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: 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.

Another update: I recently (Jan 2010) learned that Murat Akcan has created a similar chart using standard backgammon notation.

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* ZP24/20*
4P
SS* ZZ or 13/7
6/4 or S
21P 5P U* or S*PR U*+DZ* or R* **3PRU+D 21$
21Z 24/22
5P
24/21
or Z
P** ZP11P 4PSPZS U+D24/21
6/2* or Z
P or ZS or R U+DZR* 3P
1P*
RU+D 21Z
31P 24/22
5P or
7P 5P
Z PZZP 22P 4PZ or S PZSU+D ZPS5P DR3PRU+D 31P
41$ * or
7P 5P
$*U*$ P24/20*
4P
SS* ZR*21P +
(5P or 3P)
U*R*R or S** +
4P
Z* R*3PRU+D 41$
41Z 24/22
5P
Z P **ZP 22P 4P or
11P 4P
Z or S PZR*U+D24/21
6/2*
R* S or R24/16*
+ 2P*
24/20
6/1* or
Z or R
P*3P
1P*
RU+D 41Z
51$ 7P 5P$*U*$ P24/20*
4P
13/10
6/4
S* 13/8
6/4
or Z
R21P 5P S*PRU*+DZ* R*3PRU+D 51$
51Z 24/22
5P
$ or
24/21
P** ZP11P 4PD or SP ZRU+DU or D
or S or
24/21
6/2*
PRU+DZ P*3P
1P*
RU+D 51Z
61P 7P 5P$PZZ P11P 4PZ or S PZRU+DU or Z PRU+DR or ZR 3PD7P 2P 61P
32D 7P 5P$P$$ or Z P22P 4P
or 20P or
11P 4P
Z or DPZ S21P 5PD PR*U+DR* R*3PRU+D 32D
32S 4P* 24/23
6/4*
P 24/23
8/4*
ZP 11P 4P*13/10
6/4*
P* 13/8
6/4*
6/4* +
(13/7 or
24/18)
U+D 13/10
8/4*
P13/4* U+4P*13/4*R* 3P
1P*
R U+D 32S
32Z 24/22
5P
6/3* or ZPU or Z
or 8/3*
Z or RP11P 4P6/3* +
(3/1* or
24/22 or
13/11)
PZ or
**
S5P 3P*24/20
6/3* or
13/9
6/3*
P*R*U+DR*13/3*3P*
1P*
R
or
S
U+D 32Z
42P 7P 5PZ P Z Z P 22P 4PZ P Z S 5P 3P S or D P S or R U+D Z P or R 3P R U+D 42P
52D 7P 5P$P$$P 11P 4PDPD S5P 3PDP S or RU+DD R*3P R U+D 52D
52Z 24/22
5P
Z or
6/3*
P13/8Z P11P 4P13/11
6/3*
PD or Z S or R5P 3P*13/9
6/3*
P* RU+DZ13/3* 3P*
1P*
RU+D 52Z
62R 24/22
5P or
7P 5P
24/21 *Z*ZP13/9*
4P
U or SD* or
Z*
Z$ or Z5P 3P Z* or D*PZU+D*
or 5P*
D*S*3P
1P*
RU+D 62R
62$ 7P 5P$*U* $ or ZP24/20*
4P
13/10
6/4 or D
S*13/8
6/4
S or $ 5P 3P or
21P 5P
S*P13/4U*+DZ* R*3P R U+D 62$
62S 7P* 5P13/11
8/7*
P13/9
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 UPZ*U+D 24/20
6/1*
R*3P
1P*
**U+D* 62S
43D 7P 5P$P$$P 22P 4PZ or DP ZR*21P 5P DR*R*U+DR* R or S3PRU+D 43D
43S 24/22
5P*
$* P* 6/5* +
(13/9 or
24/20)
$* 24/18
6/5*
11P 4P13/11
8/5*
P Z $* 5P* 3P 8/5* +
(24/20
or 13/9)
$* R* 5P* R* P 3P
1P*
RU+D 43S
43Z 4P* 24/23
6/4*
P 24/23
8/4*
Z or
24/23
6/1*
P11P 4P* 6/4* +
(13/10 or
24/21)
P* 13/8
6/4*
R*U+D 8/4* +
(13/10 or
24/21)
R*13/4*24/16*
+ 4P*
13/4*R 3P
1P*
RU+D 43Z
43U 4P**** P* ** $* 13/7
6/5*
11P 4P* 8/5*
6/4*
P* 13/8
6/4*
$*5P* 3P24/20
8/5*
$* 13/4*13/5*
+ 4P*
13/4*
or Z
P 3PSU+D 43U
53P 7P 5PZ or $PZZP 11P 4PSPDS or $U+D D or ZPSU+DZ or D P3PRU+D 53P
63R 24/22
5P or
7P 5P
*24/23
13/10*
Z or $Z or $P11P 4PZ* PZ$ or S10P* 3P S* or D*D*S*U+D Z or
6/1*
24/20
S3P
1P*
RU+D 63R
63S 7P* 5P13/11
8/7*
P8/7* +
(13/9 or
24/20)
13/7*P* 11P 4P24/21
6/4 or
Z or S
or U
13/7*24/22
6/1*
or Z
Z* 7P*ZPR*U+D R*Z* 3P
1P*
**U+D* 63S
54D 7P 5P$P$$P 22P 4PDPDR* 21P +
(3P or
10P)
DR* R or S24/16*
+ 9P
D or RR 3PRU+D 54D
54Z 24/22
5P*
$*P*$* $*P 11P 4P 13/11
8/5*
P Z $* 5P* 3P 13/9
8/5*
$*13/7
8/5*
5P*Z P3P
1P*
RU+D 54Z
64P 7P 5P$P$$ P22P 4P or
11P 4P
D or Z PZ or D$ or SU+D or
5P 3P
D PSU+DDP 3PRU+D 64P
64R 7P 5PZ*P$$P 11P* 4PS* or D*S*D* S*5P 3PSPS U+DZS or P 3P*
1P*
RU+D 64R
64S 7P* 5P8/7* +
(24/22
or 13/11)
P or
8/7*
24/21
8/7* +
(24/20
or 13/9)
13/7*P*R*S13/7* 24/22
6/1*
R*7P*ZR* Z*16P* or
(* + 9P)
24/20
6/1*
Z* 3P
1P*
**U+D* 64S
65R 7P 5P$P$ or Z$ or Z P11P 4PSPDS U+DZPSU+D ZP or S3P
1P*
RU+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)

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