Just because the coin landed on tails four times in a row doesn't mean that going to someone else's coin-flip game is going to get you any more wins in the future. You could make the argument that maybe my coin or dice aren't perfect and favor one side, but bitcoin has perfect dice.
I don't think you understand why pool hopping really is profitable over the long term as
compared to switching roulette tables or slot machines and why gamblers fallacy doesn't apply to block finding probability.
Proportional pool luck is determined by current difficulty factor and hash rate.
There is a certain statistical point at which blocks will be *usually* found given a large enough statistical sample (100, 1000 or more blocks)
A gambler can't *expect* to get a certain amount of heads or tails in a coin flip because the statistical probability
of either one is always 50% (assuming it can't fall on it's side) over the long term.
A miner can expect 95% of blocks to be solved in the long term at 1.56m difficulty and roughly 9½ hours spent at 600ghash/s.
If the occurrence of rounds surpassing 9½ hours becomes significantly more than 5% in the long term (let's say 20%), the miner can expect foul play.
Just as if a coin would consistently fall on the tails side over 1 million throws (let's say to a 70:30 ratio), you could suspect the casino has a weighted/rigged coin.
3-8% would probably pass as variance
I certainly understand the maths behind pool hopping; if you had five identical proportional pools and just hopped to the next at the start of its new round, hoping to sip the cream from short rounds, you could hope for a significant return above the baseline (at the expense of full-time miners). I do not address the quantum valuation of individual shares; quote: "The past luckiness of a pool, or even how long the current round is, has nothing to do with how much you will make in
future rounds". Actually that should be clarified to "how much you make
over a period of time in future rounds", for in rounds you simply get your share of 50BTC.
You are saying if some rounds go three times as long as the average (ignoring the ones that are one third length), I should expect foul play?? As my example above, that is like saying if I flip heads three times in a row (87.5% chance of that not happening in three coin flips), then the coin is probably fixed. Your previous posts with some graphs and the statement that a round "already passed 100% probability of hitting block" shows that you are not estimating probability correctly when making your assessments; a
statistician can expect an average of 89.753% of rounds to be solved by 9.5 hours at 600Gh/s. Feel free to change to a different proportional pool if you desire, for their past luck does not predict or affect future winnings either (but their fees will..) I would recommend a high hashrate pool, because their 80th percentile variance will be 5 minutes to 2 hours instead of 26 minutes to 9.6 hours, and you might get less bent out of shape. Their pool threads will probably get an earful of "why are my round payments 1/5 as much" though...