Mining rewards based on pool size

[davejh]

As part of my attempts to understand mining stats I built some more simulations of mining in various different ways with the same hash rate. This includes solo mining, mining in very small pools and mining in large pools. I wanted to understand just how much the size of a pool really affects the likely payouts over the current useful lifespan of a mining setup.

The results are at: http://hashingit.com/analysis/32-the-gamblers-guide-to-bitcoin-mining

Feedback appreciated, as always (I especially appreciate comments about typos and grammatical mistakes )

[TheRealSteve]

You and user eephoich should get together
https://bitcointalk.org/index.php?topic=651463.0

[ggoner]

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

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.

The larger factor is the difficulty, which is largely in direct relationship to the total hash rate. If you have more luck before the hash rate goes up you will earn a higher reward. If your lucky streak is after the hash rate increases you will earn a lower reward. What is the probability of each event over 15 difficulty increases? Wouldn't it average out for the average miner? Individual results may vary.

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 only magic elixir is to be very very lucky. In which case you should solo mine. Are you a lucky guy? Gonna bet your whole investment on it?

[davejh]

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

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.

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.

[ggoner]

My bad on the 10% miners, the double coins was on solo mining not pool mining.

Thanks, I'm more comfortable with what you are representing.

I can see now that the variance for each pool size is caused more by the difficulty changes than anything else. If the difficulty remained static, results would be much more uniform over a long period of time. At least that is what I would expect.

[davejh]

My bad on the 10% miners, the double coins was on solo mining not pool mining.

Thanks, I'm more comfortable with what you are representing.

I can see now that the variance for each pool size is caused more by the difficulty changes than anything else. If the difficulty remained static, results would be much more uniform over a long period of time. At least that is what I would expect.

Yes, as the difficulty changes reduce to 0 (on average - they can't actually hit 0 and just stay there) then the advantages for larger mining pools would be eliminated in the longer-term. The problem, of course, is that it's unlikely we'll see a 0% average difficulty any time soon.

[jonnybravo0311]

Great article as usual davejh.

I think the final graph in the piece sums it up exceedingly well.  If you're an "investor" you go with any pool that has 10% or more of the total network's hash rate.  If you're a "gambler", you go with solo mining or the very small pool.  Most of us know this is true, but what I believe to be the very telling part of that final graph is that you DON'T need to mine on the largest pool - that the earnings curves from 10% on up are extremely closely spaced together.

[davejh]

Great article as usual davejh.

I think the final graph in the piece sums it up exceedingly well.  If you're an "investor" you go with any pool that has 10% or more of the total network's hash rate.  If you're a "gambler", you go with solo mining or the very small pool.  Most of us know this is true, but what I believe to be the very telling part of that final graph is that you DON'T need to mine on the largest pool - that the earnings curves from 10% on up are extremely closely spaced together.

Certainly that was one of the interesting things to me. When difficulties are changing at 1.5% to 2% per day then larger pools are definitely safer, but at the 1% level there's not a huge amount to justify the need to participate in a huge pool. At 0.5% growth per day the justifications become even smaller and as we hit the brick wall on process technology then 0.5% changes (or smaller) will seemingly be more likely to be the norm (0.5% per day would still represent 6.17x per year - still a phenomenal growth rate by most technology standards).