# See you in the Bahamas on your yacht :-)

## Lotto

The Lotto

Introduction:

The lotto is a game where a certain amount of numbers are used of which six are picked by a player. If successful the numbers picked match those six selected out of a ball machine. The amount won depends on the quantity matched. The more numbers matched the better.

In America a typical lotto system consists of 52 numbers. In the UK it’s 49 and in Ireland it’s 45.

In mathematics the entire number of combinations in order to win can be determined by a certain formula developed by a branch of science dedicated to probabilities. It is as follows:

(Amount of numbers factorial) / (Amount chosen factorial)

But what does factorial mean?

Best explained by an example:

If the amount of numbers is 52 and the amount chosen is 6 then factorial, represented by an exclamation mark ! is a multiplying factor based on the amount chosen.

If the amount chosen is 6 then the factorial used is:

6! (Six factorial)

6 x 5 x 4 x 3 x 2 x 1

The total amount of numbers will then correspond with:

52! (52 factorial)

52 x 51 x 50 x 49 x 48 x 47

In mathematics combination is represented by the letter C . In notation then the following formula would then hold true:

Total Number of Combinations

= (Total numbers factorial) ! / (Numbers chosen factorial) !

Or

(Total numbers factorial) ! C (Numbers chosen factorial) !

What then is the total number of combinations for a 52 number system. It is

52! C 6! Or

(52 x 51 x 50 x 49 x 48 x 47) / (6 x 5 x 4 x 3 x 2 x 1)

= 14658134400 / 720

= 20358770

Just over 20 million combinations.

If you were in Ireland then the combinations would be just 8145060 based on a 45 number system. (Over 8 million) (However, that may change soon with more numbers being added.)

In the UK it would be 13983816 (about 14 million)

Is there a way you can raise the odds on winning?

Yes there is.

You can reverse engineer the lotto !!

And no it’s not a sinister attempt at something illegal !!!!

It’s all quite mathematical or as Spock would say quite logical!!!

How it works:

Over 20 million combinations is a lot and I doubt even the richest person in the world would buy that many tickets. What is needed is a system that is a subset of a superset of numbers

That subset is achieved by dividing the total range of lotto numbers into groups of smaller size determined by the quantity drawn.

If the total range of numbers is 1 - 52 and the amount drawn initially is 6, then we divide 52 by 6.

When 52 is divided by 6 though we get 8.6666 numbers per group which is obviously not an even number!

To get around this I have chosen to give the first 5 groups 9 numbers and the last one 7 to make up 52.

If we give each group a letter from A – F we can now define a range for each group.

A will cover numbers 1 – 9

B will cover numbers 10 – 18

C will cover numbers 19 – 27

D will cover numbers 28 – 36

E will cover numbers 37 – 45

F will cover numbers 46 - 52

Six numbers can come from any or all groups. The groups will come out in combinations just like the numbers chosen.

Group combinations

6! C 1! = (6/1) = 6

6! C 2! = ((6x5)/(2x1)) = 15

6! C 3! = ((6x5x4)/(3x2x1)) = 20

6! C 4! = ((6x5x4x3)/(4x3x2x1)) = 15

6! C 5! = ((6x5x4x3x2)/(5x4x3x2x1)) = 6

6! C 6! = 1

That subset is achieved by dividing the total range of lotto numbers into groups of smaller size determined by the quantity drawn.

If the total range of numbers is 1 - 52 and the amount drawn initially is 6, then we divide 52 by 6.

When 52 is divided by 6 though we get 8.6666 numbers per group which is obviously not an even number!

To get around this I have chosen to give the first 5 groups 9 numbers and the last one 7 to make up 52.

If we give each group a letter from A – F we can now define a range for each group.

A will cover numbers 1 – 9

B will cover numbers 10 – 18

C will cover numbers 19 – 27

D will cover numbers 28 – 36

E will cover numbers 37 – 45

F will cover numbers 46 - 52

Six numbers can come from any or all groups. The groups will come out in combinations just like the numbers chosen.

Group combinations

6! C 1! = (6/1) = 6

6! C 2! = ((6x5)/(2x1)) = 15

6! C 3! = ((6x5x4)/(3x2x1)) = 20

6! C 4! = ((6x5x4x3)/(4x3x2x1)) = 15

6! C 5! = ((6x5x4x3x2)/(5x4x3x2x1)) = 6

6! C 6! = 1

Number combinations within a group of 9.

In other words how many ways to take 1 – 6 numbers out of a group.

9! C 1! = 9

9! C 2! = (9x8)/(2x1) = 36

9! C 3! = (9x8x7)/(3x2x1) = 84

9! C 4! = (9x8x7x6)/(4x3x2x1) = 126

9! C 5! = (9x8x7x6x5)/(5x4x3x2x1) = 126

9! C 6! = (9x8x7x6x5x4)/(6x5x4x3x2x1) = 84

Number combinations within a group of 7

7! C 1! = 7

7! C 2! = 21

7! C 3! = 35

7! C 4! = 35

7! C 5! = 21

7! C 6! = 7

Number ratios:

The lotto can use up to 6 groups. Numbers then will come out in ratios from one group to another.

Just one group will have 6 drawn from it and is extremely rare.

2 groups will simply be

## 2 Group ratios

Click thumbnail to view full-size

3 groups will be more diverse

## 3 Group ratios

4 groups have less quantity drawn

5 groups even less

Finally 6 groups with just one drawn per group

When choosing numbers it is best to go for 3 and 4 group systems as they allow you to grab as many numbers as possible per group.

If I wanted to pick 2 numbers from group A (1-9) then the ENTIRE combinations would be

And 3 numbers

And a whopping 4 numbers !!

## Well there you have it

I hope this gives you ideas on how to crack the lotto. Have fun but never become obsessed with it.

See you on your yacht in the Bahamas.........

.......And then I woke up. ;-)