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Lottery/Powerball math question

tusenfem has, i think provided the odds assuming the numbers were drawn in the order you listed. If the numbers could be drawn in any order the odds are 120 times less or about 1 in 200,000 (again I think, a while since I did any probability)

Nope I did not, then there would only be 1s in de numerators.
 
What I mean by this is not just whether you can win with matching numbers in a different order. If the order doesn't matter to whether you win, then it doesn't matter to the order that they're drawn in. And in that case, they don't even have to announce the numbers in the order that they're drawn, they could just list them in ascending order every time. So is that how it's done? Do they list it in ascending order, or in draw order?

I went back through a number of previous results, and in every case the 5 main draw balls were reported in ascending order. I didn't find a description of this, but I suspect (like many other lotteries) the draw order is irrelevant for this portion.
 
summary

This jackpot was R113m, which had 20 winners, carried over 17 draws
Previous jackpot was R121m which had 1 winner, carried over 21 draws.
Previous jackpot was R31m which had 1 winner, carried over 5 draws
Previous jackpot was R77m which had 1 winner, carried over 18 draws

I haven't gone further back.

Considering that immediately prior to this event there had been close to 60 draws with 3 winners, it does seem a bit unusual that there would be 20 in this one.

mitigating:
- there are more entries with higher value jackpot
- there may have been more winners exactly because of the unusual number sequence

That's very cool.

I'd say the results could be easily explained by the birthday numbers as already noted, which a hell of a lot of people take.

It wouldn't be any surprise to find 20 families with those dates for birthdays, and some people do like to take consecutive numbers - if you hit 3, 4 or 5 winning numbers on a multi-number ticket you get several times the prize.

Say I take 1-8 as my numbers in a multi and 4 of them come in, I will get six times the win for 4 numbers.

I can remember when $113M rand was an astronomical amount of money. Only $10M kiwi these days. Our jackpots go up to $30-35M. Euro and US reach insane numbers.
 
If I ever find a way to cheat and fix the lottery numbers you can be sure I'm going to avoid picking an obvious pattern so I don't have to share my ill-gotten loot with a score of random strangers.
 
If I ever find a way to cheat and fix the lottery numbers you can be sure I'm going to avoid picking an obvious pattern so I don't have to share my ill-gotten loot with a score of random strangers.

Or just the opposite to make any investigation a bit more complex?
 
If I ever find a way to cheat and fix the lottery numbers you can be sure I'm going to avoid picking an obvious pattern so I don't have to share my ill-gotten loot with a score of random strangers.

There will be other people out there looking to avoid any obvious pattern, and if they choose the same algorithm for doing so you'd end up splitting it with them. I'm not sure if they still do it, but here they used to publish how frequently each number was selected both by people on their tickets.

If things were strictly random the thing to do would be to pick the 5/6/7 least commonly selected numbers. In reality I expect hundreds perhaps thousands of people would be trying the same thing.
 
Or just the opposite to make any investigation a bit more complex?

ISTR a previous thread in this forum on this topic. It was noted then that Florida was one jurisdiction in which the frequency of all numbers played was reported. I'm not sure that this still true and am too busy right now to check. But one thing I remember from the discussion last time is how often 1-2-3-4-5-6 are played, based, presumably, on your reasoning.

Because of how many people play birthdates, I would, if I played, never use a number under 31 in order to increase my odds of collecting an un-shared prize if I won.
 
Here's a fun tool for NZ's Lotto numbers - shows how many times each number has come up, and I've linked to number of times since a number was last drawn.

You wouldn't think all of 32, 33 & 34 hadn't come up in the past 15 or more draws on a random generator, but that's how it works. Interestingly, the over 15 draws contains a pair of consecutive numbers as well as the triple. Neither 8 nor 9 has been seen for over two months, 27 and 18 draws respectively.

(Your non-birthday idea would have sucked over the past 4 months!)

http://lottoresults.co.nz/tools/lotto/number-last-seen
 
Here's a fun tool for NZ's Lotto numbers - shows how many times each number has come up, and I've linked to number of times since a number was last drawn.

You wouldn't think all of 32, 33 & 34 hadn't come up in the past 15 or more draws on a random generator, but that's how it works. Interestingly, the over 15 draws contains a pair of consecutive numbers as well as the triple. Neither 8 nor 9 has been seen for over two months, 27 and 18 draws respectively.

(Your non-birthday idea would have sucked over the past 4 months!)

http://lottoresults.co.nz/tools/lotto/number-last-seen

Ah. But, when it does pay off, think of collecting the prize all alone.
 
Haha!

You could spend a lot of money trying.

Then there are people who win it twice.

I love random chance.
 
I think maybe my OP wasn't quite clear on the question. I didn't mean that sequence in that order. I think tusenfem (which I thank him for) is correct that regardless of the order, the odds are around 1 in 24mil. The reason i think that is only because I did a bunch of google-calculating before creating this thread and that was the answer I kept getting to.

I think the odds become astronomically smaller of drawing them in that particular order, but i'll qualify that by adding that it's been ages since I did any meaningful probability calcs as either.

Nope I did not, then there would only be 1s in de numerators.

Aaah yes. So 120 times more unlikely for the numbers to come out in ascending order.

(1/45) * (1/44) * (1/43) * (1/42) * (1/41) * (1/20) = 1 to 3,410,383,400 if I'm doing my math right.
 
5,6,7,8,9 and 10 - A bit dodgy

Not so much the sequence, as we all know the odds in lottery of getting that are the same as every other 6 numbers.

The part that is a bit dodgy is the 20 people picking it and sharing first prize.

And the 6,283 who picked 5,6,7,8,9 and didn't guess the bonus ball would be 10.

https://www.bbc.com/news/world-africa-55154525

South Africa's lottery probed as 5, 6, 7, 8, 9 and 10 drawn and 20 win

An unusual sequence of numbers drawn in South Africa's national lottery has sparked accusations of fraud after 20 people won a share of the jackpot.

Tuesday's PowerBall lottery saw the numbers five, six, seven, eight and nine drawn, while the PowerBall itself was, you have guessed it, 10.

The organisers say the sequence is often picked. But some have alleged a scam and an investigation is under way.

It is extremely rare for multiple winners to share the jackpot.

The organisers said 20 people purchased a winning ticket and won 5.7m rand ($370,000; £278,000) each.

Another 79 ticketholders won 6,283 rand each for guessing the sequence from five up to nine but missing the PowerBall..........

.......... South Africa's National Lotteries Commission (NLC), said it would investigate the draw, which it called unprecedented.
 
Not so much the sequence, as we all know the odds in lottery of getting that are the same as every other 6 numbers.



The part that is a bit dodgy is the 20 people picking it and sharing first prize.



And the 6,283 who picked 5,6,7,8,9 and didn't guess the bonus ball would be 10.



https://www.bbc.com/news/world-africa-55154525
Apologies mods.

Didn't see other thread.

Forgive me my atrocious spelling from my wee phone keyboard.
 
Let me ask a question, since I'm not very familiar with powerball. Does the order even matter?

What I mean by this is not just whether you can win with matching numbers in a different order. If the order doesn't matter to whether you win, then it doesn't matter to the order that they're drawn in. And in that case, they don't even have to announce the numbers in the order that they're drawn, they could just list them in ascending order every time. So is that how it's done? Do they list it in ascending order, or in draw order?

I went back through a number of previous results, and in every case the 5 main draw balls were reported in ascending order. I didn't find a description of this, but I suspect (like many other lotteries) the draw order is irrelevant for this portion.

Bowl is Correct. Zig, this has probably already been answered to your satisfaction, but the order that the numbers are drawn in is not relevant.
 
It's this kind of thing that made me stop doing the lottery not long after it was introduced in the UK. The point was that 1,2,3,4,5,6 was as likely as any other combination. The fact that people can hardly believe that such a combination could ever come up was the illustration I needed to realize just how unlikely any combination was.

And yet these are still bad numbers to choose because of how likely it is people will choose consecutive numbers compared to other combinations. The luck is "random" but not how people choose the numbers. And of course, people expect the lottery numbers to "look" random. When they do not, they start to suspect something untoward even if no such thing has happened.
 
It's this kind of thing that made me stop doing the lottery not long after it was introduced in the UK. The point was that 1,2,3,4,5,6 was as likely as any other combination. The fact that people can hardly believe that such a combination could ever come up was the illustration I needed to realize just how unlikely any combination was.

Another way to illustrate that is to ask "what is the chance that the numbers drawn this week will match the ones drawn last week?"

Most people would consider it almost impossible even though it is just as likely as having the winning numbers match the numbers you pick.
 
Another way to illustrate that is to ask "what is the chance that the numbers drawn this week will match the ones drawn last week?"

Most people would consider it almost impossible even though it is just as likely as having the winning numbers match the numbers you pick.

True! This is a good illustration that the human mind is bad at understanding statistics. We want to form patterns, and as someone posted earlier, are not good at understanding true randomness. Go into any casino and look at the roulette table. They usually have a sign showing the most recent numbers. People like to use this as a means to "predict" which number will come up next. Of course, the previous numbers have absolutely no effect on the next spin of the wheel, and no number is "due".

People will find it weird that the lottery 1-2-3-4-5-6 combination is 25 million to 1 and think something is up. But every draw of this lottery results in a winning combination that is 25 million to 1.
 
One of my early jobs was at a combination convenience store/ice cream parlor chain in Eastern upstate New York, and we sold an unusually large amount of lottery tickets. For the simple daily three number and four number drawings, the state limits the number of people who can bet on a particular number in a particular drawing. For numbers like 7-7-7, 1-2-3, or 1-2-3-4, people would usually have to bet a week in advance because large numbers of people would bet on those sorts of sequences and quickly hit the limit, then move on to playing them for the next day, and the day after that, and so on.
 
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