The possibilities for 1st prize in a Lotto game such as UK Lotto where each line has six distinct integers from a Pool of 49 is 13,983,816. Each line has the same chance of being drawn as any other.

If you played one line your chances of a match for all six integers in one draw is 1/13,983,816 or 0.0000000715112 or 0.00000715112%.

The table below shows your chances of success for one draw with distinct combinations for 1 and multiples of 10 to 11,111,111 lines and the balance of 2,872,705 to make 13,983,816. Adding the probabilities gives 1 or certainty for 13,983,816 distinct combinations.

Lines

Probability

1

0.0000000715112

10

0.0000007151124

100

0.0000071511238

1000

0.0000715112384

10000

0.0007151123842

100000

0.0071511238420

1000000

0.0715112384202

2872705

0.2054306921659

10000000

0.7151123842018

Plays per Draw and Draws can be interchanged so in the UK Lotto playing 1813 plays per draw over 1584 draws from November 1994 gives 2,871,792 plays with a 20% chance of a 1st prize win.

An important concept is proportionality in terms of plays made and chances of success. Time and time again in this field of interest, Lotto number analysis, you will find the facts misconstrued by not taking into account proportionality especially by numerologists whether outed or not.

An example is consecutive ascending Numerical Order numbers of which there are 44 for a Pick 6, Pool 49 Lotto game as in the table below.

Comb6

01 02 03 04 05 06

02 03 04 05 06 07

03 04 05 06 07 08

04 05 06 07 08 09

05 06 07 08 09 10

06 07 08 09 10 11

07 08 09 10 11 12

08 09 10 11 12 13

09 10 11 12 13 14

10 11 12 13 14 15

11 12 13 14 15 16

12 13 14 15 16 17

13 14 15 16 17 18

14 15 16 17 18 19

15 16 17 18 19 20

16 17 18 19 20 21

17 18 19 20 21 22

18 19 20 21 22 23

19 20 21 22 23 24

20 21 22 23 24 25

21 22 23 24 25 26

22 23 24 25 26 27

23 24 25 26 27 28

24 25 26 27 28 29

25 26 27 28 29 30

26 27 28 29 30 31

27 28 29 30 31 32

28 29 30 31 32 33

29 30 31 32 33 34

30 31 32 33 34 35

31 32 33 34 35 36

32 33 34 35 36 37

33 34 35 36 37 38

34 35 36 37 38 39

35 36 37 38 39 40

36 37 38 39 40 41

37 38 39 40 41 42

38 39 40 41 42 43

39 40 41 42 43 44

40 41 42 43 44 45

41 42 43 44 45 46

42 43 44 45 46 47

43 44 45 46 47 48

44 45 46 47 48 49

If playing these 44 consecutives over 1584 draws the chances of a 1st prize match for 69696 plays is only 0.5%. However, for the 14 million random numbers generated using the Mersenne Twister algorithm playing the 44 lines we can expect about 44 successes. We actually get 39 of which 29 are distinct as in the table below with much to the consternation of numerologists 44 45 46 47 48 49 repeating twice. This is not unexpected as the 14 million generated random numbers only has 63% of the distinct combinations so 63% of 44 is 28. See Random Lotto Numbers using the Mersenne Twister

Comb6

Cnt

05 06 07 08 09 10

3

13 14 15 16 17 18

3

35 36 37 38 39 40

3

15 16 17 18 19 20

3

26 27 28 29 30 31

2

09 10 11 12 13 14

2

36 37 38 39 40 41

2

14 15 16 17 18 19

2

30 31 32 33 34 35

2

44 45 46 47 48 49

2

24 25 26 27 28 29

2

03 04 05 06 07 08

1

04 05 06 07 08 09

1

11 12 13 14 15 16

1

02 03 04 05 06 07

1

29 30 31 32 33 34

1

33 34 35 36 37 38

1

37 38 39 40 41 42

1

38 39 40 41 42 43

1

39 40 41 42 43 44

1

41 42 43 44 45 46

1

42 43 44 45 46 47

1

43 44 45 46 47 48

1

27 28 29 30 31 32

1

Colin Fairbrother

This article first published on the web 5/3/2011 and has been viewed 5356 times. The author may be contacted at fairbros@bigpond.com. To generate sets of Lotto numbers to play for most Lotto games around the world go to LottoToWin ^{®} where for a US$5.00 annual subscription you can store the numbers as well, to check later for wins. The numbers produced have no duplicate subset combinations of two integers (if applicable) or three integers, use all the integers for the particular Lotto game and maximize the coverage of the potential winning main number. The articles on this site have been selected from the many at the forum LottoPoster