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"

Article Source: http://www.content.onlypunjab.com

About the Author: Ralf Guven is the founder partner of Vitalinfocenter.com since 2000 and an expert of Backgammon. To find out more tips, tricks, strategies and information on how to play better backgammon visit Backgammon Tips & Advice.

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