Arithmetic complexity shows the variations of differences between the numbers of analyzed tickets. The formulae is:

Arithmetic Complexity(t) = D(t) - (r-1)

where *D(t)* is the count of unique differences between all ticket numbers and *r* is the count of numbers in the analyzed ticket.

In a 6/xx lottery the Arithmetic Complexity value ranges from 0 to 10. About 74% of all possible combinations have the Arithmetic Complexity value in the range of 8 to 10.

Let's analyze ticket 1-2-3-4-5-6. The differences between all ticket numbers are:

2-1 = 1

3-1 = 2

4-1 = 3

5-1 = 4

6-1 = 5

3-2 = 1

4-2 = 2

5-2 = 3

6-2 = 4

4-3 = 1

5-3 = 2

6-3 = 3

5-4 = 1

6-4 = 2

6-5 = 1

There are 5 unique differences: 1, 2, 3, 4, 5 so the Arithmetic Complexity of this ticket is 5-(6-1) = 0

The same analysis of ticket 1-2-4-8-13-21 shows the following differences:

2-1 = 1

4-1 = 3

8-1 = 7

13-1 = 12

21-1 = 20

4-2 = 2

8-2 = 6

13-2 = 11

21-2 = 19

8-4 = 4

13-4 = 9

21-4 = 17

13-8 = 5

21-8 = 13

21-13 = 8

None of the differences above repeat so there are 15 unique differences so the Arithmetic Complexity of this ticket is 15-(6-1)=10

These statistics are available in summary form and also as per-ticket properties.

See also Arithmetic Complexity filter.