Re: iPod classic on shuffle
Not to be antagonistic, but are you basing your "look at any previous results" on an actual study? Because I've never come across anything which would confirm or even hint at that.
Perhaps an easier way of understanding the probabilities is to remove the numbers painted on those balls entirely, as their sole purpose is to distinguish one ball from the next and possess no sequential/factorial/etc. correlation to each other. So if, over the numbers, we randomly assigned painted each ball with the representation of an animal, (1 = grizzly bear, 2 = squid, 3 = porpoise ... 23 = salmon, 24 = raccoon, 25 = flamingo... 38 = dung beetle, 39 = fruit bat, 40 = salamander, etc.), you probably wouldn't expect there to be any such "semi-patterns" you spoke of before, would you? Your brain might, however, start to suggest to you that patterns exist where in fact they do not. Maybe you would notice that never does anyone ever win with exclusively land creature balls and deduce that you could increase your chances of winning by ensuring that each combination has at least one bird or fish. This would merely be your brain trying to find a logical pattern where one does not exist...any combination of six land creatures, six non-vertebrates, etc. would have exactly the same chance of winning as any randomly chosen combination.
Hopefully that non-numeric perspective helps make sense of why the statistical theory must hold true in practice. And even if not, at least now you can least be somewhat amused at the thought of a lottery player leaning forward towards the TV, stub in sweaty hand, desperately pleading "come on porpoise!"
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No antagonism felt or meant - hopefully just an interesting bit of debate.
I understand what you are saying, but even you must see that certain 'patterns', or maybe 'rules' can be applied to winning numbers. If not in a hard and fast way, at least in a vague general way that can narrow down probabilities. Even in your animal version, I think it would be more likely in practice for a cluster of similar animals plus a random spread to come up rather than either a set all from the same type or a set where all are different or indeed, say, a set of animals with consecutive alphabetical names.
Here are the last 50-odd winning numbers.
http://www.national-lottery.co.uk/player/p/drawHistory.do
I think this is a fairly typical sample, that could be replicated again and again.
My theory of 3-from-one-row plus 3-spread out only works in about half of these answers, but I think even if it only works half the time, that would at least - if only fractionally - narrow the odds.
Certainly nothing even approaching 6-in-a-row - and presumably nothing like that has ever come up.
Not sure that I can put it better than that.