for all you mathematician/statisticians
 

lottery numbers are from 1 - 49. i want to know if certain numbers come up more often than other. if say after 10 million iterations would we be looking at a normal distibution curve and if so what numbers would fall between +- 2 standard deviations.

cheers

big sinky

No, the numbers are almost certainly random still. Any given set of balls may have a bias, but each new set changes that bias.

And in answer to the unasked question: no, you're not going to win millions....


M

I agree, if the balls are chosen completely at random then no balls will be chosen more than any others and so, after an infinite number of selections, you will not get a classic normal distribution shape by plotting ball numbers by number of times chosen because it will be a straight horizontal line!

it's random........there's no way to determine what the curve will look like.

Sounds like a load of balls to me!


<cackle> :D

What curve?

The numbers on the balls are discrete, so all you can plot over time is a histogram showing the frequency with which each is selected.

If the selection is truly random - and a lot of effort goes into ensuring that it is - then after a large number of draws, the shape of that histogram WILL be flat. Every ball will be drawn just as often as every other ball.

I do laugh at people who try to predict what the draw will be by looking at past draws and working out which balls have come up most often. All you achieve by doing that is increase the chances that if you do win, you'll have to share your prize with other idiots who have done the same.

The best way to pick numbers is completely at random. Since nothing you do can alter the chances of a win, the best you can hope for is that you've picked numbers that nobody else has picked, and thereby maximise the chance that you won't have to share your winnings.

I wonder how many people still pick 1,2,3,4,5,6 - In the early days of the Lottery Camelot told the "Idiots" that approx 6,000 people were doing this - Oh How I wished that 1,2,3,4,5,6 came up and you had 6,000 people telling their bosses to shove their jobs up their arses only to find out they'd only won £665.54 :D.

This has the frequency breakdown:

http://www.national-lottery.co.uk/pl...requencyAll.do

Good luck!

if you compare the previous 12 months to all games ever drawn, you will see that the results are completely different - i.e. meaningless.

Absolutely.


Not in practice: you should select one or more numbers over 31, as a lot of people play birthday dates, and some of them only birthday dates. Historically speaking, every time the draw has been made up of numbers under 32, there were a lot more winners than on average.

Andy and Claudius aren't you missing the point?
Surely the aim is to select the same numbers as will be drawn NOT numbers that everyone else doesn't choose?? I know you can more likely predict one set than the other BUT having chosen 42, 43, 44, 45, 46, 47 do I feel smug when 1, 2, 3, 4, 5, 6 come out because I'm not one of the losers that went with the herd?

I'd be soooo gutted if I had to share my 6,000,000 with 12 other people..

Probably right - in fact you could probably write a whole PhD thesis on how to maximise your average winnings based on the methods other people are likely to be using to pick numbers. Of course, if lots of people adopt any system then that system becomes statistically less effective. You see the same thing happen in evolution - it pays to have a different immune system to your peers, for example.

Then there are those little keyrings with balls in, which are more likely to pick numbers that lie on the edges of the square - so they're best avoided too.

Personally I don't play the lottery. By keeping the money, my average is better than 99.999% of people who do play...

No - because you *can't* predict which numbers are going to be drawn. Otherwise we'd all be doing it.

I'm afraid you're the one that's missing the point.

The numbers drawn are random. That means you cannot predict the numbers that will be drawn.

The numbers that other people select, are not random. They're biased, in favour of birthdays, numbers that fall at the edges of pick-your-lottery-numbers keyrings, non-consecutive numbers, popular 'lucky' numbers and so on.

Therefore, although you can't do anything to make your selection more likely to be drawn than any other, you can improve your chances that if you win, you won't have to share with so many others.

...and therefore, sharing our prize amongst lots of other people :)

No, I'm not. :) The point is that predicting the drawn numbers is impossible. What you can do, however, is try to minimise the chances of having to share it.

Don't be silly - what we would have is a nationwide agreement that each contestant is given the opportunity to win the lottery on a particular date.

Mr. C_772, you will be pleased to hear that you have been nominated to win the lottery on 12th July, 2114. Your prize will be £1.

hth

:)

Sorry, didnt see your reply AndyC...

Where is Saxo boy when you need him? :)

It's is possible (although very unlikely) that you could draw balls a million times and everytime it's the same number.

[QUOTE=AndyC_772]What curve?
All you achieve by doing that is increase the chances that if you do win, you'll have to share your prize with other idiots who have done the same.
QUOTE]

I do understand all the above guys.. honest.. It this that made me smirk.. Taking the intellectual high ground because your numbers are chosen more intelligently while some poor simpleton walks off with his large cheque.. or even a cheque for a mere £650 notes..

As already stated there is no way to maximise your chances of winning (other than buying a lot of tickets), the numbers come out completely at random.

You can however maximise your chances of not having to share the jackpot with anyone else. One obvious rule is to not play the numbers 1-12 as loads of people pick their numbers based on birth dates. In fact playing the numbers 32-49 only might be good.

So the man taking the "intellectual high ground" (or shall we call it "intellectual mole hill" ;)), has just as much chance (i.e. so close to zero as makes little difference) as walking off with a cheque as the poor simpleton. The only difference is that intellectual guy is likely to win more money, should more than 3 of his numbers come up.

Actually the man on the intellectual mole hill wouldn't enter the lottery because he would know it was a tax on the statistically challenged! ;)

:D

Must use that phrase at work some time ;)

ajm... I'm with you actually..

as its all random, I always pick last weeks winning numbers for the following week.

Back to the original question...

In terms of the frequency of which particular numbers occur on a series of random draws, assuming the draws behave as independent random variables with uniform distribution, i.e. each ball is equally likely to be selected, the distribution of frequency should be Poisson.

For a very large number of draws the central limit theorem applies and the Poisson distribution can be reasonably approximated to a Normal distribution.

I've already looked at the stats for these (albeit years ago) and the draws follow the sort of trends expected from an independent draw, so it would appear there are no trends outside the norm. Your best bet, as people point out, is to maximise expected return on the stake (1) only playing rollovers and (2) avoiding other peoples' choices (which improve your expected return on all but 3 numbers) - but about the best I could come up with gave a return of around 90p in the £.

Pah! What a load of rubbish. Didn't really think that through did I?

I remember doing the analysis... and I remember using Poisson... but of course it isn't a Poisson distribution (can't believe you lot didn't spot that)

The distribution is binomial. Each lottery draw is an event and at each event a ball is either drawn or not, with probabilities 6/49 of being drawn or 43/49 of not being drawn.

However the binomial distribution is a pig to work out large number of events, so we approximate it with a Poisson, with parameter lambda = (np) where n is the number of events and p is the probability of a success. So, for example, if we are considering 1,000 draws the probability of x occurrences for a single drawn number is taken for the Poisson distribution with parameter 1000*6/49.

The mean and variance of the distribution are both lambda, so the most likely no. of occurrences is 1000*6/49, approx. 122, and the 1 standard deviation is sqrt(122), or about 11. For large numbers of draws, a normal distribution fitted to this is about right.

2 standard deviations represents 95% likelihood, which means about 1 in 20 numbers could fall outside this area - since there are 49 numbers, this probably isn't a good measure of whether they are statistically valid! Strictly speaking, we should apply a hypothesis test, but chances of being outside 6 standard deviations is pretty slim, so probably a good "first cut" test of independence.