carl

Yes, but the order is irrelevant in the lottery. They just sort the ***** for convenience. As each ball comes out of the machine it has no idea which ***** have come out previously.

As an example, you could add up all the numbers of the six ***** and you'd find that 21 is much rarer than (say) 139 but that's because there are more combinations that add up to 139 than there are that add up to 21. The chance of drawing an individual combination is the same for any combination. Remember you're dealing with combinations, not permutations -- the order doesn't count in combinations.

In your example, if 49 is drawn it will automatically be the highest ball. But if 40 is drawn there are so many combinations that involve numbers over 40 that it's got very little chance of being the highest ball. The other five ***** must all be in the range 1-39, which means that for 40 to be the highest (assuming it's already been drawn) the chance is (39!/34!)/(48!/43!)=0.33 (roughly). So there's a 2/3 chance that 40 won't be the highest ball.

It's kind of like the birthday paradox, in which if you have a room with 26 people in it (IIRC) the chance of two of them sharing a birthday is 50%. It starts off by multiplying up numbers like (1/365)*(1/364) etc. but as you get going it soon comes down to around 0.5.

[Edited by carl - 11/5/2002 6:11:47 PM]

DavidRB

This is a set of graphs showing the number of times each ball has appeared as the lowest, 2nd lowest, etc. up to the highest ball drawn after sorting:


If I've misunderstood probability and the number 6 is just as likely to be the highest number as 49, then I stand corrected. Does that mean I have to give my winnings back?

[Edited by DavidRB - 11/6/2002 9:01:58 AM]

MarkO

You have indeed misunderstood. The statistics of the ***** in the past has no bearing on the statistics of that ball in the future. One ball must be the highest, mustn't it? However, just because it's come up more than any other ball doesn't mean it'll continue that trend in the future.

What those graphs show is a mean distribution curve, and they're as you'd expect to see for a range of numbers. Clearly, 6 is far more likely to be the lowest number than 49 is simply because it is lower in value. However, you don't win the lottery by guessing the lowest number, you win by guessing the correct permutation.

Think about it. If I flip and coin, and get 'tails' 6 times in a row, then according to your suggestion the statistics imply that on the following flip 'tails' will be almost guaranteed. Which, of course, is total rubbish.
No, it means that you're just as unlikely not to have any winnings in the first place as if you picked any other set of numbers.


[Edited by MarkO - 11/6/2002 9:23:16 AM]

MarkO

That's right. That's my point. I knew it was there somewhere. Thanks merkin. Bizarrely, I even mentioned it in an earlier post.

Ironically, the post in which I started by saying "What do you mean you disagree, merkin? It's fact!".

[Edited by MarkO - 11/6/2002 3:45:26 PM]

MrDeference

we are getting all out of synch here.
25/14m is no where near winning.
7m/14m is still only a 50% chance.

The ***** in a bag is a redherring because they are linked events.

[Edited by MrDeference - 11/6/2002 3:56:02 PM]

MrDeference

I was saying that the analogy to the ***** in a bag didn't apply. We are now in agreement about that.

Merkin + Mark, we too are in agreement about how the probability works out, and coincidentally in disagreement with MarkO's statement that bought me into the thread. Viz:
EDIT: Hasty post directed at Carl. Getting a bit frustrated that we all agree, but are arguing

[Edited by MrDeference - 11/6/2002 4:13:36 PM]

carl

I don't understand what the problem is

Buying two tickets doubles your chance of winning (from 1/14e6 to 1/7e6)

Buying two tickets does not halve your chance of losing -- in fact it hardly changes it. It goes from (14e6-1)/14e6 to (14e6-2)/14e6.

That's it

[Edited by carl - 11/6/2002 4:17:11 PM]

carl

OK, but it's around that level.

1st person can have any date (1)
2nd person has 1/365 chance
3rd has 2/365 chance
etc.

Multiply them all up and it comes in around the low-to-mid 20s.

[Edited by carl - 11/6/2002 4:34:24 PM]

MrDeference

Rubbish. For 2 people to have the same birthday with a probability of 1 you would need to fill the entire calendar and then put in the 367th person which would guarantee one shared birthday.

Oh good. Once again I see we are talking at crossed purposes... sorry.

[Edited by MrDeference - 11/6/2002 4:36:06 PM]

Sprint Chief

I should have finished this off really shouldn't I

Expected return from jackpot, playing two different sets of numbers is (2/14000000)*(JackpotReturn/NumOtherWinners+1)

Expected retun from jackpot, playing one set of numbers twice is (1/14000000)*(JackpotReturn*2)/(NumOtherWinners+2)

If you work this out, the expected return is better from the first option. [NB NumOtherWinners does not include you and may be zero or more]

Do I win the Mr Logic award then

Edited to correct typing the equation wrong

[Edited by Sprint Chief - 11/6/2002 10:01:06 PM]

RAF1

iTrader: (5)

Hi there,
was just reading on ceefax that a 19yr old has won £9.7m on saturdays lottery....(Lucky B4stard)

just wondering if any1 here has ever won anything on the lotto...?

Cheers.
Raf.

(happy daydreaming....."what i would do with 9 million quid.......")

bioforger

iTrader: (1)

Yeh he has a criminal record for.. wait for it, yes aggrevated carjacking [img]images/smilies/mad.gif[/img] Theres no justice eh

merkin

[img]images/smilies/mad.gif[/img] should have forced him to give the cash to his victim.

jasonwrxowner

Merkin,

Did you get me my piccy last night?

merkin

Jason,

erm, I got a wee bit pished, and couldnt remember the name of the company, sorry mate, I do have random pics taken at funny angles of some of them with me looking slightly worse for wear, but I dont suppose thats much use

Dark Muppet

Looking at it laterally, at least he won't need to go car jacking anymore. He can just buy the car he wants to drive...

Dark Muppet

In fact, the governement could give all car jackers a million quid to stop them doing it again....

merkin

"he has as much right to win the lottery as anyone"

Not if he's paid for his ticket with the proceeds of crime he doesnt.

MarkO

Never won, cos I've never played it. The whole thing is a complete rip-off, and a tax on stupid people.

TopBanana

Yeah it is a tax on the stupid and the poor, but £1 a week is hardly a huge 'exposure' is it. Just a bit of fun

dogmaul

i find it funny these people who dont have jobs but spend £10-£20 a week on tickets its bloody stupid

DavidRB

It isn't just the lottery. With any form of gambling, the less people earn, the bigger the change in lifestyle they will receive from a big win, hence the larger percentage of their income they are willing to gamble.

Now if you really want to be interesting, answer the question whether 1,2,3,4,5,6 is more likely to win the lottery than 1,5,20,30,40,49.

TopBanana

No it isn't. Not that interesting really

TonyBurns

iTrader: (3)

Yup it does make you a bit mad to see someone like an aggrivated car jacker winning the lottery [img]images/smilies/mad.gif[/img] now i hope he drives his Porsche somewhere nice and gets a gun shoved to his head, that would be justice

Tony

DavidRB

Depending on whether you consider even and random to be the same thing or not, it's actually less likely to win.

TopBanana

Prove it then!

P1Fanatic

Spoken like a true crim.

Avi

S.B.

I won a tenner once.

carl

Originally posted by jlangg:If you don't understand why it is true, then you wouldn't understand the proof. Each ball selection is an independent event. If you throw a die six times you're just as likely to get 6,6,6,6,6,6 as you are to get 6,4,2,4,5,3