Backgammon - True Probabilities!

When you read other articles about backgammon dice roll probabilities you will notice an approach of accepting "2+1" and "1+2" as two different possibilities! But I don't like this way of thinking, in my point of view these two results are very same. It's only a situation when one dice comes "1" and the other "2", 1 on left dice, 2 on right dice, or 1 on red dice, 2 on the blue one! But when you say loudly the number to play is 2 and 1, that's it!

Backgammon is not a game that you play with left dice and right dice separately, it's a game that you play by the result of two dices. So I consider them like values to play "1 and 2" or "3" which also mean two possibilities, but in a different way. This is important when you consider "5+4" as "5 and 4" or "9"; also double6 as "12" or "18" or "24"! And in my way too, there are 36 possibilities: 6 different doubles, 15 combinations, and 15 sums of 2 dices!

So when you are obliged to leave a blot (a single or weak checker) try to avoid positions attainable by 6, then 4, then 5 and 3. And prefer 7 to 8! Check the followings to find out why!

Double numbers: 6

Double 1 means 4 times 1; or 1, 2, 3, 4
Double 2 means 4 times 2; or 2, 4, 6, 8
Double 3 means 4 times 3; or 3, 6, 9, 12
Double 4 means 4 times 4; or 4, 8, 12, 16
Double 5 means 4 times 5; or 5, 10, 15, 20
Double 6 means 4 times 6; or 6, 12, 18, 24

Possible combinations: 30

1 + 2 = 1, 2, or 3
1 + 3 = 1, 3, or 4
1 + 4 = 1, 4, or 5
2 + 3 = 2, 3, or 5
1 + 5 = 1, 5, or 6
2 + 4 = 2, 4, or 6
1 + 6 = 1, 6, or 7
2 + 5 = 2, 5, or 7
3 + 4 = 3, 4, or 7
2 + 6 = 2, 6, or 8
3 + 5 = 3, 5, or 8
3 + 6 = 3, 6, or 9
4 + 5 = 4, 5, or 9
4 + 6 = 4, 6, or 10
5 + 6 = 5, 6, or 11

Probability of numbers that you may get in 100 rolls:

1 = 9 times
2 = 10 times
3 = 11 times
4 = 12 times
5 = 11 times
6 = 13 times
7 = 03 times
8 = 04 times
9 = 03 times
10 = 02 times
11 = 01 time
12 = 03 times
15 = 01 time
16 = 01 time
18 = 01 time
20 = 01 time
24 = 01 time

Percentage (in 100 rolls):

% 10.35 for "1"
% 11.49 for "2"
% 12.64 for "3"
% 13.79 for "4"
% 12.64 for "5"
% 14.94 for "6"
% 03.45 for "7"
% 04.60 for "8"
% 03.45 for "9"
% 02.30 for "10"
% 01.15 for "11"
% 03.45 for "12" and
% 01.15 for "15","16","18","20" and "24"