I only have to reference the polmine miners who are fleeing the pool now that they are stuck on a 9 million block.
Willing to be proved wrong, someone might want to supply a link that shows, over a period of a month or longer, for 1000Mhash mining (ie, non trivial) the average return from sitting versus hopping?
The actual Mhps is not important, just the efficiency.
I suggested a reasonable hash rate because operating at 1 Mhash there are appreciable probabilities of not completing shares or making a reasonable contribution. At least when calculating at a reasonable speed and reasonable time span, so of those noise effects drop away.
I there were no pools (everyone was their own pool- solo), or one pool, I have a chance of finding the block for every share I crunch. If I am in a pool where people come in and out, or I jump around, my chance of finding a block does not change, nor does it change for anyone else. A bit like playing roulette (which I don't do because of the stacked odds) - one spin or table is much like another. If hopping worked so well, people would be doing this in casinos.
Great thing random chance. Full points to the poster mentioning "gambler's fallacy".