- Decreasing chances for small pools to create blocks and attract more mining power to grow. With no reward on mid-size pools all miners should prefer to mine on big pools with better expectations for return on investment, rather than supporting new pools.
I stopped reading here. This isn't correct.
Expected return is not increased by using a larger pool. Mining is not a race, it's a random lottery.
But I understood that if a pool has more people it has more chances of winning the lottery, is this incorrect?
Yes, but the winnings are split proportionally among those extra people.
That said, with a larger pool it's less likely that your block reward will be orphaned by another block that manages to propagate to the network faster than yours. But that's not a big effect right now in terms of profitability because fees aren't very important - a rational miner will keep their blocks small to keep that orphan risk down.
That makes sense to me.
The centralization problem is that a new small mining pool or an existing pool that becomes small after the arrival of a new ASICs pool has no incentives to continue mining because the expected time to find a block could become bigger than a lifetime. Therefore, it's better join the bigger pool to receive a fraction of the reward now at current difficulty than expect a large reward in an infinite time frame, specially with increasing difficulty.
This is exactly what happens right now with solo mining.
But the reward is much bigger. Each miner can choose the appropriate risk/reward they want. Huge pools with low variance should be able to charge more fees (since most miners prefer low variance), therefore the incentive to have a smaller pool works out.