National Lottery - Probabilty and number selection

Anyone here good with probability analysis? :)

Started a direct debit about 6 months ago for the national lottery, twice weekly draw with same number set. To be honest i never really watch it, the draw etc. Won £10 last year, and only found out when i got a email.

Yesterday i got a email saying i had won again. Logged in to find that i had matched 5 numbers winning about £1200 (a good part of which i will donate to my usual charity) Annoyingly our 6th number was 45 and the 6th ball to come out was 46. Rather close to the shared million jackpot. But hey better than nothing.

Question is... going forward with my direct debit if 5 of your 6 numbers have come out is there less of a probability of ever winning keeping the same numbers you won with before? If i was going to keep the DD going would you think wise to choose a completely new set of numbers? or keep my current one (of which 5 numbers of the 6 came up already) Really can not decide.

Statistically it makes no difference if you keep your numbers or change them entirely.

I think the odds of the balls comming out again are the same as them not comming out again

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Originally Posted by Jay

I think the odds of the balls comming out again are the same as them not comming out again

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Not strictly true but I know what you're trying to say. The odds of your set of numbers coming up are exactly the same odds as any other specified set of numbers coming up

They are separate trials, so the odds of 45 coming out again are the same as 46 coming out again.
So changing your numbers won't give you a better chance, as each epoch is a random draw.

The fun concept of trials, this reminds me of one of my favourite interview questions to ask, see this excellent wikipedia article:
http://en.wikipedia.org/wiki/Monty_Hall_problem

Well worth a read, and when you draw out the probability tree it all makes sense.

You got 5 numbers and only won £1200? :O_o1:

Think of it this way... Do you think the Balls have any memory of how many times they have been draw? Add into this they use different machines and Ball sets.

No.. they don't, so it will not effect the odds.

However our brains are designed to look for patterns even when a patten does not exist. So its very common for a human to believe the fact a ball has been draw a lot before makes it more or less likely (oldly some people believe it is more likely as its a "golden" ball, and some people think it is less as it has "had its fair share".).

What is true is if you get a "random" (puedo random) balls generated by machine you are more likely to win big if you win. As people tend to pick things like birthdays to build the numbers they use, so more people use 1-31 than 32+

I had a friend who always got a random selection and said that way if he missed a week he would not have "his numbers" come up.

Other lottery questions.

If you enter the same draw price are you more likely to win and if you enter two different draws once? Yes

If you enter two different draws are you more likely to win more money than entering the same draw twice (given the jackpot being at the same level)? Yes

If you're now up on the deal I'd stop doing the lottery immediately, tbh. The prizes are significantly lower than the probabilities against matching the numbers, so over a long period you are likely to spend signficantly more than you win. This should be obvious, given that they donate half of the takings to charity and spend vast amounts on running the actual lottery itself - where do you think that money comes from? ;)

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Originally Posted by Barrichello

Annoyingly our 6th number was 45 and the 6th ball to come out was 46. Rather close to the shared million jackpot. But hey better than nothing.

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since the balls have numbers only for differentiation, 45 is no closer to 46 than it is to 1, 5, 20, 33 whatever. your not guessing the amount of balls in a jar or something, you weren't one off.

so cancel your DD, do your best to forget your numbers, and never check another draw ever again

Try playing "Lottery Roulette". Everyone picks 6 numbers, but DOES NOT buy a ticket for those numbers. You then all watch the draw together and pray that your 6 numbers don't come up :D

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Originally Posted by MadduckUK

so cancel your DD, do your best to forget your numbers, and never check another draw ever again

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Indeed. Any form of gambling is in fact a guaranteed loss for 99.9999% (if not 100%) of players in the long term. Once you're up, you should basically quit playing. I just don't bother playing in the first place, so I'm always up.

However, the lottery has other things going for it, such as being an indirect (and possibly inefficient) way of donating money to charity.

I agree about the analysis of the odds, but not about stopping playing.

First, odds.

If looking at a sequence of events, do a specific event either rely on previous ones, or affect future ones? If not, look at it isolation.

Take a coin toss. Assume, for simplicities sake that the coin is not loaded in some way, and that it never lands on it's edge, or gets stuck to the ceiling, etc. So, you have 50% chance of heads, and 50% chance of tails.

Where people often get confused is between two questions :-

1) What the chances of getting 10 heads in as row?

2) If I've had heads the last 9 times, what's the chances of getting another one?


In the first question, it's 50% x 50% x ...... 50% (10 times).

In the second question, it's just 50%.

Animus said it, they're separate trials. Oolon said it ... there's no memory.

If you toss a coin, the chances of a given outcome (heads) are 50% whether it's the first toss of the millionth. The chances of getting a jackpot on a lottery with a given number set this week are they same as the were last week or next week. The events are not linked.


But for cancelling the DD, that's about more than just statistics. Or, it can be, anyway.

The chances of getting a really big win, or indeed a jackpot, are very small indeed but if you do, it's a life-changing event. So, for most of us, does a quid or two a week really make much of a difference? No. Will we get a financial return on it? Probably not. But do you get an entertainment value from it? Do you get a buzz from the possibility of a big win? Perhaps? Do you get a chance, albeit a very small one, of a life-changing win? Only if you stump up the pound or two.

Anyone doing it as an investment because they expect to win is a naive optimist. Unless they win, at which point it was the best few quid they ever spent.

But if you're doing it because you can afford it and because you want to .... go right on. And why not?

Lottery = 100% luck. Simples

Personally, I find it funny what Adam Smith had to say on the subject "National Lotteries they are a tax on stupidity". Particularly as there is a conservative think tank called the "Adam Smith Institute" and conservatives introduced the national lottery in the first place. So i don't play, if its just a bit of fun for someone, I see no harm in it, however for some its its seen as the only hope they have to get out of there current situation which does worry me.

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Originally Posted by Saracen

Do you get a chance, albeit a very small one, of a life-changing win? Only if you stump up the pound or two.

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:rolleyes: why stop at the lotto then, think of all the other lotteries that you are not winning right now because you are not taking part. how can you sleep at night seeing theoretical win after theoretical win pass you by is what i want to know.

The lottery is a tax on hope, not on stupidity. I agree pretty much with what Saracen said.

To use the accountancy term of 'opportunity cost', if you don't buy a ticket a week, what could be done with 52 quid a year? I buy a couple of tickets a week. Most of the time I lose, but it's worth it for the thrill, the hope and the miniscule chance. I do also use lucky dips, as I'd be rather sick if I kept the same numbers, missed one week and they came up..

Number selection is different, though. Whilst each number is equally likely to come up, the income you'll gather differs based on your selection. The number of winners when all numbers are less than 31 will statistically be higher, because people tend to select birthdays for draw numbers.

Similarly, if 1 2 3 4 5 6 ever comes up, don't expect any millionaires - probably not even any 10,000UKP winners for 6 numbers..

Well, each to their own. I'd rather give the few quid a week directly to charity, without the lottery tax along the way. The odds are so long as to be ridiculous, not to mention unexciting (to me, at least).

Besides, surely the better thing to do is to just go to a bookies and bet that you can guess this week's lottery numbers. Then, if you get it right, you're guaranteed to be getting ~£10+ million (13,983,816 to 1 odds, right?) rather than sharing the pot. No idea if this is actually possible, but certainly seems like the better way of doing things to me.

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Originally Posted by Fraz

Besides, surely the better thing to do is to just go to a bookies and bet that you can guess this week's lottery numbers. Then, if you get it right, you're guaranteed to be getting ~£10+ million (13,983,816 to 1 odds, right?) rather than sharing the pot. No idea if this is actually possible, but certainly seems like the better way of doing things to me.

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Hmm interesting, but if you only 5 right you won't get anything

... and no indirect way of donating to charity.

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Originally Posted by The_Wheelhouse

... and no indirect way of donating to charity.

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meh, probably better that way - you get more control

not that this idea would actually fly, but anyway

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Originally Posted by MadduckUK

:rolleyes: why stop at the lotto then, think of all the other lotteries that you are not winning right now because you are not taking part. how can you sleep at night seeing theoretical win after theoretical win pass you by is what i want to know.

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Way to go selectively quoting and taking something WAY out of context.

What part of the preceding bit of the paragraph you quoted don't you understand?

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The chances of getting a really big win, or indeed a jackpot, are very small indeed but if you do, it's a life-changing event. So, for most of us, does a quid or two a week really make much of a difference? No. Will we get a financial return on it? Probably not. But do you get an entertainment value from it? Do you get a buzz from the possibility of a big win? Perhaps?

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I sleep completely free from concerns about the lottery, largely because I rarely do it. If I happen to be passing a ticket office and the mood catches me, I might have a ticket. Mostly, I don't.

You slap on a rolleyes and then try to parody what I said by implying I think I might be missing out on some win. That's pretty much the opposite of what I said, and a parody which is typical of the attitude of a few people on this forum that gets me really annoyed.

One day I'll will the lottery, one day I'll play the lottery.

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Originally Posted by Saracen

If I happen to be passing a ticket office and the mood catches me, I might have a ticket. Mostly, I don't.

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try hard.

anyway, good luck tomorrow http://i41.tinypic.com/jtrk03.gif

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Originally Posted by Saracen

The chances of getting a really big win, or indeed a jackpot, are very small indeed but if you do, it's a life-changing event. So, for most of us, does a quid or two a week really make much of a difference? No. Will we get a financial return on it? Probably not. But do you get an entertainment value from it? Do you get a buzz from the possibility of a big win? Perhaps? Do you get a chance, albeit a very small one, of a life-changing win? Only if you stump up the pound or two.

Anyone doing it as an investment because they expect to win is a naive optimist. Unless they win, at which point it was the best few quid they ever spent.

But if you're doing it because you can afford it and because you want to .... go right on. And why not?

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I totally agree, that's my attitude too. I played the lottery with the same numbers every week from the first week- illegally at first, as I was 15 1/2 when it started. Carried on for about three years, in which time I won 10 quid- on the draw that took place on a Sunday, as Diana's funeral was on the Saturday. Next time a royal dies, I'm going all in:p:p. On the rare occasion that I failed to buy a ticket the draw was far more exciting- "YES! That's not my number. YES! That's not mine either!":lol:

But I stopped when they introduced the Wednesday draw. The overall jackpots went down, and they doubled the weekly subscription fee- and as a skint student, that actually mattered to me. Now I just play when there's a decent rollover- I still use my original numbers on the original National Lottery, and go for a lucky dip on the Euro Millions.

And- I know the odds (approx 70m-1 for the Euro Millions), and I don't expect to win. 1 or 2 quid buys me a day or two of very pleasant daydreaming when I'm stood by the side of the road, possibly in the rain, watching buses come and go. The last big Euro Millions Rollover was especially sweet, as the winner took a day to come forward. I hadn't checked my ticket, so that was an extra day of possibility for me. I eventually checked my ticket- I had no numbers at all- but it was well worth the money IMO:).

I say change your numbers and like Syllopsium said choose numbers in a way that
most people wont. So have several high numbers and a couple in sequence like

22 29 36 41 43 44

That way if you do win chances are you win more.

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Originally Posted by TheAnimus

The fun concept of trials, this reminds me of one of my favourite interview questions to ask, see this excellent wikipedia article:
http://en.wikipedia.org/wiki/Monty_Hall_problem

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I first heard about it from watching 21, it's quite an interesting concept.

The other one I like is the loaded revolver question:
2 consecutive chambers in a standard 6 chamber revolver are loaded with bullets, the chamber is spun and put against your head and the trigger pulled, you can choose to spin the chamber after a successful round (where you dont die obviously)
Assuming you survive the first round do you spin or not for the second round?

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Originally Posted by finlay666

The other one I like is the loaded revolver question:
2 consecutive chambers in a standard 6 chamber revolver are loaded with bullets, the chamber is spun and put against your head and the trigger pulled, you can choose to spin the chamber after a successful round (where you dont die obviously)
Assuming you survive the first round do you spin or not for the second round?

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No.

If you've survived the first round, you've picked one of four empty chambers, and only one of those four chambers would be followed by a bullet, so you've got a 3/4 chance of not shooting yourself on the second pull. If you spin, you've got a 2/3 chance of not landing on a bullet. So your chances are greater if you don't spin.

Only, that's the intuitive answer, isn't it? So I don't see where the puzzle is...

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Originally Posted by scaryjim

No.

If you've survived the first round, you've picked one of four empty chambers, and only one of those four chambers would be followed by a bullet, so you've got a 3/4 chance of not shooting yourself on the second pull. If you spin, you've got a 2/3 chance of not landing on a bullet. So your chances are greater if you don't spin.

Only, that's the intuitive answer, isn't it? So I don't see where the puzzle is...

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Intuitive... well common answer is to spin again as it's seen as a 5 chamber gun so 4/5 you pick an empty chamber which is where the problems start

Yeah it's strange, the odds of the same numbers coming up are the same as you winning the lottery.

But, you could look at it like this.

The odds of the numbers being the same every week - Do you ever see this happening? It's extremely rare, happens every 20 - 50 years.

The odds of a new set of numbers winning - It happens every single week (apart from the week that will get the same numbers twice)

So, you are better off changing your numbers if you do win the lottery. ;)

(but hell, if you do win, I'm sure you can afford two bloody lines, a tramp can afford two lines)

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Originally Posted by SammEl

So, you are better off changing your numbers if you do win the lottery. ;)

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Please read the thread and redact your comment as required.

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Originally Posted by SammEl

The odds of the numbers being the same every week - Do you ever see this happening? It's extremely rare, happens every 20 - 50 years.

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So that's why it happened last year (and has happened before in other countries including Mexico)?
http://www.telegraph.co.uk/news/news...ght-draws.html

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Originally Posted by finlay666

Intuitive... well common answer is to spin again as it's seen as a 5 chamber gun so 4/5 you pick an empty chamber which is where the problems start

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but - the problems *says* it's a six chamber gun! So - the common answer is just plain dumb? I mean, I'm as cynical as the next person (and the next person on this occasion is my wife, so that's pretty damn cynical!) but surely most people aren't *that* dumb?

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Originally Posted by scaryjim

but - the problems *says* it's a six chamber gun! So - the common answer is just plain dumb? I mean, I'm as cynical as the next person (and the next person on this occasion is my wife, so that's pretty damn cynical!) but surely most people aren't *that* dumb?

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It's not being dumb, it's about approaching the problem the wrong way, there are a lot of puzzles that are very simple if you approach them correctly but most approach them in the wrong way

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Originally Posted by finlay666

So that's why it happened last year (and has happened before in other countries including Mexico)?
http://www.telegraph.co.uk/news/news...ght-draws.html

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Did I say it never happens? No, Mr Dimley666 - The official statistic is it happens every 20 - 50 years per lottery, go do another Google search.

You're either trying to just dissagree with me on something over and over again, or being a complete moron and not reading my whole post.

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Originally Posted by SammEl

You're either trying to just dissagree with me on something over and over again, or being a complete moron and not reading my whole post.

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I read your while post, realised what nonsense and tosh it was and commented on such, given that you disagreed with what was proven previously to be true that randomly choosing numbers each time is a better method to do.

Do you even understand the concepts of mathematics involved, perms and combs, atomic/sequential events and the like?

You never said for [b]one[/n] lottery it's every x years, given that each lottery is different this isn't exactly accurate either. Given that for your statistic to be correct with 50 years having 5000 draws then the odds of two consecutive draws must be a LOT less than the actual 1 in 1.9554711 × 1014 odds that the UK lottery gives, unless you aren't counting correctly

Where exactly is this official statistic then? As Google is not an alternative to a sound education in mathematics

Mr Toon - You love a fight init boi.

I won't post anything for you, I know the statistic, it's a fact, if you want to, go and look it up so you can look at yourself and see a prat. I honestly don't care, a forum is not a place for me to prove myself to you.

In other news, I found out Finley was from Newcastle and now is lower on my board than he was before, which was 6 feet under.

Feeling hot in that magma chamber?

Finlay666 and SammEl - enough! Any more of this nitpicking and sniping and
its a 3 month suspension - got it?

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Originally Posted by finlay666

It's not being dumb, it's about approaching the problem the wrong way, there are a lot of puzzles that are very simple if you approach them correctly but most approach them in the wrong way

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I will admit that I failed the Monty Hall problem the first time (and even though I understand it now, it still amazes me), but I called it right on the revolver one (scaryjim's solution just seem more intuitive to me).

Thanks all for your advice and some very interesting points. Decided we are going to keep our numbers! :)

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Originally Posted by TooNice

I will admit that I failed the Monty Hall problem the first time (and even though I understand it now, it still amazes me), but I called it right on the revolver one (scaryjim's solution just seem more intuitive to me).

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As I said they are questions that on their own are not difficult if approached in the correct way, however many do approach them from the wrong way which makes them far more difficult.

There are a plethora of others including the pirate gold problem (Which someone, through a research paper proceeded to solve to n pirates), the island of cheating husbands conundrum and the torch bridge crossing problem that seem to be favourites in interview situations now, as they require analytical thinking and being able to approach problems from a variety of positions.

There are similar puzzles in the book "How would you move mount Fuji"
http://www.amazon.co.uk/How-Would-Mo...1678805&sr=8-1

It's quite an interesting read if you like those sorts of puzzles

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Originally Posted by Barrichello

Thanks all for your advice and some very interesting points. Decided we are going to keep our numbers! :)

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Only reason I see for changing your numbers (to a different set if at all, no need to change them weekly) is to pick uncommon combinations so should you win you share with fewer people should you get enough numbers :)

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Originally Posted by SammEl

Mr Toon - You love a fight init boi.

I won't post anything for you, I know the statistic, it's a fact, if you want to, go and look it up so you can look at yourself and see a prat. I honestly don't care, a forum is not a place for me to prove myself to you.

In other news, I found out Finley was from Newcastle and now is lower on my board than he was before, which was 6 feet under.

Feeling hot in that magma chamber?

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Ok lets try this again.

You can't just say something is fact because you know a statistic.

We know the probability of winning the lottery is:

1 in:
6/48*5/47*4/46*3/45*2/44*1/43

Now if there are two draws a week, 52 weeks a year (remember this isn't true), and 50 years we have
2*52*50 This is the number of trails

now, we don't even have to multiply to see that 2*52*52 is considerably less than that, so we don't really have enough trails in 50 years do we.

Now one of the key concepts here about random trails is its not a certainty at all, but hopefully you can see how the numbers pail together, the distance is to great.

As someone who uses simple statistics for their daily bread, I get VERY upset with the press, even the broadsheets, and don't get me started on the government press office, they are just wrong from a point of un-bridled ignorance.

Now in this thread, we've provided links, explanations, some of them such as the Monty Hall I hope people find/found fun, I certainly do, the perfect logic and beauty of the solution is quite pleasing.

If you think any of this is incorrect, then please feel free to link your original source (google didn't turn it up easily for me!) and some of us here will explain as best we can whats gone wrong.

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Originally Posted by Allen

You got 5 numbers and only won £1200? :O_o1:

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I had 5 numbers last year an only got £952. :(

if it makes u feel any better the difference between
6/48*5/47*4/46*3/45*2/44*1/43
and
5/48*4/47*3/46*2/45*1/44

Is VERY significant.

But solace in numbers with these things rarely helps.

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Originally Posted by TheAnimus

if it makes u feel any better the difference between
6/48*5/47*4/46*3/45*2/44*1/43
and
5/48*4/47*3/46*2/45*1/44

Is VERY significant.

But solace in numbers with these things rarely helps.

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I'm lost in the 'Toryness' of it all :p

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Originally Posted by Blitzen

I'm lost in the 'Toryness' of it all :p

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Is that because all the lottery machine does is put a lot of spin on the balls ;)

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Originally Posted by TheAnimus

if it makes u feel any better the difference between
6/48*5/47*4/46*3/45*2/44*1/43
and
5/48*4/47*3/46*2/45*1/44

Is VERY significant.

But solace in numbers with these things rarely helps.

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By comparison, yes. But in absolute terms they're both insignificant.

5 balls - 0.000057%
6 balls - 0.0000078%

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Originally Posted by Blitzen

I had 5 numbers last year an only got £952. :(

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Screw that... I would get yourself to the bookies and put a quid on the irish lottery picking 3 numbers.

If all 3 are in the 6 numbers drawn then you get ~ £610 which is a lot better than the measly £10 you get on the National Lottery.