# Explain these Lotto statistics
**URL:** https://boards.straightdope.com/t/explain-these-lotto-statistics/77849
**Category:** Factual Questions
**Created:** [August 24, 2001, 4:04am UTC](https://boards.straightdope.com/t/explain-these-lotto-statistics/77849 "2001-08-24T04:04:13Z")
**Posts on this page:** 9
**Page:** 1
### Author:  [@BingoBurringo](https://boards.straightdope.com/u/BingoBurringo)
#### Post date: [August 24, 2001, 4:04am UTC](https://boards.straightdope.com/t/explain-these-lotto-statistics/77849/1 "2001-08-24T04:04:13Z")
This web pages explains the odds at winning powerball:
[http://www.powerball.com/pbprizesNodds.shtm](http://www.powerball.com/pbprizesNodds.shtm)
So explain to me, if there are only 42 powerballs, how come the odds of hitting the powerball are 1 in 74? And if your best odds of winning are 1 in 74, how are the overall odds of winning ANYTHING dropped to 1 in 35?
There’s 49 regular balls and 42 powerballs.
What’s the equation for figuring the odds of winning?
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### Author:  [@SmackFu](https://boards.straightdope.com/u/SmackFu)
#### Post date: [August 24, 2001, 4:29am UTC](https://boards.straightdope.com/t/explain-these-lotto-statistics/77849/2 "2001-08-24T04:29:08Z")
Hey, I answered this at work today.
That page isn’t listing the odds of picking the powerball correctly. It’s listing the odds of **only** getting the powerball and having no other matches. Which is less than 1 in 42, because there are a lot of combinations where you would get one other ball correct.
I think if you add up all the combinations on that page that include a powerball in them, it should total to 1:42. Doing a quick calc, just including the one other ball + powerball combo (which is 1:118 odds) raises it to 1:45.
And if you add up all the odds on that page, it should come to 1:35.
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### Author:  [@don\_t\_ask](https://boards.straightdope.com/u/don_t_ask)
#### Post date: [August 24, 2001, 5:01am UTC](https://boards.straightdope.com/t/explain-these-lotto-statistics/77849/3 "2001-08-24T05:01:48Z")
> [@](#):
>
> \*Originally posted by SmackFu \*
> \*\*Hey, I answered this at work today.
>
> That page isn’t listing the odds of picking the powerball correctly. It’s listing the odds of **only** getting the powerball and having no other matches.\*\*
SmackFu
What you say is true, but they are correct in the odds they quote. To only get the powerball you **must** fail to pick the other numbers. The chances of this are
44_43_42_41_40
49_48_47_46_45
By the 1 in 42 odds of getting the powerball = 1 in 73.75
Every other time you pick the powerball you get at least 1 of the white numbers.
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### Author:  [@23skidoo](https://boards.straightdope.com/u/23skidoo)
#### Post date: [August 24, 2001, 5:04am UTC](https://boards.straightdope.com/t/explain-these-lotto-statistics/77849/4 "2001-08-24T05:04:03Z")
> [@](#):
>
> \*Originally posted by BingoBurringo \*
> \*\*This web pages explains the odds at winning powerball:
>
> [http://www.powerball.com/pbprizesNodds.shtm](http://www.powerball.com/pbprizesNodds.shtm)
> So explain to me, if there are only 42 powerballs, how come the odds of hitting the powerball are 1 in 74? And if your best odds of winning are 1 in 74, how are the overall odds of winning ANYTHING dropped to 1 in 35?
>
> There’s 49 regular balls and 42 powerballs.
>
> What’s the equation for figuring the odds of winning? \*\*
Odds for winning any prize should be better than the odds of winning any one prize in particular.
Chances of me finding a particular show that I like on television are low, but chances of me finding _any_ show I like are better. Same with playing the lottery.
**SmackFu** is right, 1/74 refers to the odds of winning the lowest prize without winning any higher prizes. That means you would get the power ball, but NONE of the regular balls.
(44_43_42_41_40)/(5_4_3_2_1) = 1,086,008 ways to get the only the powerball.
1,086,008/80,089,128 = approximately 1/74
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### Author:  [@BingoBurringo](https://boards.straightdope.com/u/BingoBurringo)
#### Post date: [August 24, 2001, 9:23pm UTC](https://boards.straightdope.com/t/explain-these-lotto-statistics/77849/5 "2001-08-24T21:23:11Z")
> [@](#):
>
> \*Originally posted by 23skidoo \*
> \*\*
>
> > [@](#):
> >
> > \*Originally posted by BingoBurringo \*
> > \*\*This web pages explains the odds at winning powerball:
> >
> > [http://www.powerball.com/pbprizesNodds.shtm](http://www.powerball.com/pbprizesNodds.shtm)
> > \*\*
>
> (44_43_42_41_40)/(5_4_3_2_1) = 1,086,008 ways to get the only the powerball.
>
> 1,086,008/80,089,128 = approximately 1/74 \*\*
Is this equation correct?
If there are 49 balls, the equation starts at 44?
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### Author:  [@SmackFu](https://boards.straightdope.com/u/SmackFu)
#### Post date: [August 24, 2001, 10:04pm UTC](https://boards.straightdope.com/t/explain-these-lotto-statistics/77849/6 "2001-08-24T22:04:13Z")
You’ve got 5 numbers on your card. So if you don’t want to match any of them, the ball you choose has to be one of the other 44 numbers. Then the next ball you choose can’t be the same as the first one, and still can’t match those 5 on your card, so there are 43 choices. And so on.
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### Author:  [@DaveRaver](https://boards.straightdope.com/u/DaveRaver)
#### Post date: [August 25, 2001, 2:11am UTC](https://boards.straightdope.com/t/explain-these-lotto-statistics/77849/7 "2001-08-25T02:11:47Z")
Explain this… the number 16 still has not come up all year in New York Lotto. Not even as a supplemental number!
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### Author:  [@hajario](https://boards.straightdope.com/u/hajario)
#### Post date: [August 25, 2001, 3:09am UTC](https://boards.straightdope.com/t/explain-these-lotto-statistics/77849/8 "2001-08-25T03:09:50Z")
> [@](#):
>
> \*Originally posted by DaveRaver \*
> \*\*Explain this… the number 16 still has not come up all year in New York Lotto. Not even as a supplemental number! \*\*
Good god, Man. You’ve been reading this board since '99 and you ask a question like this? Are you serious?
The answer: random chance.
Haj
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### Author:  [@SmackFu](https://boards.straightdope.com/u/SmackFu)
#### Post date: [August 25, 2001, 3:11am UTC](https://boards.straightdope.com/t/explain-these-lotto-statistics/77849/9 "2001-08-25T03:11:30Z")
16 came up on February 7th, 2001. ([NY Lotto results](http://www.nylottery.org/winner/lottores.php3))
Theoretically, in a single drawing, the chance of a chosen number not coming up is 88% (45/51). The chance of that happening in 67 straight drawings (the number since January 1st) is 88% raised to the 67th power. Which is 0.02%, pretty slim odds. But… that’s the odds of a specific number not coming up. You have to multiply that by 51 to get the odds for any number. Which makes it around 1%. Which isn’t very unlikely at all!
[sup](if I did the math right)[sup]