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## Maths help needed for new business project

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1227 posts
Joined 11/2009

Hey guys, iv been busy latley working on a new business idea in involving lotto numbers and need to get some 'basic im thick' probabilities down.

Take a 45 number lotto draw, with 6/7 numbers drawn.
What is the prob of picking 3 numbers and matching 3 out of 7 drawn?
what is the prob of picking 3 numbers and matching 3 out of 6 drawn?
If I offer odds of 315/1 out of 7 drawn, what's my edge gona be?
if I offer odds of 620/1 out of 6 drawn, whats my edge gona be?

What is the probability picking and matching 4 numbers out of 6 and 7 drawn in a 45 number draw?
What is the probability of picking and matching 2 numbers out of 6 and 7 drawn in a 45 number draw?
What is the probability of picking and matching 1 number out of 6 and 7 drawn in a 45 number draw?

I know some guys here look to get stuck into some math, although this mabey quite basic for some of you.Any help would be very much appraciated.

#### huntse

1432 posts
Joined 11/2010

There's a good explanation of the maths behind lotteries here, and you really need to understand this backwards if you're going to make it your business so rather than just spoonfeed you the answers I'm going to say you should read, learn and inwardly digest that page.

1227 posts
Joined 11/2009

Tbh I am just looking for the spponfed answers =-) as my business will not be dependant on me knowing how to calculate these odds, it will just be dependant on the calculated odds being correct.
Anyway that page is like double dutch to me =-O

#### shuttle

3333 posts
Joined 11/2008

Tbh I am just looking for the spponfed answers =-) as my business will not be dependant on me knowing how to calculate these odds, it will just be dependant on the calculated odds being correct.
Anyway that page is like double dutch to me =-O

This honestly seems like a bad idea...

138 posts
Joined 05/2010

Hire me, I'll calculate the odds for you

#### BaseMetal

2051 posts
Joined 01/2010

If you are making a moderate size business out of this you should get some mathimatician to explain a few things about not just the probability of a hit but also the expected variance. Some weeks you, as the business, may get lucky and have only 1/2 the expected winners and some weeks twice the expected, you will see good runs and bad like poker. You would need to get a good estimate of the bankroll needed to sustain a bad run.

I'll try to answer one of your questions. I may get sloppy - I often do, and I may not understand the question properly.

Take a 45 number lotto draw, with 6/7 numbers drawn.
What is the prob of picking 3 numbers and matching 3 out of 7 drawn?

I'll do this for 6 drawn numbers. I think you are asking that if a punter picks 3 numbers out of the original 45 what is the probability of all 3 being in this weeks 6 lottery drawn numbers?

Originally there are 45 possible numbers, the punter picks numbers a,b,& c.
To win a, b and c have to all be in the lottery winners (the 6).
The chance/probability of 'a' being one is 6 out of 45, or 6/45. So for b to be a winning number also there are now only 5 good numbers left out of 44, so 5/44 and similar for c is 4/43.
These probabilities can be multiplied together to give the probability of a,b & c all in the 6 and this is:
6/45 x 5/44 x 4/43 = 120/85140 = 1/ 709.5
To break even you could charge odds of 1 to 708.5, ie, if you charge \$1 a go and the punter wins you pay out \$708.50 (plus return the \$1) to exactly break even over the long run.

Another way of looking at the same question is how many ways are there to pick 3 numbers out of 45 = X.
And then how many ways to pick 3 numbers from 6 = Y.
Dividing these two results, Y/X should produce the same result.

It is easy to calculate the variance of such a bet and by using this you can estimate the needed bankroll requirement for a known risk of ruin within a set period.

Warning - I have been drinking so this could all be the beer talking.

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