Colin Fairbrother

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whether other than through sheer luck the odds can be bettered.

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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 5487 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
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