PPS pools
Proportional. PPS is something else entirely.
Oops.
So it's not like Poker at all. You can still play poker if everyone knows the odds, you can't mine in prop if everyone hops.
The mining halting is really the function of the optimal hopping strategy. In poker playing the perfect strategy is close to impossible, but if everyone did, the situation would be close - everyone would win and lose the same on average.