The Irish Lotto

comet

If I buy 2 lines of numbers for each draw (twice a week), on average how many years would it take me to win the lotto?

ecksor

What's the rules nowadays, pick the right 6 numbers out of 42?

comet

Yeah, 6 numbers from the pool of 42 to win the jackpot

MiCr0

sounds like homework

feylya

36,316,980 years? Hmm, probably not right there. Ah well.

smiles

The lotto is a game where you give someone a euro and they give you 20 cent.

It's all in the variance.

<< Fio >>

smiles

Originally posted by comet
If I buy 2 lines of numbers for each draw (twice a week), on average how many years would it take me to win the lotto?

What do you mean by win the lotto?
There are many different classificiations of winning -- winning 20 euro, or 1 million.

<< Fio >>

comet

Originally posted by smiles
What do you mean by win the lotto?
There are many different classificiations of winning -- winning 20 euro, or 1 million.

<< Fio >>

By "win" I mean win the jackpot i.e. get all 6 numbers

Hairy Homer

To the nearest year:

25,220

comet

Originally posted by Hairy Homer
To the nearest year:

25,220

that sounds about right.....care to share the calculations/source

Corben Dallas

25000 years ............so we'll all be dead then Ted!

They should get rid of the crappy 3 numbers >U win a €2 scratch card whoop de doo
***wonders is this a cynical attempt to clear the backlog/up the sales numbers of scratch cards** ?:|

infact scrap all wins up to 4numbers and have 5 numbers wins €20,000-30,000
@ teh moment u can get 5 numbers AND the bonus numbers and still only get a few grand. The next rank is 6 numbers with a guaranteed €750,000 (< I think?)every draw

IMO its way too much of a gulf in prize money terms.

Hairy Homer

Originally posted by comet
that sounds about right.....care to share the calculations/source

Long time since I did a maths exam.

The probability of perming a single sequence of six numbers from a total of 42 is (I can't remember the term but it works out as 42!/((42-6)! x 6!)

which factors out to

42 x 41 x 40 x 39 x 38 x 37/(6 x 5 x 4 x 3 x 2 x 1)

which works out as one chance in 5,245,786

So if you do four lines a week that's equivalent to one chance in 1,311,446.5

Divide by 52 to convert that to years:

One chance in 25,220.125 years

That;s the probability. Whether that's the same as the mean time to getting it right I'm not sure. As I say, long time since I did a maths exam.

comet

Thanks,
I had heard a figure a while but couldn't remeber what it was or how to get but this figure sounds good

I have played Lotto for about 4 years, so that leaves me with 25,216 years to go. Problem is will the earth and me still be here that far in the future and even if we are will the Lotto still be running??

davros

This was bothering me a little. Over 25,000 years, I might win the lotto several times or I might not win it at all.

So I was fiddling around with some smaller games and I decided that another way of asking the question would be: after what length of time would my expected earnings be equal to exactly one jackpot.

So you would have to add up:

(prob. of winning once) x (1 jackpot)
+ (prob. of winning twice) x (2 jackpots)
+ (prob. of winning thrice) x (3 jackpots)
...

...and it turns out you get... exactly the same answer

So, um, that probably didn't add much to the discussion

aphex™

A friend of the family apparently won the lotto twice in 18 months. And he didn't really need the money either, he is a doctor.
I believe there are ways to increase your odds, but you'd need some serious cash behind you to work it. I worked in a big newsagents for a while, i sell an unbelievable about of lotto tickets, none of which have won any jackpot, kinda puts you off the game.

Capt'n Midnight

About the only thing you can do is to pick numbers that other people don't pick so that if you win you don't share a prize.

The bonus number is to stop syndicates from earning enough on the smaller prizes to make it worth their while buying of every combination when the prize fund goes over a certain amount. - Another variation on this is working out what is the minimum jackpot such that buying one of every ticket would more than likley break even.

alleepally

This months focus magazine covers this exact questions and also lots of other interesting bits and bobs on gambling.

Worth a read. At all good newsagents now.

aphex™

Originally posted by Capt'n Midnight
buying one of every ticket would more than likley break even. [/B]

Wow! i'd like to be in that syndicate!
but you could win and still be unlucky by sharing the prize!
Also im not sure it'd be even physically possible to buy one of every ticket, cos you'd need a hellova lot of minions to fill out the lotto forms! The margin of error would feck things up a bit..You'd have to take over a shop too, maybe three in the few days you have before the draw.

There are over 5,200,000 combinations of 6 numbers from 42. Each ticket has 10 panels? thats 520,000 tickets to fill out and get into the draw.

Originally posted by alleepally
This months focus magazine covers this exact questions and also lots of other interesting bits and bobs on gambling.

Worth a read. At all good newsagents now.

ah excellent! cheers thanks for the tip off!

daveirl

This post has been deleted.

Syke

Originally posted by daveirl
The reason we now have 42 numbers is because years ago when there were 36, a syndicate did win by trying to buy all the combinations. They worked out that the match 5's etc..., made it worthwhile to do.

i remember that. they won all the match 4 and 5s aswell which made it worth their while.

thats an interesting question. how much more than the jackpot would you expect to win if you bought all the combinations?

i guess you need to know how they allocate the winnings.

Ciaran

I think that only worked because the match 4s were €100 that week for some reason.

Syke

Originally posted by Ciaran
I think that only worked because the match 4s were €100 that week for some reason.

how would they have known that in advance. they only decide the prize monies on the night.

smiles

Ok, in the lotto we have 6 numbers drawn at random from 42. Then a 7th (bonus) number is drawn.

Let X = #matches in the first 6 numbers.

First thing you need to note is that the lotto draw is a hypergeometric distribution. (not a binomial as mosr people here are using). In a lotto game, selection of successive balls is not independent because the balls are not put back into the machine.

f(x) = [ 6Cx ][ 36C(6-x) ] / [ 42C6 ] , x = 0, 1, 2, 3, 4, 5, 6.

ie.
(number of ways to match x out of 6 numbers)*(number of ways to not match the remaining 6-x numbers) / (number of ways you can select 6 numbers from 42)

where [ FCn ] is (the binomial) "F choose n"

The reason we use the hypergeometric for this is because when you look at the binomial probability of matching 3 out of 6 numbers, this does not exclude the possibility that you actually matched a total of 5 out of the 6 numbers... it just tells you how likely you are to match at least 3, whereas the hypergeometric tells you the probability of matching 3 numbers and not matching the remaining 3.

I'll ignore the bonus number for a sec.

So using the above formula you can work out the probability of matching x amount of numbers

f(0) = 0.3713060
f(1) = 0.4311941
f(2) = 0.1684352
f(3) = 0.0272218
f(4) = 0.0018014
f(5) = 0.0000411
f(6) = 0.0000002

The bonus number is selected from the remaining 36 balls. So we look at the joint distribution (Y) of matching x out of 6 numbers and also 1 out of 36.

If you take it that prizes are as follows:
€0 matching less than 3 numbers
€10 matching 3 + the bonus
€28 matching 4 numbers
€100 matching 5 numbers
€5,000 matching 5 + the bonus
€1,000,000 matching 6 numbers

So

€0 = 0.9981571
€10 = 0.002268483
€28 = 0.0018014
€100 = 0.0000411
€5,000 = 0.000001141
€1,000,000 = 0.0000002

So your average earnings from a €1 line is €0.28293903 ..... but it's all in the variance of the earnings.... (€200030.50) .....

..................

Ok, hope that makes some sense to everyone else!!

<< Fio >>

aphex™

Originally posted by Capt.Sparrow
how would they have known that in advance. they only decide the prize monies on the night.

No if its a promotion they announce it beforehand, to sell alot of tickets. Ie they did this recently.
Anyway i think what actually might have happened was the syndicate bought >3/4 of all the combinations so they had a big chance of winning. I dont think they run match 4 for €100 too much.

irishgeo

anyone have a spreadsheet which will allow me to enter the numbers we have for the draw and then enter the 3 sets of winning numbers and then check the numbers separately for each draw.

and let me know how many numbers i matched in each draw etc.

TomF

Tonight's Lotto Plus 1 and Plus 2 both came up with 2, 6, and 29 (and 29 also appeared in the Lotto).

I can appreciate that randomness being what it is, this will happen now and again, but I've been watching my tickets for a long time and this repeating kind of thing happens fairly often and it makes me go "Hmm."

The Lotto page doesn't have the numbers in the order they occur, but in numerical order. I wonder if anyone has studied the frequencies of order in Lotto draws.

If I were energetic and moneyed, I would have a video record of the way the balls are stacked at the beginning of every draw, and how they fall and try to learn if that influences the order of appearance of the numbers. Maybe the red balls are always on top and the blue balls always on bottom in the stacks: I've never written-down what I see at the start of a draw.

kilman

I've noticed this pattern also(that Lotto plus numbers seem to quite often have 2 or 3 numbers from the main draw).
Unfortunately my Quick Pick always seems to pick the incorrect ones.

Actually do you find that your Quick Pick numbers are often quite similar?

K

clearz

Originally posted by smiles
What do you mean by win the lotto?
There are many different classificiations of winning -- winning 20 euro, or 1 million.

<< Fio >>

See that is the problem with you "know it alls". What do you think sombody means when they say "Win the lotto" obviously the jackpot but then again me been a computer programmer I like to see logical patterns.

smiles

Originally posted by clearz
See that is the problem with you "know it alls". What do you think sombody means when they say "Win the lotto" obviously the jackpot but then again me been a computer programmer I like to see logical patterns.

well done with that.... :rolleyes:

<< Fio >>

ecksor

Originally posted by clearz
See that is the problem with you "know it alls". What do you think sombody means when they say "Win the lotto" obviously the jackpot

What's wrong with seeking clarification of that? This is the maths forum after all, obvious isn't always correct.

but then again me been a computer programmer I like to see logical patterns.

You're a computer programmer who objects to people seeking clarification? You must have very clearly written and unambiguous specifications and requirements to work from in your job.