I agree with kano. The Gambler's Fallacy isn't restricted to just discrete cases. It's exactly what you described - the belief that recent bad luck increases the chances of good luck. For independent events (such as finding blocks) this is false. The LLN doesn't work by anticorrelating proximate events, and the fallacious belief that it does is, once again, the gambler's fallacy.
Meni,
I know exactly what you are getting at, and that is not what I intended with my original statement. I should have been more explicit what I was referring to. You're and kano are reading into what I said in one way, I meant it another.
As our average shares per block is significantly higher than the expected value, over the next X blocks, where X is arbitrarily "large", our average shares will tend toward the median. The only way for that to happen is to have rounds whose total shares are near or below the median. That's why now is a good time to mine here for the next X blocks.
I wasn't talking about this block, or the next, or the one after, etc. in my original statement. I talking about the next X blocks, even though I wasn't explicit in saying that.
Now, seriously. I'm done. I need to study.
I'm sorry, but this is still wrong.
Yes, there will be rounds whose total shares are below the median. No, the frequency of such rounds over the next X blocks is not affected whatsoever by the fact that we've had recently some rounds with total shares above the median. No, now is not a better time to mine here than any other.
It is instructive to understand that while (number of occurences / number of attempts) approaches the probability of occurrence for n->Infinity, (number of occurences - expected number of occurrences) does
not approach 0, rather it increases in absolute variance for larger n.
You don't need to discuss this further if you don't want. Either you take my word for it or, when you have the time, read up on the matter, gain some experience, run simulations etc.
Man nice run of blocks
I know, right!? 99.95%, 99.99%, 98.24%, all in a row. Keep 'em coming!
Let's not, the share ratio is way off. Although I did get 10% of the shares on 1 block. Hard to see the effect on payouts with dgm. It's pretty clear on the namecoin blocks though.
Forget the share ratio. For every block found you get rewarded for shares you submitted in the past. In other words, more blocks per time unit = more money.