While I will always defer to Meni with regards to the rigorous math, and I respect Luke-Jr's abilities and contributions to the bitcoin community, saying that any sort of credit system is not ultimately a downward spiral into oblivion over a long enough time frame is ludicrous.
You can take evidence, if from no other source, than trying to graph the luck of a pool, and it just happens to be a problem I've been working on lately. There is a lower bound to good luck, that being 1 share. There is no upper bound to bad luck - that is why, eventually, a pool issuing credit based on future work will eventually end up in the negative.
That said, it's entirely possible that in practice, that this eventuality would not happen in the expected pool lifetime, but to say that it will never happen is pure fallacy. The time frame for it happening is another issue entirely, and I would have no idea how to even try to calculate that.
The
law of large numbers means that over time, any miner/pool's rewards will always drift toward average in the long run.
You beat me to posting. This is a fallacious interpretation of the law of large numbers known as the
gambler's fallacy. The ratio between the pool's lifetime rewards and lifetime expected rewards will tend to 1, but their difference (which is the buffer) will not tend to 0 and will grow unboundedly in average magnitude.
No, gambler's fallacy is just assuming that the
next block will move the buffer/credit toward 0. Over a long timeperiod, the law of large numbers
does apply. The difference, while it might grow, will also have diminishing
relevance, at least with ESMPPS. Real-world experiences show that the difference does
not in practice grow unbounded, however.
ESMPPS is more complicated, but not very different from this regard, so I'll focus the discussion on SMPPS. The relevance of the difference does not diminish, because what determines the attractiveness of mining
now (which is relevant for current miners considering quitting, and others considering joining) is the current difference, not the relative difference compared to the pool's lifetime earnings.
The mentioned "real-world experiences" are about as relevant as me tossing a coin and stating "real-world experience shows that coins land on tails". It's random. The statistical properties of the process are understood. Whatever you try to deduce from the experience has no bearing on what we expect from the process, it only means that your sample is too small. The expected magnitude of the difference does grow without bound as time passes, that's a fact. We can discuss the specifics of this growth if you'd like.
There is a lower bound to good luck, that being 1 share. There is no upper bound to bad luck - that is why, eventually, a pool issuing credit based on future work will eventually end up in the negative.
Actually, this has nothing to do with it. You'd have the same problems if both good and bad luck were bounded, or if bad luck was bounded and good luck was unbounded. Even a "reverse pool" which pays for found blocks and is paid for every share, will have the exact same long-term risk as a normal pool. The central limit theorem guarantees that whatever the payout distribution for a single round looks like (as long as its variance is finite), the process will over the long run be equivalent to Brownian motion.