Every combination has exactly the same chance as any other combination, even if it did appaer 10 weeks in a row, in the following draw the stats are reset.
Each combination does have a different chance of appearing in different positions on a ticket but the overall odds always remain unchanged,
In a 6/49 lotto there are 13,983,816 different 6 ball combinations, you pick one line per bet you have one in 13,983,816 of winning the jackpot.
Distributions come in to play when talking less than 6 hits in a 6/49 but the overall odds can never change no matter which combination you select
I will now demonstrate
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In a 6/49 draw
1,712,304 combinations of the possible 13,983,816 combinations have ball 1 as the lowest ball
178,365 combinations of the possible 13,983,816 combinations have ball 2 as the 2nd ball
15,180 combinations of the possible 13,983,816 combinations have ball 3 as the 3rd ball
990 combinations of the possible 13,983,816 combinations have ball 4 as the 4th ball
44 combinations of the possible 13,983,816 combinations have ball 5 as the 5th ball
1 combination of the possible 13,983,816 combinations have ball 6 as the 6th ball (01 02 03 04 05 06)
1,712,304 + 178,365 + 15,180 + 990 + 44 +1 = 1,906,884
So 1,906,884 possible combinations in the 6/49 have at least one number that intersects one of the combination 01,02,03,04,05,06
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Now to prove that there is a difference for whatever line chosen I will pick last week's lotto draw results which were 07 09 20 21 30 37 and repeat the above
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In a 6/49 draw
850,668 combinations of the possible 13,983,816 combinations have ball 7 as the lowest ball
731,120 combinations of the possible 13,983,816 combinations have ball 9 as the 2nd ball
624,834 combinations of the possible 13,983,816 combinations have ball 20 as the 3rd ball
430,920 combinations of the possible 13,983,816 combinations have ball 21 as the 4th ball
451,269 combinations of the possible 13,983,816 combinations have ball 30 as the 5th ball
376,992 combination of the possible 13,983,816 combinations have ball 37 as the 6th ball
850,668 + 731,120 + 624,834 + 430,920 + 451,269 + 376,992 = 3,465,803
So 3,465,803 possible combinations in the 6/49 have at least one number that intersects one of the combination 07,09,20,21,30,37
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By changing the numbers from 1,2,3,4,5,6 to 7,9,20,21,30,37 we have increased the odds of intersecting a single number by 1,558,919 to 1
We can go further and do the same for two ball combinations, however this gets a little more complex in the approach as instead of 6 ball positions we now have 15 possible pair positions to deal with, (6 numbers break into 15 pairs
1 2|1 3|1 4|1 5|1 6|2 3|2 4|2 5|2 6|3 4|3 5|3 6|4 5|4 6|5 6
In a 6/49 draw
01: 178,365 combinations of the possible 13,983,816 combinations have ball pair 1 2 at position 1 2
02: 15180 combinations of the possible 13,983,816 combinations have ball pair 1 3 at position 1 3
03: 990 combinations of the possible 13,983,816 combinations have ball pair 1 4 at position 1 4
04: 44 combinations of the possible 13,983,816 combinations have ball pair 1 5 at position 1 5
05: 1 combinations of the possible 13,983,816 combinations have ball pair 1 6 at position 1 6
06: 15,180 combinations of the possible 13,983,816 combinations have ball pair 2 3 at position 2 3
07: 990 combinations of the possible 13,983,816 combinations have ball pair 2 4 at position 2 4
08: 44 combinations of the possible 13,983,816 combinations have ball pair 2 5 at position 2 5
09: 1 combination of the possible 13,983,816 combinations have ball pair 2 6 at position 2 6
10: 990 combinations of the possible 13,983,816 combinations have ball pair 3 4 at position 3 4
11: 44 combinations of the possible 13,983,816 combinations have ball pair 3 5 at position 3 5
12: 1 combinations of the possible 13,983,816 combinations have ball pair 3 6 at position 3 6
13: 44 combinations of the possible 13,983,816 combinations have ball pair 4 5 at position 4 5
14: 1 combinations of the possible 13,983,816 combinations have ball pair 4 6 at position 4 6
15: 1 combinations of the possible 13,983,816 combinations have ball pair 5 6 at position 5 6
178,365+15180 +990 +44 +1+15,180 +990 +44+1 +990 +44 +1+44 +1 +1 = 211,876
So 211,876 combinations in the 6/49 have two numbers that intersects one of the possible 15 pairs found in the combination 01,02,03,04,05,06
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Again repeat for last week's numbers
In a 6/49 draw
01: 178,365 combinations of the possible 13,983,816 combinations have ball pair 7 9 at position 1 2
02: 15,180 combinations of the possible 13,983,816 combinations have ball pair 7 20 at position 1 3
03: 990 combinations of the possible 13,983,816 combinations have ball pair 7 21 at position 1 4
04: 44 combinations of the possible 13,983,816 combinations have ball pair 7 30 at position 1 5
05: 1 combinations of the possible 13,983,816 combinations have ball pair 7 37 at position 1 6
06: 29,232 combinations of the possible 13,983,816 combinations have ball pair 9 20 at position 2 3
07: 33,264 combinations of the possible 13,983,816 combinations have ball pair 9 21 at position 2 4
08: 28,880 combinations of the possible 13,983,816 combinations have ball pair 9 30 at position 2 5
09: 23,400 combinations of the possible 13,983,816 combinations have ball pair 9 37 at position 2 6
10: 64,638 combinations of the possible 13,983,816 combinations have ball pair 20 21 at position 3 4
11: 29,241 combinations of the possible 13,983,816 combinations have ball pair 20 30 at position 3 5
12: 20,520 combinations of the possible 13,983,816 combinations have ball pair 20 37 at position 3 6
13: 21,660 combinations of the possible 13,983,816 combinations have ball pair 21 30 at position 4 5
14: 17,100 combinations of the possible 13,983,816 combinations have ball pair 21 37 at position 4 6
15: 4,845 combinations of the possible 13,983,816 combinations have ball pair 30 37 at position 5 6
178,365 +15,180 +990 +44 +1 +29,232 +33,264 +28,880 +23,400+64,638 +29,241 +20,520 +21,660 +17,100 +4,845 =467,360
So 467,360 possible combinations in the 6/49 have two numbers that intersects one of possible 15 pairs found in the combination 7,9,20,21,30,37
By changing the numbers from 1,2,3,4,5,6 to 7,9,20,21,30,37 we have increased the odds of intersecting a pair by 255,484 to 1
So to cap this up, the lines you choose do appear to change the odds however
And a big However
Each pair appears the same number of times in the total combinations
Just different amounts in different ticket positions.
The fact is that in the 6/49 draw
Each 2 ball combo appears a total of 178,365 times
Each 3 ball combo appears a total of 15,180 times (1 in 56.6559)
Each 4 ball combo appears a total of 990 times (1 in 1,032.4)
Each 5 ball combo appears a total of 44 times (1 in 55,491.3)
Each 6 ball combo appears once 1: (1 in 13,983,816)
So the conclusion here is shuffling numbers about increases odds on some combinations but then in the same instance decreases the combinations in other ticket positions.
Always leaveing the overall odds unchanged.
Here is a small snippet taken from LSA that shows each 2 ball combo positions in a 6/49 draw, note they all add up to 178,365
1=1 2 = 178,365 0 0 0 0 0 0 0 0 0 0 0 0 0 0 = 178,365
2=1 3 = 163,185 15,180 0 0 0 0 0 0 0 0 0 0 0 0 0 = 178,365
3=1 4 = 148,995 28,380 990 0 0 0 0 0 0 0 0 0 0 0 0 = 178,365
4=1 5 = 135,751 39,732 2,838 44 0 0 0 0 0 0 0 0 0 0 0 = 178,365
5=1 6 = 123,410 49,364 5,418 172 1 0 0 0 0 0 0 0 0 0 0 = 178,365
6=1 7 = 111,930 57,400 8,610 420 5 0 0 0 0 0 0 0 0 0 0 = 178,365
7=1 8 = 101,270 63,960 12,300 820 15 0 0 0 0 0 0 0 0 0 0 = 178,365
8=1 9 = 91,390 69,160 16,380 1,400 35 0 0 0 0 0 0 0 0 0 0 = 178,365
9=1 10 = 82,251 73,112 20,748 2,184 70 0 0 0 0 0 0 0 0 0 0 = 178,365
10=1 11 = 73,815 75,924 25,308 3,192 126 0 0 0 0 0 0 0 0 0 0 = 178,365
11=1 12 = 66,045 77,700 29,970 4,440 210 0 0 0 0 0 0 0 0 0 0 = 178,365
12=1 13 = 58,905 78,540 34,650 5,940 330 0 0 0 0 0 0 0 0 0 0 = 178,365
13=1 14 = 52,360 78,540 39,270 7,700 495 0 0 0 0 0 0 0 0 0 0 = 178,365
14=1 15 = 46,376 77,792 43,758 9,724 715 0 0 0 0 0 0 0 0 0 0 = 178,365
15=1 16 = 40,920 76,384 48,048 12,012 1,001 0 0 0 0 0 0 0 0 0 0 = 178,365
16=1 17 = 35,960 74,400 52,080 14,560 1,365 0 0 0 0 0 0 0 0 0 0 = 178,365