Backgammon Opening Replies

Below is a summary chart of what current (as of October 2009) backgammon theory says are the best ways to play the second roll of a money game. The thirty rows are the thirty most commonly seen first moves, and the twenty-one columns are the twenty-one possible second rolls.

I have also produced a one-page printable PDF version of the chart below. If you don’t like my PDF file, then you are welcome to play with the HTML version of the chart.

My primary source of “current theory” is the “2nd roll” tab at Stick Rice’s BGOnline website. If Stick’s rollout indicates several plays that are close—where I have arbitrarily defined “close” to mean less than 0.010 equity—then I list all the plays. (If Snowie and GNU Backgammon disagree, then at minimum, I include the top play of each bot.) If Stick does not provide a rollout, then GNU Backgammon 4-ply evaluation is my authority.

I should mention that Tom Keith has also posted rollouts of opening replies at Backgammon Galore. An important difference is that Tom reports cubeless equities whereas Stick’s rollouts are all cubeful. Nevertheless, the two sets of rollouts are largely in agreement. Also at Backgammon Galore is a summary chart by Stanley Richards that is similar in spirit to the chart below, except that his chart contains more information than mine and does not fit onto a single page.

The abbreviations used in the chart below are a version of Nactation, a system of notation invented by Nack Ballard. They are explained in detail underneath the chart. For experts, let me remark that I do not adhere strictly to Ballard’s conventions; for example, my definition of slotting is narrower than Ballard’s, and I use Z for a reverse split even if one of the dice is a 1 or a 5. (In particular, if you go to Stick’s website to find more information, you will need to look for 21S instead of 21Z.) Also, I have avoided advanced nactation; doing so would of course allow me to compress the table even further, but would make the chart even less readable to intermediate players, who after all are the target audience.

Update 1: For those who prefer full-blown nactation, I am delighted to be able to offer you Nack Ballard’s version of my chart. Thank you very much, Nack, for putting in the effort to create this! Note: Bill Calton has formatted Nack’s chart to fit on a single page.

Update 2: (Jan 2010) I recently learned that Murat Akcan has created a similar chart using standard backgammon notation. Unfortunately, the chart seems to be no longer online.

Update 3: (Nov 2023) Andreas Völter sent me his version of the chart.

11 21 31 41 51 61 22 32 42 52 62 33 43 53 63 44 54 64 55 65 66

21$ 7P 5P $ or Z * U* Z P 24/20*
4P S S* Z Z or 13/7
6/4 or S 21P 5P U* or S* P R U*+D Z* or R* ** 3P R U+D 21$

21Z 24/22
5P 24/21
or Z P ** Z P 11P 4P S P Z S U+D 24/21
6/2* or Z P or Z S or R U+D Z R* 3P
1P* R U+D 21Z

31P 24/22
5P or
7P 5P Z P Z Z P 22P 4P Z or S P Z S U+D Z P S 5P D R 3P R U+D 31P

41$ * or
7P 5P $ * U* $ P 24/20*
4P S S* Z R* 21P +
(5P or 3P) U* R* R or S ** +
4P Z* R* 3P R U+D 41$

41Z 24/22
5P Z P ** Z P 22P 4P or
11P 4P Z or S P Z R* U+D 24/21
6/2* R* S or R 24/16*
+ 2P* 24/20
6/1* or
Z or R P* 3P
1P* R U+D 41Z

51$ 7P 5P $ * U* $ P 24/20*
4P 13/10
6/4 S* 13/8
6/4
or Z R 21P 5P S* P R U*+D Z* R* 3P R U+D 51$

51Z 24/22
5P $ or
24/21 P ** Z P 11P 4P D or S P Z R U+D U or D
or S or
24/21
6/2* P R U+D Z P* 3P
1P* R U+D 51Z

61P 7P 5P $ P Z Z P 11P 4P Z or S P Z R U+D U or Z P R U+D R or Z R 3P D 7P 2P 61P

32D 7P 5P $ P $ $ or Z P 22P 4P
or 20P or
11P 4P Z or D P Z S 21P 5P D P R* U+D R* R* 3P R U+D 32D

32S 4P* 24/23
6/4* P 24/23
8/4* Z P 11P 4P* 13/10
6/4* P* 13/8
6/4* 6/4* +
(13/7 or
24/18) U+D 13/10
8/4* P 13/4* U+4P* 13/4* R* 3P
1P* R U+D 32S

32Z 24/22
5P 6/3* or Z P U or Z
or 8/3* Z or R P 11P 4P 6/3* +
(3/1* or
24/22 or
13/11) P Z or
** S 5P 3P* 24/20
6/3* or
13/9
6/3* P* R* U+D R* 13/3* 3P*
1P* R
or
S U+D 32Z

42P 7P 5P Z P Z Z P 22P 4P Z P Z S 5P 3P S or D P S or R U+D Z P or R 3P R U+D 42P

52D 7P 5P $ P $ $ P 11P 4P D P D S 5P 3P D P S or R U+D D R* 3P R U+D 52D

52Z 24/22
5P Z or
6/3* P 13/8 Z P 11P 4P 13/11
6/3* P D or Z S or R 5P 3P* 13/9
6/3* P* R U+D Z 13/3* 3P*
1P* R U+D 52Z

62R 24/22
5P or
7P 5P 24/21 * Z* Z P 13/9*
4P U or S D* or
Z* Z $ or Z 5P 3P Z* or D* P Z U+D*
or 5P* D* S* 3P
1P* R U+D 62R

62$ 7P 5P $ * U* $ or Z P 24/20*
4P 13/10
6/4 or D S* 13/8
6/4 S or $ 5P 3P or
21P 5P S* P 13/4 U*+D Z* R* 3P R U+D 62$

62S 7P* 5P 13/11
8/7* P 13/9
8/7* 13/7* P* 11P 4P 24/21
6/4 or
S or U 13/7* 24/22
6/1* Z* 7P* Z or U P Z* U+D 24/20
6/1* R* 3P
1P* ** U+D* 62S

43D 7P 5P $ P $ $ P 22P 4P Z or D P Z R* 21P 5P D R* R* U+D R* R or S 3P R U+D 43D

43S 24/22
5P* $* P* 6/5* +
(13/9 or
24/20) $* 24/18
6/5* 11P 4P 13/11
8/5* P Z $* 5P* 3P 8/5* +
(24/20
or 13/9) $* R* 5P* R* P 3P
1P* R U+D 43S

43Z 4P* 24/23
6/4* P 24/23
8/4* Z or
24/23
6/1* P 11P 4P* 6/4* +
(13/10 or
24/21) P* 13/8
6/4* R* U+D 8/4* +
(13/10 or
24/21) R* 13/4* 24/16*
+ 4P* 13/4* R 3P
1P* R U+D 43Z

43U 4P** ** P* ** $* 13/7
6/5* 11P 4P* 8/5*
6/4* P* 13/8
6/4* $* 5P* 3P 24/20
8/5* $* 13/4* 13/5*
+ 4P* 13/4*
or Z P 3P S U+D 43U

53P 7P 5P Z or $ P Z Z P 11P 4P S P D S or $ U+D D or Z P S U+D Z or D P 3P R U+D 53P

63R 24/22
5P or
7P 5P * 24/23
13/10* Z or $ Z or $ P 11P 4P Z* P Z $ or S 10P* 3P S* or D* D* S* U+D Z or
6/1*
24/20 S 3P
1P* R U+D 63R

63S 7P* 5P 13/11
8/7* P 8/7* +
(13/9 or
24/20) 13/7* P* 11P 4P 24/21
6/4 or
Z or S
or U 13/7* 24/22
6/1*
or Z Z* 7P* Z P R* U+D R* Z* 3P
1P* ** U+D* 63S

54D 7P 5P $ P $ $ P 22P 4P D P D R* 21P +
(3P or
10P) D R* R or S 24/16*
+ 9P D or R R 3P R U+D 54D

54Z 24/22
5P* $* P* $* $* P 11P 4P 13/11
8/5* P Z $* 5P* 3P 13/9
8/5* $* 13/7
8/5* 5P* Z P 3P
1P* R U+D 54Z

64P 7P 5P $ P $ $ P 22P 4P or
11P 4P D or Z P Z or D $ or S U+D or
5P 3P D P S U+D D P 3P R U+D 64P

64R 7P 5P Z* P $ $ P 11P* 4P S* or D* S* D* S* 5P 3P S P S U+D Z S or P 3P*
1P* R U+D 64R

64S 7P* 5P 8/7* +
(24/22
or 13/11) P or
8/7*
24/21 8/7* +
(24/20
or 13/9) 13/7* P* R* S 13/7* 24/22
6/1* R* 7P* Z R* Z* 16P* or
(* + 9P) 24/20
6/1* Z* 3P
1P* ** U+D* 64S

65R 7P 5P $ P $ or Z $ or Z P 11P 4P S P D S U+D Z P S U+D Z P or S 3P
1P* R U+D 65R

11 21 31 41 51 61 22 32 42 52 62 33 43 53 63 44 54 64 55 65 66

D : Bring two checkers Down from the midpoint

P : Make a Point (to emphasize that it is, say, the 5-point, we write "5P")

R : Run one of the back checkers to the outfield

$ : Slot the 5-Point, and bring one checker down from the midpoint

S : Split the back checkers using the larger die value, and bring one checker down from the midpoint

Z : Split the back checkers using the smaller die value, and bring one checker down from the midpoint

U : Move both back checkers Up

* : Hit (** denotes a double hit)

+ : And (strictly speaking, this is redundant, but it is occasionally inserted for clarity)

D	:	Bring two checkers Down from the midpoint
P	:	Make a Point (to emphasize that it is, say, the 5-point, we write "5P")
R	:	Run one of the back checkers to the outfield
$	:	Slot the 5-Point, and bring one checker down from the midpoint
S	:	Split the back checkers using the larger die value, and bring one checker down from the midpoint
Z	:	Split the back checkers using the smaller die value, and bring one checker down from the midpoint
U	:	Move both back checkers Up
*	:	Hit (** denotes a double hit)
+	:	And (strictly speaking, this is redundant, but it is occasionally inserted for clarity)

Backgammon Opening Replies

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