Nobody can predict the future, but the past is not as mysterious; the number of shares already submitted during this round, at the time of deciding on a course of action, directly affects the estimates of what the eventual length of the round will be.
Umm - how can you start a sentence with a fact and end it with the exact opposite of that factual statement?
You've just stated correctly that you cannot predict the future, but then said the past affects the future.
Simplest link to verify it:
http://en.wikipedia.org/wiki/Gamblers_fallacyI'll put it this way:
Once you have mined n shares, there is absolutely no change in the probability of finding a block in the next share than there was in all of the previous shares back to the first.
I might have to reword this sentence in a way which is less dramatic but also less ambiguous.
What I meant is that, if a future event is random and independent of the past, you can't predict it better than the prior probability.
But if the event is not independent of the past, you certainly can improve upon the prior.
"Number of shares remaining until round end" is independent on the past. "Eventual total number of shares at the end of current round" is certainly dependent on the past. At round start, "probability that the round will have >3D shares" is 5%. If 2D shares have already been found, this probability is 37%. If 2.9D have been found it's 90%, and if 3D or more have been found it's 100%.
And, pertinently, the eventual total number of shares at the end of current round (denoted N) is what matters, since your payout for every share you submit is B/N. If E[B/N] is less than what you could get per share elsewhere (which is B/D), you should mine elsewhere.
And I'll repeat the simple example - if 2D shares have already been found, then necessarily N>2D so E[B/N] < B/(2D), so you want to mine elsewhere.
Secondly, regarding your copy of Roulo's suggestion that pools that pay based on share% mined are affected detrimentally by hoppers
(or: hoppers make more BTC by hopping)
So, if I say something which is true, and which was already said before many times, and I'm properly citing an influential paper about it, redoing the calculations myself and adding calculations and results which were never published before, then I'm "copying"?
Let me use the simplest way to disprove a theory: An example that fails the theory will show it to be false.
Take this statement from Roulo's document:
It means that with optimal strategy it is possible to gain on average 28% of ones hashrate by switching from the pool after 43.5% of the current difficulty number of shares have been contributed. Notice that the function is fairly flat and even after switching after λ = 1, one can gain a fairly respectable 22% of ones hashrate.
Thus stating that from 43.5% to 100% (λ = 1) there is a gain between 28% and 22%
Yet a simple example with 50% shows this to be false:
If you mine with a share% of 10% at a site for 50% of the expected time to find a block, then, your shares will be worth on average 5% instead of 10% (since your % will slowly drop, after you leave, to 5% (on average) until the block is found)
During this time you can go to another pool with the same hash rate and do the same thing ... and thus get a total of 10% (5% from each) ... which is what you would have got to start with - not anywhere near 20% extra ...
You'll have 5% of the shares. You'll have more than 5% of the reward because you will have more shares in short rounds than in long rounds.