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Comment by mrb | Hacker News Reader

They draw 6 balls out of 50. There are C(50,6) = 15,890,700 possible draws (C(n,k) = binomial coefficient)

45 of the draws are made of 6 consecutive numbers (1-2-3-4-5-6, then 2-3-4-5-6-7, etc, until 45-46-47-48-49-50)

A single draw has a 45 out of 15,890,700 chances of being 6 consecutive numbers

A single draw has a probability of 1-(45/15,890,700) of NOT being 6 consecutive numbers

Assuming 1000 draws (lotteries) per day, in a year we expect probability (1-(45/15,890,700))^(1000*365) = 36% that none of the lotteries draw 6 consecutive numbers

So there is a 64% probability that at least one lottery will draw 6 consecutive numbers in a year. If there are 1000 draws per week (instead of per day) the probability is still 17% that this will happen in a year.

So this South African draw is kinda expected.

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According to a comment elsewhere in this HN discussion, it seems there are rather something like <200 draws a week. That gets us to just a 3% chance of this happening in a given year. That's still quite a bit more than one might intuit, but not quite as drastic.

Of course, as others here already pointed out that there are far more "suspicious" patterns (e.g. other arithmetic progressions like 5-10-15-20-25-30, primes, ...). And of course they often play by different rules, etc.

3% chance in a given year. And for how many years when it didn't happen have we been running this many lotteries? Probably right around 33.

Not to mention the reverse consecutive numbers, the same numbers, the +=2 numbers, the -=2 numbers, the prime numbers, and all the other sequences that people would find "suspicious" because "omgfwow that could never happen"

These six numbers could've been drawn in any order.

5-10-15-20-25-30, 1-2-3-11-22-33; yeah there are a bunch more that people would find suspicious.

Wikipedia says that powerball is out of 69 balls, not out of 50, and in the U.S. there are only about 100 draws per week. I cant imagine the worldwide numbers are more than an order of magnitude higher (I guessed it at 200/week in a sibling comment). That’s 7.5x more potential draws, and 5x-35x fewer draws per week, which would change the numbers quite a bit, making the weekly chance way way lower than your estimate.

I did check this South African powerball. They have 50 balls.

If they are 200 draws per week, the probability is 26% over 10 years.

You compete (as understood from the article) in Powerball by 50 choose 5, 20 choose 1. So 1 in (50!/(5!⨉45!)⨉20 = 42.375.200. There are 15 ascending "suspicious" winning sequences, as the choice of Powerball is always last and thus must be 6-20. Therefore the chance of winning Powerball with a "suspicious" sequence is 15 in 42.375.200. If there are 1000 Powerballs drawings per day for a year, that gives a chance of approximately 12% of happening at least once a year.

https://www.wolframalpha.com/input/?i=binomial+calculator&as...

Without going into detail about why your math is flawed, which it is -- a basic viability check would be to consider: if there was a 64% probability of some event happening each year, don't you think in your lifetime you'd have seen quite a few instances of that thing happening?

If you read a daily digest of global lottery results, yes!

This might not be in the news because it's so rare. It might just be a slow news day.

...or "crazygringo's" 1000 per day guess could be way, way off, and anybody, like "mrb," accepting it blindly as a basis for their own calculations is guilty (of failing to think critically) by association

Why is the maths wrong?

It starts with the literal first sentence of the comment -- "They draw 6 balls out of 50." No, they don't.

thats... not math.

calculating C(50, 6) is, as is everything that follows.

Maybe he is referring to the fact that not all of the lotteries have the same structure? Idk it still seems like a good estimate to me

64% likelihood seems like a good estimate to you? Just take a second and consider whether you'd take the following bet: Your $1000 against my $5000 that anywhere in the world in 2021, a state-run lottery (with at least 5 balls out of at least 50, and a sixth out of at least 20) will have a perfectly sequential result.

You're being offered 5 to 1 odds on a probability that you just estimated to be significantly better than a coin flip. Are you in? Or does your gut tell you that 6 perfectly sequential numbers is crazy unlikely?

Sure, how do you want to do that bet?

I'm 100% serious about making this wager, I've sought out the wisdom of HN for help with a "smart contract" to guarantee trust.

https://news.ycombinator.com/item?id=25306489

At the same time, I'm not a thief -- to be entirely certain that you want to make this bet, have you read the entire thread, where alternate probabilities (far less than 64%) are proposed? You're aware that the original assumption of 1000 lottery draws per day was a guess from thin air with no research nor basis in fact? You're aware that mrb's calculations overstated the number of possible conforming sequences and undercounted the total number of potential outcomes? If you acknowledge that you're aware of all of this and still want to proceed, let's do it, no joke, I'm 100% in.

It’s crazy unlikely for any particular lottery but there are a ton of draws and a ton of lotteries, and it only needs to happen once in a year. I probably would take that bet if it were feasible but then again I like to gamble.

Terrific, the same comment I replied to konjin applies to you as well. I'll absolutely make this bet if there's a trustable platform.

Just curious, if a random HN commenter said, there's about a 64% chance that at least one human being will grow to 12 feet tall in 2021, would you take that wager also? I mean, there are a ton of people on the planet, and it only needs to happen once.

The difference is it’s biophysically infeasible for any human to mature and live as a 12 foot tall adult, considering there is a very small number of 7 feet tall people in 2020. Whereas there is no such constraint for any given sequence of numbers if the lottery allows for them to be drawn. I would rather wager on whether you will continue being an annoying pedant. I prefer my odds there.

There is no 64%. It's hypothetical if there were 1000 draws per day. If you want to proof their math wrong please do more than calling it flawed.

He states a conclusion -- "So this South African draw is kinda expected" -- referring to THIS DRAW, not a hypothetical example.

If you have the time,would you mind expanding on this with the detail that you mentioned?

>probability of some event happening each year, don't you think in your lifetime you'd have seen..

No. This is not particularly newsworthy. But for most HN users and this event the answer is: no, but I did see it on HN and it will probably get re posted cyclicaly ;)

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