Quote from: ggoner on July 01, 2014, 12:33:24 AM

The heading on the pool graph doesn't make sense. (The second graph on the page.)

Thanks! That's exactly the sort of grammar error I never seem to notice - should now be fixed

Quote from: ggoner on July 01, 2014, 12:33:24 AM

Not sure I am following your graph for pools. They seem to suggest there is a big difference over an extended period of time. For the most part luck is luck. It averages out over time like flipping a coin. When pool mining, a larger pool has more consistent luck over a short period of time, but your reward is smaller for each piece of luck. In a smaller pool your luck is more eratic unless you look at it over a longer period of time. But your reward is larger for each piece of luck. It averages out to be similar when you look at it over a long period of time. (That is, unless you are in a pool that has extended periods of bad luck.) Many people are impatient. They want the coin NOW. That is the draw of larger pools. But large pools can have bad luck too.

Yes, over time there can be a very wide variance with smaller pools or when solo mining. As pool sizes increase then the variance reduces dramatically. As you point out this is a function of luck, and yes, over time this somewhat averages out, but when the network is expanding then early luck is much more important than later luck. The larger pools are much more likely to be averagely lucky at a consistent rate so they don't have as much downside risk or as much upside potential.

If you look at the last graph it's showing that the average BTC payout is almost the same for any of the pool options (not so for solo mining), but smaller pools have much more variance.

Quote from: ggoner on July 01, 2014, 12:33:24 AM

Maybe I just don't get what you are trying to do. Perhaps if you graphed actual pool results for a number of pools of various sizes over 6 months you would be able to see a correlation to your predictions, or not. I could be wrong, but it doesn't seem like 10% of the miners mining in pools would be making twice the average coin. If its true... which pool is that?

The numbers are generated from running 10M mining simulations for each pool size combination so they represent all of the potential outcomes and the probability of each one. Actual results will fit in there somewhere but will always follow a slightly different path. The simulations predict how likely any particular path will be in the future.

The issue of random behaviour is something I've discussed in some of the earlier articles on the site. Random chance and the problems of inferring hash rates from measured data affect the statistics in quite surprising ways at times.

In terms of the 10% of miners. If you look at a pool in which my hypothetical miner was running their hashing as part of a pool that has 1% of the total hash rate then the normal range would be in the range 31.5 to 37.5 BTC; it's not 2x outside that though.