National Lottery - Probabilty and number selection

[Barrichello]

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.

[Salazaar]

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

[Jay]

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

[Salazaar]

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

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

[TheAnimus]

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.

[Allen]

You got 5 numbers and only won £1200?

[oolon]

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

[scaryjim]

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?

[MadduckUK]

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.

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

[Kata]

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

[Fraz]

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

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.

[Saracen]

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?

[psu1]

Lottery = 100% luck. Simples

[oolon]

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.

[MadduckUK]

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

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.

[Syllopsium]

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..