The increasing hashrate is relevant, since had it been stable, in the long run the profit per day from mining on any pool (or even solo) would be the same: it converges to the expectation. (This is what I referred to as "recovering expectation".)
It does not converge to the expectation after the fact. This is the gamblers fallacy. You expect to be near the expectation, indeed, but after your first dice is cast your winnings and losses are _permanent_ and have no bearing on the future results.
Sure all winnings are permanent, and independent on all instants. What I'm saying has nothing to do with this though:
If the the difficulty is constant, your payout per day converges to the expectation of the payout on the first day, which is the same on any pool. The variance is irrelevant. If the difficulty increases, your winning per day does
not converge to the expectation on the first day, since the expectation itself changes (goes to 0).
This makes the variance and consequently choosing the pool relevant.
Beyond that, the difference in variance between mining in a 10% hashrate pool and a 40% hashrate pool is negligible— the variance is dominated by the network finding variance long before that point.
I didn't get the last point.
There is pretty substantial differences in the mining income for the whole network... once you're up at the 10% level the overall network variation is a substantial part of the variation you experience, the change in your 10%-tile income between 10% and 40% pools is pretty small.. a percent or so.
It's an example of the tragedy of the commons. Being selfish and letting others solve the problem or sacrificing one's interest for the sake of a negligible contribution to the greater good.
Usually "tragedy of the commons" refers to interests being out of alignment (e.g. whats good for you is bad for everyone). Arguably the issue is a freeloading loss, but I'm doubtful. Considering that hardware companies are successfully selling hardware at price _far_ beyond what reasonable models of future income show is profitable, it's really hard for me to buy that miners are acting rationally enough to be micromanaging operating costs to the point where they're sitting around not writing functionality because they hope someone else will.
OK I agree that what is rational is one thing, and what people do is another.
I think miners get to experience the variance very quickly though. Probably it often goes like this:
a miner with his new rig joins a small pool because it's good for all. He watches his incomde for a
couple of hours and sees that it is zero. Meanwhile ghash gets a few blocks. He thinks - well, I could
have already made some coin! Damn. I guess I have to stick to my pool because now we are more likely to find a block! Wait, this is gambler's fallacy. What I was doing in the past few hours does not influence my future income. I can just as well switch to ghash now and start earning me some coin!!!
Of course there are also some who quickly get a profit from that 1% pool, but it being a 1% pool, most don't.
Every nameable centeralized pool has been hacked (except f2pool afaik, but it hasn't been around that long), in some cases with _large_ amounts stolen. In the case of ghash.io in addition to taking the operators funds they executed doublespends to the tune of 3kbtc lost. And thats after the survivorship bias— many pools in the past were popular and vanished with users funds. By comparison I don't think P2Pool is risky at all, it's the centralized pools that are risky even if you're counting on selling your coin before ecosystem damage makes it worthless.
yes that's an important consideration and a different argument.
Ultimately I think it would have been easy to make P2Pool dominate the network, and then the variance argument would play in its favour, had it not been for the fact that with P2Pool you need to maintain a copy of the blockchain.