While I agree that the mathematical probability of each event is independent, I also believe there is more going on than just pure random numbers. If you are consistently getting low best share numbers over a period of time, it is logical to predict that it is unlikely to have a sudden best share of over 64 billion.
My best share climbed to about 30 billion just before solving the block. I'm not saying its always like this, I just look for patterns, anything to help know when it is more likely to happen.
Just my opinion, and what works for me. I'm interested to know what "system" if any, others use...
There is no system, it's a common flaw most people make with statistics - ignoring something called sample vs population.
Statistics has a whole analysis of exactly that - what sample size is required to give an expected accuracy of predicting the population.
If someone sees a small sample that has their desired result, most will incorrectly assume that effect to be more apparent than it is.
The simplest and most obvious example of the expected result is to look at the pools that have mined hundreds or thousands of blocks.
Look at their long term block finding 'luck' (ignore Eligius - their pool management and code suck)
If there was some magic way to get more blocks, no doubt some pools would be finding more blocks than expected.
Instead, of course, pools that have mined many blocks are averaging close to the expected 100% luck.
