PPLNS was created to close an exploit in proportional-style payouts, where you could join the pool which solved the most recent block (and as such, their share counters reset.) The reason this works is because *if* the pool gets another block quickly, the "new" miner who just joined will receive an unfair portion of the payouts compared to those who had been mining for a longer period of time. If the pool did not find another block "quickly" (as defined by your pool hopping algorithm), then you would switch to the next pool which found the most recent block, and repeat.
The reason this doesn't work with PPLNS, even if you know the value of N, is because you cannot force a payout "round" to be short. The last N shares are unaffected by any found blocks, therefore no counters are reset. It is, in effect, a rolling window of time. No matter when you join/leave, you're not going to gain an unfair advantage.
I agree with most of that. Where I disagree is Prop is random, based only on blocks. PPLNS has a non random factor N
whose value is not publicly available. They both can be gamed just like any lottery, but in lotteries and Prop, all the variables
are known or available to all. In PPLNS N is only known to some.
That "rolling window of time" is regular as defined by N while block time is strictly random. That gives those who know the
value of N an advantage. You can still time your mining to maximize the values of your shares if you know N.
If N was public it would be fair.
... you just said right there, block time is strictly random. This means, because proportional starts counting everyone's work when they mine a new block, this means the round length is indeed random. Now, you can definitely figure out N if you care enough, but it doesn't matter, as long as N is large enough and does not change.
EDIT: Whenever you begin mining (in a PPLNS system), your shares start being counted there. Even if you know N, there is no point whatsoever in pool hopping - this is because no matter when you join, your share won't change. You can see this clearly because N makes the round time constant - instead of random, like with proportional.
