If it's done properly, it's the same as any other sequence, right?

I don't know how many balls they have and whether there is replacement to tell you the actual number, but there shouldn't be anything special about this one among all the other possible sequences, except that it's more likely to be guessed.

Actually, it's more!

1,2,3,4,5,6 and 10,11,12,13,14,15 and even 2,4,6,8,10,12 would have had the same amount of attention and scruitny.

So "what are the odds that a sequence of numbers would come out that would look 'funny' to many people" is now not one out of n, it's several hundred out of n.

I was thinking what's the odds that any number drawn will have a special relationship to the number drawn before, where the degree of specialness is determined by how many people hearing the number think "huh, that's weird"

Yes, but there are vastly more non-incrementing sequences than incrementing sequences.

Many repliers are computing the probability of this exact draw, but probably a more relevant consideration of "this" is "the odds of a 'suspiciously regular' combination being drawn". The probability of one of those occurring is (the number of such sequences you name):42,375,200, or that number over 42,375,200.

There is some inherent fuzziness in what you consider a "suspicious sequence", obviously. If you stick to entire sequences you don't get very many; however, if you consider "1 2 3 4 5" in the original numbers to be suspicious regardless of the bonus ball draw, then the number of such sequences starts going up fairly quickly. (Include things like [1,3,5,7,9], [2,4,6,8,10], [3,6,9,12,15], etc.)

It's pretty easy to get up to a couple thousand "suspicious sequences". For the sake of roundness and being a bit conservative, let's say there are 423 "suspicious sequences", in which case the odds of hitting one are roughly 1 in 100,000. You may choose to add another order of magnitude of "suspicious sequences" pretty easily, in which case it goes to 1 in 10,000. Given the number of draws done for this sort of lottery (dozens or hundreds a day, I'd guess), it's inevitable that sooner or later one would be hit on lotteries of this size.

Some of the challenge in weighting the number of sequences is they aren't all equally "suspicious". [1,2,3,4,5] is what most people would consider a "dead giveaway" (right or wrong), whereas [1,2,4,8,16,32] would probably bother fewer people. Some people might still find even [1,2,3,4,18,bonus 6] suspicious ("look how 'close' it was to 12345!"). So there's just some intrinsic fuzziness to the answer of how likely this is.

The same as any other combination of numbers. It's just harder to wrap your head around.

It’s the same likelihood to draw the numbers, however more people are likely to buy that sequence of numbers as it is a very common sequence that people think of.

According to the article (assuming you're looking at this particular sequence):

> The chances of winning South Africa's PowerBall lottery are one in 42,375,200

Yes, as others pointed out, this particular sequence is the same as every other sequence. Or, the one person who said 100% is referring to the probability of something that already happened.

To give you a more charitable interpretation, the South African lottery Powerball can be 1-20 so there are 20 straights possible so 20 in 42,375,200. Or roughly 1 in 2,000,000 or roughly 40,000 years of weekly draws to see a straight.

I think there are only 16 straights possible since you can't start with 17, 18, 19, or 20

Yes, you're right. In this case, the Powerball comes last. So increasing straights can't end with 1, 2, 3, 4, or 5. However, you could have wrap around straights. So 15 or 20 depending if you allow the wraparound.

It depends on how many samples. The odds that this specific drawing would yield this result should be one in 42 million, but the odds that a lottery somewhere would yield this result in our lifetime is substantially greater.

The same as any other combination, as quoted in the article, 1 in 42 million.

The question most people are probably thinking of is "What are the chances of any sequence of numbers being drawn?", not just this specific one in the article.

And that is, literally, quite close to one in a million.

Actually no, because this lottery picks five balls from a pool of 50 and then one ball from a pool of 20. So there are only 15 possibilities where the whole draw is six consecutive numbers (from 1-2-3-4-5/6 to 15-16-17-18-19/20).

Does draw order matter in this lottery? Cause if not it's a lot more likely.

No, in fact the numbers were not drawn sequentially but arranged in order after. The only exception is the powerball, the 10 in this case, which always is last in the draw and positioned last in the final numbers.

This can be seen in the official announcement: https://youtu.be/11RN1pEnrTo

Isn't the real question "what are the odds of the lottery being random if this suspicious sequence comes up so soon"? I.e. given a specific sequence, how many weeks should you expect to wait before you see it? In the extreme if you would expect to see 1,2,3,4,5,6 after 500,000 weeks, but you see it in the first week, then probably the lottery is not random, right?

Exactly the same as for any other sequence of numbers.

Which is 1 : 42,375,200.

However, the probability of ending up with a sequence like this is still quite low - probability of coming up with six consecutive numbers is 40 : 42,375,200 i.e. less than one in a million.

Correction: as pointed out, the sixth ball is picked from range 1-20, which more than halves the probability to less than one in 2 million.

100%

Up to which resolution is a fundamentally deterministic world ruled out?