@shamathana
Of course you can contrive scenarios where certain entry/exit-patterns get more; payments do have a random component and so some patterns will result in more or less in the short run. (Sometimes betting on red at the roulette wheel results in gains over the next few spins.)
But there are an equal prevalence of scenarios where those same entry/exit-patterns, using information available at the moment of participate/don't-participate decisionmaking, get less.
really? please show me i do not see that! i should have processed all cases: shorter, average and longer rounds. and they look like hopping prop too me. shorter rounds: u get all of the extra rewards, average rounds: you even out with the normals, longer rounds u get less from the deficit(which is not the excatly right word since u still get paid, but not so much as u should have on average. yes i speak english as a foreign laguange :-P).
The 'proof' you request is trivial: PPLNS payments are completely determined by a formula whose only inputs are future unknowable events uncorrelated with the recent past. There is thus no way to look at the history of a pool and decide, 'now if I enter(leave) I will get more(less)'. At every moment, the prospective value of participating is equal. Hence, no hopping by any rational miner.
@ future unknowable events uncorrelated with the recent past
yes, and true for prop too. the deciding factor is in hopping prop/pplns, that if the round is better than average u get the reward, but if it's below average u still make more than the normalo. i can go into more details if u wish, but first i will eat.
@At every moment, the prospective value of participating is equal
equally random, because it is infuenced by the N = difficulty * 2 shares still wanting to be generated after urs.
Even a miner who is able to predict with certainty an upcoming inrush of new participants, or outrush, doesn't gain any net gain in expected-return. More co-miners mean a block will be hit quicker (by wall-clock time), but also old shares will expire quicker (by wall-clock time). Knowing an influx or outflux is imminent just means variance over time will fall or rise respectively, as is the case with any pool expanding or contracting. Not that expected return will rise or fall.
yes true, but still not the point. nobody knows the future and hoppers don't know it either. they KNOW if they hop they get most of the sharevalue increases(shorter rounds) and less of the shavevalue decreases(longer rounds) from the pool.