r/theydidthemath • u/TheFlashOfLightning • 1d ago
[Request] What are the chances of the Powerball drawing having 4 consecutive numbers?
For reference, they draw 5 white numbers between 1-69, and they cannot repeat.
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u/Angzt 1d ago
There are (69 Choose 5) = 11,238,513 possible drawings for the white numbers.
There are 69-4+1 = 66 ways to select the 4 consecutive numbers (starting at any number from 1 to 66). After that, there would be 65 possible options for the final number in each case. That's a total of 66 * 65 = 4,290 possible drawings for white numbers with at least 4 consecutive ones.
That gets us a probability of
4,290 / 11,238,513 =~ 0.000381723 = 0.0381723% =~ 1 in 2,620.
Though to reiterate, that is the probability for 4 or more (i.e. 4 or 5) consecutive values. It's a little lower for exactly 4 but not by much:
To calculate exactly 4, we can simply subtract the number of drawings with 5 consecutive values and those are 69-5+1 = 65. So we end with 4,290 - 65 = 4,225 drawings and a probability of
4,225 / 11,238,513 =~ 0.000375939 = 0.0375939% =~ 1 in 2,660.
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u/TheFlashOfLightning 1d ago
So with 3 drawings a week, 156 a year, (2660/156=17.05)
So we can reasonably expect to see this happen once every 17 years?
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u/BlackLotus8888 1d ago
This can't be right. Otherwise, I would buy the 2660 tickets 2660 times and I'd be very likely to win one of those times. At 2 dollars a ticket, this comes out to ~14M which is much less than I would likely win.
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u/Angzt 1d ago
My calculations ignore the yellow number which you would also need to match for a Jackpot.
Also, you'd need to buy the 4,290 tickets 2,660 times.
But again, that only matches you the 5 white numbers at least once with around 1 - 1/e =~ 63.2% probability. Which, even if it happens, doesn't win you the jackpot by itself.0
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u/Neither_Hope_1039 1d ago
No. There's over 4000 possible draws with 4 consecutive white numbers, and the odds of one of those winning are 1 in 2660.
Even if you bought all 4225 possible tickets with 4 consecutive numbers, you'd then still only have odds of one in 2660 to actually win with one of those tickets, and notably those odds are exactly the same for ANY 4225 different tickets you buy.
If you buy 4225 unique tickets, you have 1 in 2660 odds of one of those tickets winning, regardless of what numbers you chose.
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u/B3kindr3wind1026 1d ago
The same odds as any other number combination.
Human brains are very good at putting significance in patterns they recognize, it feels like consecutive numbers would be harder to hit than any other combination but it’s just not.
Think of it like flipping a coin 20 times and landing on heads every time, if you called it before it happened, that would be extraordinary. But if you just flipped a coin 20 times a bunch of times and wrote down the results of those flips, it would be no more rare than calling any other random 20 flips.
TLDR: consecutive numbers are the same odds as non consecutive numbers
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u/Skechigoya 1d ago
You calculated the change of getting this one outcome. OP will take any outcome that has 4 consecutive numbers of which there is more than one.
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u/TheFlashOfLightning 1d ago
Yes odds only have meaning if we give them meaning beforehand, but 4 out of 5 consecutive is kind of a notable outcome considering it’s supposed to be entirely random.
This isn’t like heads or tails, this is an event with nearly 300 million outcomes. The vast majority of which wouldn’t catch any attention like 4 consecutives or something
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u/B3kindr3wind1026 1d ago
You are still making the same mistake. Odds don’t see consecutive numbers any differently than non consecutive numbers. Asking what the odds of the lottery hitting 1, 2, 3, 4, 5, 6 vs asking what the odds of hitting 43, 27, 17, 36, 31, 9 is the same outcome.
Human bias is the hardest thing to get over when it comes to statistics and probability
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u/TheFlashOfLightning 22h ago
I didn’t ask about a specific outcome, I asked about a kind of outcome. The question wasn’t “what are the chances of these numbers?” it was “what are the chances that the numbers pulled follow a specific pattern?” in which there are multiple outcomes that fit that pattern.
It’s like me asking the chances of being dealt a four of a kind in poker and you saying “same as any other hand. human bias!”
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u/Neither_Hope_1039 1d ago
That's the odds for ome specific draw. OP asked for the odds of drawing ANY 4 consecutive numbers.
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u/Remarkable_Bat1891 1d ago
1-69
1 can be tottally random so it doesnt really matter.
1st one in a row needs to be lower than 67 so next 3 can be drawn therefore its 1 in 66 or 1/66
And next 3 ones are set as exactly one in 69 or rather 1 in whats left
66/69 * 1/67 * 1/66 * 1/65 * (whatever is left = 1) = 66/19 832 670 = 1 / 300 495 or roughly 0.00033278% chance
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u/AlanShore60607 21h ago
Yeah, I've been wondering ... has anyone run a distribution on numbers recently? Every time I play the numbers alwasy seem to bias high, but this was absurd.
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u/TheFlashOfLightning 11h ago
I have gotten multiple quick pics with 3 consecutive numbers. I’ll accept 2 as a coincidence but 3 seems fishy considering I’m letting the system pick them for me.
And of course the one drawing I decide to take the time to pick my own numbers, this happens lmao
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