If I were to pick numbers for a lottery perhaps, would a sequence like that be a bad idea?
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All the combinations have the same chance of occurring, what changes are the human impact on the numbers, for a lottery you in general want to pick a combination that other humans haven’t chosen, so humans will often pick sequences which include 7 or the numbers 1 to 31 for birthdays. So the chances of numbers 1 to 7 happening are the same but several hundred people may have picked the same sequence so the jackpot will be smaller.
> the probability of a sequence of say 7 consecutive numbers 1 2 3 4 5 6 7 is lower than the sequence of 7 randomly generated digts.
Well yes, that’s trivial: getting *one specific* sequence instead of *any sequence* is a rather narrower target to aim for.
What you need to consider is that it has the same probability of *any* single specific sequence assuming the draw is truly random without tricky stuff like having ten 4 balls in the bucket you pull from. 4 8 3 5 2 7 1 has the exact same probability as 1 2 3 4 5 6 7.
For the lottery the order does not matter by the way, but winning with consecutive numbers still has the same odds as nailing any other set of numbers.
The probability of any 7-digit combination being drawn is equal, be it 1234567 or literally any other combination of 7 numbers.
The small edge you can get in lotteries though is in picking numbers that are seldom selected by other people. That way, if you do win, you won’t have to split the jackpot. This is the only compelling argument to avoiding consecutive sequences or other “popular” combinations (e.g. possible birthdates, well-known sequences, etc).
I think you are asking about minimizing the number of winners to share with, not probabilities of the winning numbers,
I guess most people will select something that “looks random”. However I don’t think 1,2,3,4,5,6,7 would be the best option because there is probably someone out there with similar thoughts. I think something like 4,5,6,12,13,14,15 would be a better choice.
You heard wrong. If you’re picking 7 numbers the odds of any given sequence of numbers will be exactly the same as the odds of another given sequence of numbers. There’s nothing special about 1 2 3 4 5 6 7 as a given sequence of numbers other than people thinking it’s special.