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I recently committed to memory the likelihood of "Entering from the Bar" in a game of backgammon. i.e.

1 point defence - 97%
2 point defence - 89%
3 point defence - 75%
4 point defence - 56%
5 point defence - 31%

Besides the usual likelihood of "throwing a number x", what other statistics are there that I can learn to improve my backgammon game?

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Wow...I've only played BG for fun and memorizing stats such as the above never even crossed my mind! –  Gryphoenix Jun 14 '12 at 16:29
    
Even wondered why a computer or good human always seems to get the right dice thrown? Knowing the dice probabilities (in context of the board position) starts to remove the luck factor in backgammon and makes it more strategic and fun to play. –  ajmccall Jun 15 '12 at 7:48
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3 Answers 3

up vote 5 down vote accepted

These were all more or less directly copied from the source attributed at the bottom of the answer:

  • Directly rolling a particular number (e.g. 2) 30.55%
  • Rolling a particular double (e.g. 3-3) 2.77%
  • Rolling a particular non-double (e.g. 5-1) 5.54%
  • Rolling any double 16.66%

Chance of getting off the bar with one or two pieces and X open points:

Open
Points  1 piece 2 pieces
1       31%     3%
2       55%     11%
3       75%     25%
4       89%     44%
5       97%     69%
6       100%    100%

Chance of moving X points in a single roll: (direct and indirect combined; direct alone is always 31% for 1-6 only).

Move    Direct and
        Indirect Chance
1       31%                      
2       33%                     
3       39%                       
4       42%                       
5       42%                           
6       47%         
7       17%
8       17%
9       14%
10      8%
11      6%
12      8%
13       -
14       -
15      3%
16      3%
17      -
18      3%
19       -
20      3%
21       -
22       -
23       -
24      3%

SOURCE (and more stats): http://www.paulspages.co.uk/bgvaults/tips/dicerolls.php More info on observed Backgammon statistics: http://www.bkgm.com/motif/stats.html

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I'd learn the chances for the roll combinations. There are 36 possible rolls, (let's say of one red and one green die) as follows:

6-6:  1/36
11:   2/36 (two 6-5s)
5-5:  1/36
10:   2/36 (two 6-4s)
9:    4/36 (two 6-3s, two 5-4s)
4-4:  1/36
8:    4/36 (two 6-2s, two 5-3s)
7:    6/36 (two 6-1s, two 5-2s, two 4-3s)
3-3:  1/36
6:    4/36 (two 5-1s, two 4-2s)
5:    4/36 (two 4-1s, two 3-2s)
2-2:  1/36
4:    2/36 (two 3-1s)
3:    2/36 (two 2-1s)
1-1:  1/36
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The chance of getting a total of x on the two dice is simply (6-|7-x|)/36 where |7-x| is the absolute value of 7-x.

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