Replies to 24/23, 13/8

Best

Nearly Best

Pretty Good

Not So Good

Here are White's best replies after Red opens 24/23, 13/8.
The EQUITY column shows the estimated cubeless equity of each potential play. The best play is displayed with a white background and the other plays are displayed with progressively darker backgrounds to give a rough idea of the amount of equity lost. Plays that give up more than 0.05 in cubeless equity are not listed at all.
The VOTES column indicates the recommendations of some selected experts:
      R = Bill Robertie, in Inside Backgammon, Volume 8 (1998).
      C = Rene Cerutti, posted to the Internet (1999).
      B = Bart Brooks, in Backgammon's Best Openings and Replies (2004).
The check marks denote the best play for each of the following situations:

Cubeless (CL): Cubeless money play.
Double Match Point (DMP): In a match which has come down to one final game.
Gammon-Go (GG): When aggressively going for a gammon win.
Gammon-Save (GS): When aggressively avoiding a gammon loss.

PLAY W      G     BG EQUITY VOTES CL DMP GG GS
24/22, 6/5(2) + .542, .147, .005
− .458, .121, .004
+.110 RBC
24/23(2), 6/5(2) + .531, .153, .005
− .469, .122, .005
+.093 (.017) (.022) (.009) (.023)
24/23, 6/5(3) + .532, .149, .005
− .468, .129, .005
+.085 (.025) (.019) (.015) (.034)
8/5, 6/5 + .527, .159, .006
− .473, .132, .006
+.080 (.030) (.030) (.006) (.052)

PLAY W      G     BG EQUITY VOTES CL DMP GG GS
24/21 + .464, .108, .004
− .536, .147, .005
−.111 C (.021)
13/10 + .458, .120, .004
− .542, .156, .008
−.123 (.012) (.013) (.010) (.031)
24/23, 13/11 + .457, .115, .004
− .543, .155, .007
−.128 R (.017) (.014) (.021) (.031)
13/11, 6/5 + .462, .121, .004
− .538, .172, .012
−.135 B (.023) (.004) (.055)
24/23, 24/22 + .455, .106, .004
− .545, .153, .005
−.139 (.027) (.019) (.045) (.031)

PLAY W      G     BG EQUITY VOTES CL DMP GG GS
13/11(2), 6/4(2) + .561, .174, .007
− .439, .122, .006
+.174 RBC (.017)
24/22(2), 6/4(2) + .545, .152, .005
− .455, .098, .004
+.146 (.028) (.031) (.074)

PLAY W      G     BG EQUITY VOTES CL DMP GG GS
8/5, 6/5 + .527, .159, .006
− .473, .132, .006
+.080 RBC

PLAY W      G     BG EQUITY VOTES CL DMP GG GS
24/21, 13/11 + .468, .115, .004
− .532, .145, .006
−.096 RB (.022)
13/11, 13/10 + .465, .130, .005
− .535, .156, .009
−.100 C (.005) (.006) (.027)
13/8 + .463, .120, .004
− .537, .153, .006
−.110 (.014) (.010) (.024) (.026)
24/22, 13/10 + .464, .116, .004
− .536, .154, .006
−.112 (.016) (.008) (.028) (.026)
24/22, 24/21 + .462, .107, .004
− .538, .152, .005
−.122 (.027) (.012) (.051) (.026)

PLAY W      G     BG EQUITY VOTES CL DMP GG GS
24/21(2), 13/10(2) + .558, .138, .004
− .442, .080, .003
+.176 RBC (.038)
24/21(2), 6/3(2) + .548, .142, .005
− .452, .086, .003
+.154 (.022) (.021) (.052) (.032)
13/10(2), 6/3(2) + .546, .169, .007
− .454, .125, .006
+.138 (.039) (.024) (.114)

PLAY W      G     BG EQUITY VOTES CL DMP GG GS
6/2*/1* + .465, .128, .004
− .535, .155, .007
−.100 RBC (.016)
13/8 + .463, .120, .004
− .537, .153, .006
−.110 (.009) (.004) (.020) (.018)
24/23, 24/20 + .461, .105, .004
− .539, .142, .005
−.117 (.017) (.009) (.054)
24/23, 13/9 + .454, .122, .004
− .546, .160, .007
−.132 (.031) (.022) (.032) (.048)
24/23, 6/2* + .453, .113, .004
− .547, .157, .007
−.142 (.041) (.025) (.053) (.045)

PLAY W      G     BG EQUITY VOTES CL DMP GG GS
8/4, 6/4 + .509, .152, .006
− .491, .140, .007
+.029 RBC

PLAY W      G     BG EQUITY VOTES CL DMP GG GS
24/21, 24/20 + .470, .108, .004
− .530, .143, .005
−.095 C (.041)
24/20, 13/10 + .468, .115, .004
− .532, .145, .006
−.096 B (.002) (.005) (.033) (.009)
13/10, 13/9 + .465, .134, .005
− .535, .159, .009
−.099 (.004) (.011) (.042)
24/21, 13/9 + .465, .121, .005
− .535, .150, .006
−.100 R (.005) (.011) (.025) (.024)
24/21, 6/2* + .460, .113, .004
− .540, .144, .007
−.113 (.019) (.020) (.051) (.023)
13/6 + .455, .118, .004
− .545, .157, .007
−.132 (.037) (.031) (.052) (.059)
13/10, 6/2* + .456, .122, .004
− .544, .166, .010
−.138 (.043) (.029) (.043) (.074)

PLAY W      G     BG EQUITY VOTES CL DMP GG GS
24/20(2), 13/9(2) + .592, .145, .004
− .408, .065, .002
+.267 RBC (.111)
8/4(2), 6/2*(2) + .576, .217, .010
− .424, .113, .005
+.260 (.007) (.033) (.129)
24/20(2), 6/2*(2) + .572, .151, .005
− .428, .075, .002
+.223 (.044) (.041) (.138) (.061)
13/9(2), 6/2*(2) + .568, .192, .008
− .432, .113, .005
+.218 (.049) (.048) (.065) (.145)

PLAY W      G     BG EQUITY VOTES CL DMP GG GS
24/23, 13/8 + .468, .118, .004
− .532, .149, .005
−.097 RBC
24/23, 6/1* + .458, .118, .004
− .542, .154, .007
−.123 (.025) (.019) (.018) (.028)
24/18 + .464, .102, .004
− .536, .154, .005
−.125 (.028) (.007) (.039) (.017)
13/8, 6/5 + .456, .119, .004
− .544, .158, .009
−.132 (.035) (.023) (.021) (.042)

PLAY W      G     BG EQUITY VOTES CL DMP GG GS
24/22, 13/8 + .475, .117, .004
− .525, .145, .005
−.079 RBC (.002)
13/11, 13/8 + .466, .126, .004
− .534, .153, .007
−.097 (.019) (.017) (.034)
13/11, 6/1* + .461, .128, .004
− .539, .165, .009
−.118 (.039) (.027) (.006) (.067)
24/22, 6/1* + .458, .117, .004
− .542, .152, .006
−.122 (.044) (.034) (.035) (.049)

PLAY W      G     BG EQUITY VOTES CL DMP GG GS
8/3, 6/3 + .487, .146, .006
− .513, .147, .007
−.029 RBC (.007)
24/21, 13/8 + .482, .118, .004
− .518, .139, .005
−.057 (.029) (.011) (.066)

PLAY W      G     BG EQUITY VOTES CL DMP GG GS
24/20, 13/8 + .482, .117, .005
− .518, .139, .005
−.059 RBC (.005) (.002)
24/15 + .485, .110, .004
− .515, .148, .005
−.069 (.010) (.010) (.012)
13/9, 13/8 + .468, .132, .005
− .532, .149, .007
−.083 (.025) (.034) (.048)
24/20, 6/1* + .468, .114, .003
− .532, .140, .006
−.092 (.034) (.034) (.036) (.030)

PLAY W      G     BG EQUITY VOTES CL DMP GG GS
8/3(2), 6/1*(2) + .518, .199, .006
− .482, .135, .006
+.100 RBC (.015) (.026)
13/3(2) + .526, .166, .006
− .474, .129, .005
+.089 (.011) (.051)
13/8(2), 6/1*(2) + .525, .165, .005
− .475, .129, .004
+.087 (.014) (.002) (.053) (.001)
13/3, 8/3, 6/1* + .514, .173, .006
− .486, .136, .006
+.064 (.037) (.024) (.061) (.038)

PLAY W      G     BG EQUITY VOTES CL DMP GG GS
13/7, 8/7 + .506, .137, .005
− .494, .136, .005
+.012 RBC

PLAY W      G     BG EQUITY VOTES CL DMP GG GS
24/16 + .477, .105, .004
− .523, .150, .005
−.093 BC
24/18, 13/11 + .468, .107, .004
− .532, .153, .006
−.112 R (.020) (.018) (.015) (.023)
13/5 + .453, .121, .004
− .547, .158, .009
−.136 (.043) (.048) (.016) (.064)

PLAY W      G     BG EQUITY VOTES CL DMP GG GS
24/15 + .485, .110, .004
− .515, .148, .005
−.069 BC
24/18, 13/10 + .469, .109, .004
− .531, .151, .006
−.107 R (.038) (.032) (.036) (.038)

PLAY W      G     BG EQUITY VOTES CL DMP GG GS
8/2*, 6/2 + .506, .160, .006
− .494, .138, .006
+.034 RBC

PLAY W      G     BG EQUITY VOTES CL DMP GG GS
24/13 + .499, .101, .004
− .501, .133, .004
−.034 RBC
24/18, 13/8 + .483, .109, .004
− .517, .145, .005
−.070 (.036) (.031) (.015) (.055)

PLAY W      G     BG EQUITY VOTES CL DMP GG GS
24/18(2), 13/7(2) + .634, .142, .004
− .366, .072, .002
+.341 RBC

Summary
Rolls in order from luckiest to unluckiest, and calculation of average equity.

(+.347) 24/18(2), 13/7(2) +.341 × 1 =   +.341
(+.273) 24/20(2), 13/9(2) +.267 × 1 =   +.267
(+.183) 24/21(2), 13/10(2) +.176 × 1 =   +.176
(+.181) 13/11(2), 6/4(2) +.174 × 1 =   +.174
(+.117) 24/22, 6/5(2) +.110 × 1 =   +.110
(+.107) 8/3(2), 6/1*(2) +.100 × 1 =   +.100
(+.087) 8/5, 6/5 +.080 × 2 =   +.160
(+.041) 8/2*, 6/2 +.034 × 2 =   +.069
(+.036) 8/4, 6/4 +.029 × 2 =   +.058
(+.019) 13/7, 8/7 +.012 × 2 =   +.025
(−.022) 8/3, 6/3 −.029 × 2 =   −.057
(−.028) 24/13 −.034 × 2 =   −.069
(−.052) 24/20, 13/8 −.059 × 2 =   −.117
(−.062) 24/15 −.069 × 2 =   −.138
(−.072) 24/22, 13/8 −.079 × 2 =   −.157
(−.086) 24/16 −.093 × 2 =   −.185
(−.088) 24/21, 24/20 −.095 × 2 =   −.189
(−.089) 24/21, 13/11 −.096 × 2 =   −.191
(−.091) 24/23, 13/8 −.097 × 2 =   −.194
(−.094) 6/2*/1* −.100 × 2 =   −.201
(−.105) 24/21 −.111 × 2 =   −.223
———
White's Average Equity −.242 ÷ 36 = −.007

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