Probability

Gus Ivey

So the question is about the lotto.

We were talkin about the new "All or nothing" Lotto draw where there are 24numbers to pick from, and you pick any 12 numbers. The idea is to either get 12numbers, or get 0 numbers - both being the jackpot.

Someone said that this is harder to win than the ordinary lotto which has (correct me if im wrong) 46 numbers and you have to get 6 numbers.

So the chances of rinning the lotto jackpot is 46 x 45 x 44 x 43 x 42 x 41 (is this correct ?

so can anybody clear up for me which draw is harder to win...

Thanks !

LeixlipRed

That's not correct. It's 46 C 6 combinations. 24 C 12 is less possible combinations and if you add in the extra chances of winning by getting 0 right as well it's easier to win this than the actual lotto.

EDIT: Don't ask me to work out the actual odds cause probabilty plus me equals fail

cavedave

The answer is here

LeixlipRed

I know how to calculate 24 C 12. That's not the odds for winning the "all or nothing draw". One over that figure is the probability of choosing 12 correct balls. But you must add that to the probability of choosing exactly 0 balls correctly too.

Pherekydes

LeixlipRed wrote: »

I know how to calculate 24 C 12. That's not the odds for winning the "all or nothing draw". One over that figure is the probability of choosing 12 correct balls. But you must add that to the probability of choosing exactly 0 balls correctly too.

The game is to match all 12 numbers OR match no numbers.

From their website:

Match All 12 Numbers – Win €500,000
Match Nothing (no number matched) – Win €500,000
Match 11 Numbers – Win €5,000
Match 10 Numbers – Win €25
Match 9 Numbers – Win €10
Match 8 Numbers - win €4

LeixlipRed

Pherekydes wrote: »

The game is to match all 12 numbers OR match no numbers.

Yep, so you calcualte the probability of getting 12 balls correct and do the same for 0 balls. Add them and thats the probability of winning the jackpot. Was that not what I said?

Reginald P. DuM

I read before that the odds of wining the normal lotto are somewhere in the region of 14,000,000 to 1. Sounds about right! The All or Nothing is a bit less than than but still cataclysmic.

Derren Brown recently suggested that you have more of a chance of dying before the draw takes place than you have of winning it.

Gives credibilty to people who refer to the Lotto as "idiot tax" I think.

MathsManiac

It's much easier to analyse than the regular lotto, as you don't have to worry about the prizes varying from week to week, or about the probability of having to share.

By my reckoning, taking all prizes into account, the expected return from the all or nothing draw, assuming it's as Pherekydes described, is €0.394. Since it costs €2 to play a panel, this is an expected return of just under 20%.

That's pretty poor. Go to the Bookie's instead!

Mellor

LeixlipRed wrote: »

Yep, so you calcualte the probability of getting 12 balls correct and do the same for 0 balls. Add them and thats the probability of winning the jackpot. Was that not what I said?

But you are really over-complicating it. No need to work it out twice, just half it.

24 choose 12 is about 2.7million
Every draw two sets of 12 are winners, the 12 they pick, and the twelve they don't. so chances of winning the jackpot are 2.7million/2

Reginald P. DuM wrote: »

I read before that the odds of wining the normal lotto are somewhere in the region of 14,000,000 to 1. Sounds about right! The All or Nothing is a bit less than than but still cataclysmic.

They aren't that high, its just over 5 million to one. Still dire though

Greenmachine

Mellor wrote: »

But you are really over-complicating it. No need to work it out twice, just half it.

24 choose 12 is about 2.7million
Every draw two sets of 12 are winners, the 12 they pick, and the twelve they don't. so chances of winning the jackpot are 2.7million/2

Reginald P. DuM wrote: »

I read before that the odds of wining the normal lotto are somewhere in the region of 14,000,000 to 1. Sounds about right! The All or Nothing is a bit less than than but still cataclysmic.
They aren't that high, its just over 5 million to one. Still dire though

Nope

Lottery Odds Calculator Results

Total numbers to draw from45Numbers drawn per draw6Total played numbers6Total 6 number combinations of 61Odds of matching 6 of the 6 played1 in 8145060.00Now try playing more numbers
See how the odds will be reduced significantly!

Mellor

Greenmachine wrote: »

Nope

Lottery Odds Calculator Results

Total numbers to draw from45Numbers drawn per draw6Total played numbers6Total 6 number combinations of 61Odds of matching 6 of the 6 played1 in 8145060.00

I was going on the basis of 42c6 numbers, which is about 5.2 million. This is what it has been as long as I've known it, and it was the last time I played. A quick google shows that it went up three years ago.
But still, its not, nor has it ever been 14 million, which was my point.

LeixlipRed

Ah I was forgetting there are only 24 balls! Very true Mellor