6 ms·
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
by mrb 6y ago
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.
- dheera 6y agoNot 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"
- computerphage 6y agoThese six numbers could've been drawn in any order.
- Freak_NL 6y ago5-10-15-20-25-30, 1-2-3-11-22-33; yeah there are a bunch more that people would find suspicious.
- listenallyall 6y agoWithout 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?
- endtime 6y agoIf 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.
- listenallyall 6y ago...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
- konjin 6y agoWhy is the maths wrong?
- listenallyall 6y agoIt starts with the literal first sentence of the comment -- "They draw 6 balls out of 50." No, they don't.
- krit_dms 6y agothats... not math.
- listenallyall 6y agocalculating C(50, 6) is, as is everything that follows.
- arolihas 6y agoMaybe 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
- listenallyall 6y ago
- BlackFingolfin 6y agoAccording 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.
- T-hawk 6y ago3% 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.
- bouke 6y agoYou 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&assumption=%7B%22F%22%2C+%22BinomialProbabilities%22%2C+%22p%22%7D+-%3E%220.00000035398063%22&assumption=%7B%22F%22%2C+%22BinomialProbabilities%22%2C+%22x%22%7D+-%3E%220%22&assumption=%22FSelect%22+-%3E+%7B%7B%22BinomialProbabilities%22%7D%7D&assumption=%7B%22F%22%2C+%22BinomialProbabilities%22%2C+%22n%22%7D+-%3E%22365000%22 https://www.wolframalpha.com/input/?i=binomial+calculator&as...
- 6gvONxR4sf7o 6y agoWikipedia 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.
- mrb 6y agoI did check this South African powerball. They have 50 balls. If they are 200 draws per week, the probability is 26% over 10 years.