have bad luck now and good luck later, but you have to look at all possible outcomes to calculate what you expect to happen.

Using the average return for your case and the case where you have good luck now and bad luck later happens to be enough for the calculated return to be what it should be:

First period: supposed to mine 1 BTC, mine 1.5 BTC instead (+50% luck)
Second period: supposed to mine 0.5 BTC, mine 0.25 BTC instead (-50% luck)

You made 1.75 BTC, more than expected.

Average of 1.25 BTC and 1.75 BTC = 1.5 BTC, what you're "supposed to mine."

Good point about the average.

However, when you factor in the additional variance introduced by high share difficulty and reject rate, and you get more variance than you would elsewhere.

Yes?

M