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Can we argue that, since the difficulty set by pools is lower than the actual one, "old" hardware remain profitable for longer and thus are used for more time. And this, indirectly, increases the actual hash rate of the entire network? (and thus difficulty as well?)
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No, you see the difficulty of a pool is lower in order for the pool to be able to verify that the miners are actually working on a solution. The shares a miner obtains are mostly not valid blocks, which is what gets rewarded in Bitcoin, paid out to the pool and then paid to the miners.
The difficulty to create a block is not influenced by a pool's share difficulty, hence the total payouts the pool makes does not change, and old hardware is just as (un-)profitable.
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Yes.
Although technically the profitability of old hardware doesn't change, it's just that the variance becomes killing if your hash rate is too low. Getting 0.1 BTC per day or having a 1 in 250 days chance of getting 25 BTC, changes the game from a lottery to a steady predictable income.
This also has the effect of allowing small miners (even with new hardware) to play along.
Yes, both those effects do increase the total hash rate of the network and thus the difficulty. And in that regard the security and decentralization of the network. Except that in most pool solutions, the pool maintainer needs to be trusted as a "centralized" party. Mixed blessing there.
Yes. Pools were invented to keep CPU miners in the game when GPU-mining begun. In the same way they are now keeping small home miners in the game, in a world now dominated by warehouse-size miners. – Dr.Haribo – 2016-03-15T10:41:36.723
hmm.. just posted my answer and then yours popped up. Initial reaction was to agree with you. But actually no, this is not true: as a user you are concerned with the payout. Pools actually do payout differently than solo-mining. They do payout lower difficulty work, while solo-mining with a high likelyhood doesn't. Of course the total doesn't change, but from the point of view of the individual one has to be very lucky to hit the 25 BTC jackpot and otherwise you get nothing. – Jannes – 2016-03-14T15:58:05.043
Yes, indeed the reason to join a pool is to spread the income over a time. Notice I did not mention solo-mining, instead only looking at the income of the mining pool. The pool redistributes its income to its miners, since the mining pool's income depends on network difficulty that is the limiting factor. The lower share difficulty does not influence the miner's income, hence it does not influence the sum of payouts. Lower share difficulty only increases payout granularity. – cdecker – 2016-03-14T16:06:16.450