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

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

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

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

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

<pre><code>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%
</code></pre>

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

CC BY-SA 3.0
2012-06-14T15:05:41.963Z
2012-06-14T15:05:41.963Z
Hyppy
<p>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:</p>

<pre>
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
</pre>

CC BY-SA 3.0
2012-07-11T21:05:00.953Z
2012-07-11T22:00:32.057Z
2012-07-11T22:00:32.057Z
Tom Au
<p>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. </p>

CC BY-SA 3.0
2014-01-27T16:26:00.813Z
2014-01-27T16:26:00.813Z
user6720
<p>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.</p>

CC BY-SA 3.0
2016-03-07T08:32:36.383Z
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.
Julia Hayward
CC BY-SA 3.0
2016-03-07T09:14:45.850Z
"Winning expectation" is not the same thing as "expected number of wins".
Nij
CC BY-SA 3.0
2016-03-05T09:18:45.180Z
2016-03-05T09:18:45.180Z
Nij
<p>I recently committed to memory the likelihood of "Entering from the Bar" in a game of backgammon. i.e.</p>

<pre><code>1 point defence - 97%
2 point defence - 89%
3 point defence - 75%
4 point defence - 56%
5 point defence - 31%
</code></pre>

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

CC BY-SA 3.0
2012-06-14T16:29:32.510Z
Wow...I've only played BG for fun and memorizing stats such as the above never even crossed my mind!
Gryphoenix
CC BY-SA 3.0
2012-06-15T07:48:05.367Z
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
<statistics><backgammon>
Backgammon Statistics To Know
ajmccall
# Backgammon Statistics To Know

(Asked by: username_0 on 2012-06-14)

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?

**Tags:** statistics, backgammon

> **Comments:**
> **username_1**: Wow...I've only played BG for fun and memorizing stats such as the above never even crossed my mind!  
> **username_0**: 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.  

---

## 4 answers

### Answer by username_2 on 2012-06-14. Score: 5 | Accepted answer

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


---

### Answer by username_3 on 2012-07-11. Score: 3

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


---

### Answer by username_4 on 2014-01-27. Score: 2

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.


---

### Answer by username_5 on 2016-03-05. Score: 1

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.

> **Comments:**
> **username_6**: 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.  
> **username_5**: "Winning expectation" is not the same thing as "expected number of wins".  

---

