- 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.