Blockheads

[HamYai]

In the immortal words of Mr Ian Dury, of the above named group, "There ain't half been some clever bastards".

So maybe someone here will be able to answer me something.

In the UK, we have a National Lottery.

You have to choose any 6 numbers (from 0 - 49) pay your quid and cross your fingers.

The odds against all six being drawn are put at something over 14m to 1.

I'm no mathematician, so I take their word for it.

What I'm not so sure about is a friend's assertion that the odds of numbers 1, 2, 3, 4, 5 and 6 appearing in the same draw (appearing in any sort of numerical order is irrelevant) is equal to any other combination of 6 random numbers.

Is he correct?

Noel Coward was a charmer.
As a writer he was a brahma.
Velvet jackets and pyjamas,
"the gay divorce" and other dramas.

There ain't half been some clever bastards
(Lucky bleeders, lucky bleeders)
There ain't half been some clever bas-tards.

Van Gough did some eyeball pleasers.
He must have been a pencil squeezer.
He didn't do the Mona Lisa,
That was an Italian geezer.

There ain't half been some clever bastards
(Lucky bleeders, lucky bleeders)
There ain't half been some clever bas-tards.

Einstein can't be classed as witless.
He claimed atoms were the littlest.
When you did a bit of splitting-em-ness
Frighten everybody shitless

There ain't half been some clever bastards.
Probably got help from their mum
(who had help from her mum).
There ain't half been some clever bastards.
Now that we've had some,
let's hope that there's lots more to come.

There ain't half been some clever bastards
(Lucky bleeders, lucky bleeders)
There ain't half been some clever bas-tards.

Okey-dokey!
Oh!
Segovia.
Da-laa la-laa da-daa da-lee
De dump di dump de dump-dump-diddle li-lee.

There ain't half been some clever bastards
(Lucky bleeders, lucky bleeders)
There ain't half been some clever bastards
(Lucky bleeders, lucky bleeders)
There ain't half been some clever bastards
(Lucky bleeders, lucky bleeders)
There ain't half been some clever........
..................................bastards.

 

[ManlyBanisters]

Yes.

 

[Deno]

well the other combination has to be pick but yes he is correct.

interesting info:

• The National Weather Service lists your odds of getting struck by lightning in any given year as 1 in 400,000 -- that's more than 200 times better odds than the "pick 6" lottery. Odds of winning the 29-state Powerball jackpot: 146,107,962:1. Odds that there will be an Extinction Level Event in any given year (i.e. killer asteroid): About 100,000,000:1
• You can improve your odds by buying more tickets more frequently, but keep in mind that the numbers are very, very large. To improve your odds to 50/50 in the Powerball lottery, you would have to buy two tickets a week, every week without fail for 702,442 years... and three months.

 

[cockoloco]

Yes, he is correct.

 

[drumstyck]

i believe the odds would be the same...just because numbers are sequential wouldnt eliminate them from the randomness...

as far as the odds...you have to pick six different numbers, there are no repeats? so the odds go from 1-in-50 to 1-in-49 to 1-in-48 and so on...

 

[cockoloco]

I believe the odds WOULD change if the numbers had to appear in a specific order.

 

[ManlyBanisters]

Would they? Surely if 1 comes up the chances of 2 being next are the same as the chances of any other number being next, then on the next ball the chances of 3 coming up are just the same as the chances of any other number coming up... and so on.

The fact that a previous number is numerically adjacent does not affect the odds of a certain number appearing.

That would be like saying I shouldn't choose my birth date and birth month as two of my lottery numbers because if my birth month comes up it is less likely that my birth date will. Probability is NOT aware they are related. The fact that the balls even have numbers on them is actually irrelevant - there could be 50 different pictures of animals, or 50 different colours - the principle is the same.

 

[B_dumbcow]

Same chances... why should

1, 2, 3, 4, 5, 6

be less likely than

22, 1, 13, 26, 9, 11

???

Those exact combinations are just as likely to come up as any others. The lottery machine just picks out random balls... and 1 is just as random as 38.



I think anyway. Someone please correct me if I'm wrong.

 

[Catchoftheday]

I believe the odds WOULD change if the numbers had to appear in a specific order.

Probably by a factor of 720. This being the different combinations of 6 digits that are possible :biggrin1:

 

[cockoloco]

Thank you all for helping me see clear!! I got dizzy there for a moment... happens when I overthink and god knows I'm an underqualified cat

 

[HamYai]

If you factor in "coincidence" which, whilst not a science, is surely a factor, if the chances of picking the correct 6 from 49 is over 14million to 1, what is the odds of those numbers coincidentally corresponding to your family's ages as well?

Surely a factor, though I know not scientifically or mathematically so.

 

[ManlyBanisters]

Surely a factor, though I know not scientifically or mathematically so.

Probability neither knows nor cares when your Aunty Mildred was born. :no:

 

[HamYai]

Probability neither knows nor cares when your Aunty Mildred was born. :no:

How'd you know I had an Aunty Mildred?

But gut feeling tells me otherwise, so I wouldn't use ages etc, (nor would I or anyone else use 123456 - which begs the question, if you wouldn't choose 123456, then you shouldn't actually choose any of them).

 

[ManlyBanisters]

How'd you know I had an Aunty Mildred?

But gut feeling tells me otherwise, so I wouldn't use ages etc, (nor would I or anyone else use 123456 - which begs the question, if you wouldn't choose 123456, then you shouldn't actually choose any of them).

Now you've got it! :yup:

 

[Phil Ayesho]

Would they? Surely if 1 comes up the chances of 2 being next are the same as the chances of any other number being next, then on the next ball the chances of 3 coming up are just the same as the chances of any other number coming up... and so on.

This is not correct.

What it comes down to in odds is cumulative versus absolute.

The odds of any given number being picked next are the same... but the odds of picking 1 thru 6 in serial order are much slimmer.

Let's just look at the subset of possible combinations of 1 thru 6 being drawn.

you can draw 123456 ( the one combination you want) OR

123465 or
123645 or
126345 or
162345 or
612345 or

And that is just by moving the position of the 6... I can do that with each of the other 5 numbers... giving 30 possible combinations that have at 4 of the numbers in serial order.... ( minus a few duplicate combinations.)

I can do that again with the order reversed and get a lot more combinations
And again with the order of the numbers entirely scrambled.

In all, there are around 90 possible combinations of those numbers

Only 1 of which is 123456.


So- while the odds of any one of those 90 combinations being drawn are equal... the odds that 123456 will be the specific combination drawn are 90-1 against.


So you have much better odds of drawing the number 1 thru 6 in any order, than you do of drawing the numbers in a specific order.

This is why most lottery schemes pay out far less for merely having the 6 numbers.... and far more for having the 6 numbers in specific order.

 

[HamYai]

This is why most lottery schemes pay out far less for merely having the 6 numbers.... and far more for having the 6 numbers in specific order.

So the fact that the UK lottery pays out the same amount whether or not we get them in the correct order is a bit of a bitch, then.

 

[D_Thoraxis_Biggulp]

I believe the odds WOULD change if the numbers had to appear in a specific order.

Advanced statistics was always my achille's heel, but I think you're right.

6 different numbers, picked from 0 - 49, in any order have the odds of:
(1/50)*(1/49)*(1/48)*(1/47)*(1/46)*(1/45)=
1 in 11,441,304,000

But assuming you have the right numbers, the odds of the right order are:
(1/6)*(1/5)*(1/4)*(1/3)*(1/2)=
1 in 720


Then again, like I said, Adv. Stat. isn't my strong point. It might be that the order odds are what make the original odds 1 in 11 Billion. If you divide that by the order odds, you get 1 in 16 million, which is closer to the stated odds. Either way, it proves that order matters. Without it, it gives rise to 719 more winning combinations.

 

[cockoloco]

Would they? Surely if 1 comes up the chances of 2 being next are the same as the chances of any other number being next, then on the next ball the chances of 3 coming up are just the same as the chances of any other number coming up... and so on.

The fact that a previous number is numerically adjacent does not affect the odds of a certain number appearing.

That would be like saying I shouldn't choose my birth date and birth month as two of my lottery numbers because if my birth month comes up it is less likely that my birth date will. Probability is NOT aware they are related. The fact that the balls even have numbers on them is actually irrelevant - there could be 50 different pictures of animals, or 50 different colours - the principle is the same.

but say, if you have 1, 2, 3, 4, 5 and 6

and the result is:

2 4 1 5 6 3 or
4 6 5 3 1 2 or
6 5 4 3 2 1, etc

you win, right?

However, if the numbers HAVE to be in a particular order, the previously named possibilities wouldn't apply to win! There's only ONE combination.

Do I make myself clear? I'm getting dizzy once again........

 

[HamYai]

So, I dunno how many tickets are actually sold each draw (but we have a population of 60 million + and whilst not everyone buys a ticket, many buy more than one many, many, many more than one, so it's fair to assume - this is a guess, mind - that more than 14 million and possible a multiplication of 14 million tickets are sold).

So how laws of averages, statistics, probabilities are that someone should win each draw.

Yet often, we have "Roll-Over'" for a significant number of draws and yet at other times, we have multiple winners of a single draw.

And there is invariably an X-Files stylee roll-over for the big Xmas draw, each and every year.

Wierd, or what?

Could it be a con?

 

[cockoloco]

:headache:* faints from dizziness *