# Backgammon Statistics To Know

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?

• Wow...I've only played BG for fun and memorizing stats such as the above never even crossed my mind! 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. Jun 15 '12 at 7:48

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

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
```

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.

You should always accept a double if your winning expectation from the current situation is 25% or more. You should never accept a double when you have less.

• Not true in match play (first-to-N-points wins) - the take/pass point varies with the match score - or in situations where a significant proportion of your losses will be gammons and backgammons. Mar 7 '16 at 8:32
• "Winning expectation" is not the same thing as "expected number of wins".
– Nij
Mar 7 '16 at 9:14