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@moth
I liked the rest of this post but i don't think this bit is necessarily right. For every number picking strategy there is an anti-strategy which consists of picking random sequences until you get one that wouldn't have been picked by someone using the strategy. If everyone else playing the lotto used the same strategy, you'd be better off with the anti-strategy than with just random numbers.
In general you need to double guess everyone else to try and avoid picking their numbers how ever you can. Of course if everyone picked according to the anti-strategy, you'd be better off with the strategy, but usually the anti-strategies allow a lot more different sequences than the strategies so are less likely to 'fill up'.
On the subject of cryptography, i think i read somewhere that CGHQ used the colossus computers they saved from the break-up of Bletchley park for filtering random sequences that were to be used in one-time pads. Taking out patches where the random sequence seemed to be following a predictable pattern technically made the pads less random, but leaving them in would have left patches where the pad didn't alter the clear text.