Power ball odds questions

Factual Questions
1

I found this about the powerball: ‘In each drawing, five balls are drawn from a drum with 69 white balls (labeled 1 through 69) and one ball is drawn from a drum with 26 red balls (labeled 1 through 26).’ leading to a jackpot odds being 1 in 292+million.

I didn’t see anything about having to choose numbers from low to high or if you can choose the same number twice. These would be my first 2 questions.

So getting a 1, the first number, is a 1 in 69 chance. If you can’t play the same number twice then the second number chosen has a 1 in 68 chance of being drawn and so on. Then the powerball number itself would be a 1 in 26 chance. That all makes sense.

I don’t play but a relative said you’ve got the same odds of winning the jackpot if you chose: 1, 2, 3, 4, 5 and a powerball number 6 as you do any other combination of numbers.

Something about this didn’t sit well with me and I disputed it based on a hunch I guess. I can’t prove it.

I immediately imagined choosing any linear sequence of numbers would lessen the odds of winning considerably. I mean the chances of any one number being drawn is one thing, but the chances of getting a continually linear sequence of numbers drawn has to diminish with each sequential number. Right? And then there’s the additional sequential powerball number 6.

If you agree, great! I ask that if you can show me the mathematical proof and it can be confirmed, I will throw back into the relatives face. That would be fun. Don’t you think?

2

This is very basic math. The odds are exactly the same if the numbers are sequential or not. Each number picked is an independent event.

3

No, that’s not true.

Easy test - don’t use numbers. Replace them with symbols.

Which of these should be more probable?

“Triangle-Square-Star-Three wavy lines- Circle”
or
“Asterisk-Star-Plus Sign-Hexagon-Right Arrow”

What if I told you there I substituted Triangle=40, Square= 41, Star=42, Three wavey lines = 43, Asterisk = 5, Plus sign = 50 and so on?

What does the symbol on the little ball matter? Does the ball itself know or care how it pops out of the hopper?

The reason it seems to be different is human beings are natural pattern recognizers. We ascribe importance to patterns, even if those patterns don’t actually exist. And out of hundreds of millions of possible combinations, there’s only a small number that would trigger our pattern recognition.

So, sure, “meaningful number pattern to humans” is less frequent than “non-meaningful number pattern to humans” but that doesn’t really mean anything to how the balls bounce about. That’s entirely about our weird brains.

4

OK. Makes sense.

I don’t play the lottery, but I can certainly ascribe patterns.

5

To answer some of the factual questions:


The order the balls are drawn in does not matter in Powerball. At least not among the 5 white ones. The red powerball is a completely separate drawing. For convenience they always sort the results of the 5 white balls low to high when reporting them regardless of what order they were actually drawn in. Likewise although you can tell the clerk which numbers you want to play in whatever order, the ticket you receive will show them sorted in order low to hi. That just makes it convenient for everyone.

A lottery could be designed where the order of draw matters. Where a ticket saying 1-2-3 would not win if the balls were drawn as 3-2-1. But it would be vastly less likely to ever be won unless there were very few balls and very few values per ball.


They draw each number without replacing it back in the pool. So it is impossible for them to ever draw the 5 whites as 1,1,2,3,4. So they don’t sell tickets with repeated numbers either.

It is certainly possible as a matter of random drawings and probability to put the e.g. first drawn number back before drawing the second, etc. That’s not how it is done for Powerball, but it is a way that could be done in some other lottery. The odds math changes slightly, but not hugely.


As the others have said, this is completely wrong.

One explanation is as above, that somehow 1,2,3,4,5,6 seems more special than 2,13,23,25,60. But that specialness is in your mind, not in the math or in the numbered balls themselves.

A more mathy way to understand it is that you have a 1-in-69 shot of drawing a 1. If you got lucky and did so, then you’ve still got a 1-in-69 shot of drawing the 2. So the odds of drawing a 1-2, given that you already drew a 1 are still just 1 in 69. And if you get lucky a second time and do draw a 2, then you’ve got a 1-in-69 shot at drawing a 1-2-3, given that you already drew a 1-2.

This kind of analysis is commonly called Bayes theorem or Bayesian probability. And delivers the exact same results whether you end up with 1-2-3-4-5 or 2-13-23-25.

Caveat: slight simplification in the above. But close enough conceptually.

6

I’ve never understood the purpose of the red separate powerball. Why not just make all the balls equal? Like, “The Powerball will simply involve drawing 6 white balls of two-digit numbers apiece.”

7

To make it harder to win and the jackpot grow faster. The lottery has learned that they sell more tickets when the jackpot prize gets really really big. Apparently more people dream of a 500 million prize and do not even buy tickets for a couple million. The multi-state Megamillions just increased their ticket price from $2 to $5 for that reason, to make the jackpot grow even faster.

8

I used to play the littery, then heard that my chances of getting struck by lightning are better. I cant take that risk

9

Also, I think you can win money by matching the five balls (or even three) without the powerball. Not the jackpot but you get something (potentially a lot…just not the big prize). So, there is a “better” (still awful) chance that you can get some payout.

10

I read somewhere you have a better chance of dying under a vending machine than hitting the jackpot in the powerball lottery.

11

The odds of winning the lottery by choosing six balls out of 69, is 1:119,877,472
(see 6 Random Numbers Between 1-69 | Number Generator )

The odds of Powerball (5 out of 69 AND 1 out of 26), is 1:292,201,33

12

You’re using with replacement. The odds would be 1 in 69; 1 in 68; 1 in 67, &c.

13

Use of a Powerball is probably popular with lottery companies as it allows fine tuning of the odds. They can add a new ball to the Powerball set, and it only changes the odds slightly, whilst adding a new ball to the ordinary ball pool changes the odds much more.
The Powerball also allows for fine tuning of the minor prizes. There is a need to ensure just the right number of minor prizes are won to keep people interested.
People can be more invested in the whole charade if there is a low murmur of small winnings that make it look less like just a steady vacuuming of money out of their pockets.

Reminds me of a very telling line from a much loved British TV series from the 70’s. Minder. In one episode the main protagonist, Terry, meets an attractive woman who is also a bookmaker. Terry likes to play the ponies. She asks him pointedly how much he thinks he wins and loses overall. He replies that he thinks he is “pretty even”. She replies, “they all think that”.

14

I’ve never met a gambler who thinks they lose money

15

This is true (there’s another thread here where a poster reckons he does really well by gambling in Vegas on slot machines! :nauseated_face: )

Although (as has been said) the numbers are completely random (so 12345 is as likely as any other combination), you can slightly alter your expected return by choosing ‘non- sequences’.
This is because if you do happen to win, there will be less players sharing your prize (as many gamblers like a pattern in the numbers they choose.)

16

Numbers in the 40s and 50s seem to be most frequently chosen. In general, numbers over 30 are far more likely to be chosen than lower numbers.

I think that the idea that sequences like 12345 are less likely than birthdays or random numbers is common.

Common Combos - UK Lotto | Lottery UK

17

Years ago I was in a newsagent with a friend who was buying a Lotto ticket for his work syndicate due to some massive jackpot. While the guy was processing the entry I said, “I hope that you have included something stupid like 1, 2 ,3 ,4 ,5, 6. If it comes up you will get the lot.” The guy printing the tickets said, “If 1, 2, 3, 4, 5, 6 ever comes up it will pay $100. You wouldn’t believe how many times a day I see it on an entry.”

18

That’s amazing. I’ve got the same combination on my luggage!

19

I would guess that many players use a birthday to help generate their numbers - so:

1-31 (day)
1-12 (month)

20

There is the thought that if you want to maximise possible share of large prizes, you only pick numbers higher than 31.

I have occasionally mused on the idea that one could reverse out the distribution of chosen numbers by analysing the payout values across all the divisions for each draw. Over enough games, any bias in number might become apparent. What likely makes is harder is those people who just buy random drawn tickets.