I was thinking do all the results have the same odds in say a standard 8 ball lottery, it feels like to me you’re less likely to get a sequential set (eg. 1, 2, 3, 4, 5, 6, 7, 8, not necessarily drawn in that order) than get a heap of balls at random, it just makes me wonder if the odds are the same or if I’m over thinking.
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The odds are exactly the same as any other combination of numbers.
Part of the reason why we tend to feel it’s less likely is in your post.
You’re comparing “a sequential set” – and you give a specific example – to “a heap of balls at random”. So you’re comparing something quite specific and small to something quite vague and large.
We do the same when we’re looking at past results. If you see a result like ’48, 7, 41, 13, 39, 1′ this goes in your mental “heap of balls at random” category. If you see a result like ‘1, 2, 3, 4, 5, 6’ that’s your “some kind of logic” category.
Now of course, there’s a lot less in the “logic” category than the “random” category, so it rarely comes up (probably you’ve never seen a result like that). Your brain is right to think the odds of a number from the “logic” category coming up are lower. Unfortunately it will tend to go a step further and go “this category comes up less often, so individual members of it must come up less often”.
TL;DR human brains take a lot of shortcuts, and are generally rubbish at probability.
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