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I realise that opinion on a specific pool is subjective and prone to change.

My question: If I am in pool A and additional miners join then my share in the pool is reduced proportionately. Additionally, the pool received more block find rewards proportionately. Similarly, the reverse if users leave the pool. My mining reward in the pool is largely unchanged.

If miners join pool B then pool A finds lees blocks proportionately and my mining reward is also reduced. The reverse is also true.

It seems that the most profitable pool, with all other things being equal, is always the pool with the most miners joining? Both because they are not joining pool B I do not suffer any loss (or, they are leaving pool C) and, because the new miners are joining pool A I do not suffer any loss.

It seems like the ideal scenario is for pool A to syphon all users from all other pools and become a conglomerated 'Mining Central'? Or rather, for all other miners in pool B and C to quit.

Please correct my assumptions if they are wrong.

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This isn't correct. Your reward is reduced (in the long run) by the same amount whenever a new miner joins, regardless of whether they choose your pool or a different one.

If they choose your pool, it's true that your share of the pool decreases, and the pool's share of the total rewards increases, but these changes don't completely cancel out. The net effect is a decrease in your reward.

Let's try an example with small numbers. Suppose there are 10 miners in the world, all having equal hash power. 6 of them, including you, belong to Pool A, and the other 4 belong to Pool B. So Pool A collects 6/10 of all rewards, and you get 1/6 of those, so you are getting 1/10 of all rewards.

Now suppose a new miner joins Pool A. Pool A will now get 7/11 of all rewards, and you get 1/7 of those, so you are now getting 1/11 of all rewards - less than before. If you work out the numbers, the pool's fraction of the total got multiplied by 1.06, and your fraction of the pool got divided by 1.16.

If the new miner joins Pool B instead, Pool A now gets 6/11 of all rewards, and you get 1/6 of those, so your share of the total is again 1/11.

As such, ignoring differences in pool administration fees and such, you get rewarded the same whether you are in a large pool or a small one. The only difference is that in a large pool, your rewards will be paid out more steadily as frequent small payments, while in a small pool, you will tend to see infrequent large payments instead.

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