Replies to 24/23, 13/11

Best

Nearly Best

Pretty Good

Not So Good

Here are White's best replies after Red opens 24/23, 13/11.
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) + .544, .147, .006
− .456, .123, .004
+.114 RBC
24/23, 6/5(3) + .539, .151, .006
− .461, .125, .005
+.106 (.007) (.009) (.001) (.014)
24/23(2), 6/5(2) + .530, .150, .006
− .470, .124, .005
+.087 (.026) (.027) (.022) (.030)
8/5, 6/5 + .522, .156, .006
− .478, .134, .006
+.067 (.046) (.043) (.025) (.065)

PLAY W      G     BG EQUITY VOTES CL DMP GG GS
24/21 + .466, .112, .004
− .534, .145, .005
−.102 (.018)
24/23, 13/11 + .465, .122, .005
− .536, .153, .006
−.103 RBC (.001) (.004) (.019)
24/23, 24/22 + .459, .111, .004
− .541, .153, .006
−.125 (.023) (.015) (.033) (.030)
13/10 + .452, .119, .005
− .548, .160, .008
−.139 (.037) (.028) (.031) (.057)
13/11, 6/5 + .457, .121, .005
− .543, .175, .012
−.147 (.046) (.019) (.018) (.078)

PLAY W      G     BG EQUITY VOTES CL DMP GG GS
13/11(2), 6/4(2) + .553, .168, .008
− .447, .128, .006
+.149 RBC (.048)
24/20(2) + .539, .135, .005
− .461, .090, .003
+.125 (.024) (.027) (.094)
24/22(2), 6/4(2) + .538, .134, .004
− .462, .090, .003
+.121 (.028) (.031) (.099) (.004)

PLAY W      G     BG EQUITY VOTES CL DMP GG GS
8/5, 6/5 + .522, .156, .006
− .478, .134, .006
+.067 RBC

PLAY W      G     BG EQUITY VOTES CL DMP GG GS
24/21, 13/11 + .471, .120, .005
− .529, .143, .006
−.082 RBC (.002)
24/22, 24/21 + .471, .115, .005
− .529, .150, .006
−.095 (.013) (.001) (.013) (.016)
24/22, 13/10 + .468, .121, .005
− .532, .154, .006
−.099 (.017) (.007) (.007) (.029)
13/11, 13/10 + .462, .130, .005
− .538, .159, .009
−.108 (.026) (.019) (.051)
13/8 + .460, .118, .005
− .540, .158, .006
−.122 (.040) (.023) (.028) (.054)

PLAY W      G     BG EQUITY VOTES CL DMP GG GS
24/21(2), 13/10(2) + .555, .140, .005
− .445, .086, .003
+.165 RBC (.018)
24/21(2), 6/3(2) + .544, .142, .005
− .456, .090, .003
+.143 (.022) (.020) (.035) (.028)
8/5(2), 6/3(2) + .525, .178, .008
− .475, .127, .006
+.104 (.062) (.059) (.141)

PLAY W      G     BG EQUITY VOTES CL DMP GG GS
6/2*/1* + .469, .130, .004
− .531, .151, .007
−.086 RBC
24/23, 13/9 + .462, .126, .005
− .538, .157, .007
−.110 (.024) (.014) (.023) (.025)
24/23, 24/20 + .462, .112, .004
− .538, .146, .005
−.111 (.025) (.014) (.050) (.003)
13/8 + .460, .118, .005
− .540, .158, .006
−.122 (.036) (.019) (.042) (.032)
24/23, 6/2* + .455, .115, .004
− .545, .154, .007
−.132 (.045) (.028) (.058) (.032)

PLAY W      G     BG EQUITY VOTES CL DMP GG GS
8/4, 6/4 + .504, .149, .006
− .496, .143, .007
+.014 RBC

PLAY W      G     BG EQUITY VOTES CL DMP GG GS
24/21, 13/9 + .470, .129, .006
− .530, .149, .007
−.080 RB (.004)
24/21, 6/2* + .467, .116, .004
− .533, .143, .007
−.097 (.016) (.008) (.034)
13/10, 13/9 + .463, .136, .006
− .537, .160, .009
−.102 C (.022) (.015) (.002) (.040)
24/21, 24/20 + .467, .117, .006
− .533, .154, .006
−.102 (.022) (.006) (.030) (.020)
24/20, 13/10 + .466, .122, .005
− .534, .155, .007
−.103 (.023) (.009) (.024) (.025)

PLAY W      G     BG EQUITY VOTES CL DMP GG GS
24/20(2), 13/9(2) + .602, .156, .005
− .398, .066, .002
+.297 RBC (.081)
24/20(2), 6/2*(2) + .587, .174, .007
− .413, .078, .002
+.275 (.022) (.030) (.076) (.053)
8/4(2), 6/2*(2) + .574, .225, .013
− .426, .112, .005
+.269 (.028) (.055) (.147)

PLAY W      G     BG EQUITY VOTES CL DMP GG GS
24/23, 13/8 + .476, .122, .005
− .524, .144, .005
−.071 RBC
24/18 + .469, .113, .005
− .531, .161, .006
−.111 (.040) (.014) (.032) (.048)
24/23, 6/1* + .459, .119, .004
− .541, .153, .007
−.119 (.048) (.035) (.040) (.052)

PLAY W      G     BG EQUITY VOTES CL DMP GG GS
24/22, 13/8 + .472, .120, .005
− .528, .149, .005
−.085 RBC
13/11, 13/8 + .464, .128, .005
− .536, .156, .007
−.102 (.017) (.016) (.000) (.031)
24/22, 6/1* + .460, .121, .004
− .540, .153, .007
−.113 (.028) (.024) (.021) (.032)
13/11, 6/1* + .459, .129, .005
− .541, .162, .009
−.119 (.034) (.027) (.008) (.054)

PLAY W      G     BG EQUITY VOTES CL DMP GG GS
24/21, 13/8 + .485, .121, .005
− .515, .138, .005
−.046 C (.032)
8/3, 6/3 + .481, .142, .006
− .519, .151, .007
−.049 RB (.002) (.009) (.036)

PLAY W      G     BG EQUITY VOTES CL DMP GG GS
24/20, 13/8 + .475, .123, .005
− .525, .149, .005
−.075 RBC (.001)
24/15 + .476, .112, .005
− .524, .157, .006
−.094 (.019) (.020) (.016)
13/9, 13/8 + .463, .134, .005
− .537, .154, .007
−.095 (.020) (.025) (.002) (.034)
24/20, 6/1* + .464, .118, .004
− .536, .153, .006
−.108 (.033) (.022) (.032) (.030)
13/8, 6/2* + .461, .124, .005
− .539, .154, .008
−.111 (.036) (.030) (.027) (.040)

PLAY W      G     BG EQUITY VOTES CL DMP GG GS
8/3(2), 6/1*(2) + .519, .204, .007
− .481, .134, .006
+.109 RBC (.003) (.010)
13/8(2), 6/1*(2) + .521, .176, .006
− .479, .131, .004
+.088 (.021) (.053)
13/3(2) + .518, .171, .007
− .482, .137, .006
+.071 (.038) (.006) (.069) (.018)
13/3, 8/3, 6/1* + .511, .179, .008
− .489, .135, .006
+.067 (.042) (.020) (.066) (.028)

PLAY W      G     BG EQUITY VOTES CL DMP GG GS
13/7, 8/7 + .500, .137, .006
− .500, .144, .005
−.007 RBC

PLAY W      G     BG EQUITY VOTES CL DMP GG GS
24/18, 13/11 + .480, .120, .005
− .520, .157, .007
−.078 RBC
24/16 + .471, .116, .005
− .530, .163, .006
−.107 (.029) (.019) (.028) (.030)
24/22, 24/18 + .463, .118, .006
− .537, .170, .006
−.126 (.048) (.033) (.038) (.059)

PLAY W      G     BG EQUITY VOTES CL DMP GG GS
24/18, 13/10 + .477, .120, .005
− .523, .156, .007
−.084 RB
24/15 + .476, .112, .005
− .524, .157, .006
−.094 C (.010) (.002) (.017) (.004)
24/21, 24/18 + .471, .112, .005
− .529, .157, .006
−.104 (.020) (.012) (.028) (.013)
24/21, 8/2* + .457, .118, .004
− .543, .147, .007
−.118 (.034) (.039) (.044) (.022)

PLAY W      G     BG EQUITY VOTES CL DMP GG GS
24/14* + .553, .141, .007
− .447, .122, .004
+.129 RBC

PLAY W      G     BG EQUITY VOTES CL DMP GG GS
24/13 + .496, .103, .004
− .504, .143, .004
−.048 RBC (.021)
24/18, 13/8 + .487, .123, .005
− .513, .155, .005
−.058 (.010) (.018) (.042)

PLAY W      G     BG EQUITY VOTES CL DMP GG GS
24/18(2), 13/7(2) + .633, .153, .005
− .367, .074, .002
+.348 RBC

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

(+.350) 24/18(2), 13/7(2) +.348 × 1 =   +.348
(+.299) 24/20(2), 13/9(2) +.297 × 1 =   +.297
(+.168) 24/21(2), 13/10(2) +.165 × 1 =   +.165
(+.152) 13/11(2), 6/4(2) +.149 × 1 =   +.149
(+.131) 24/14* +.129 × 2 =   +.257
(+.116) 24/22, 6/5(2) +.114 × 1 =   +.114
(+.112) 8/3(2), 6/1*(2) +.109 × 1 =   +.109
(+.070) 8/5, 6/5 +.067 × 2 =   +.135
(+.016) 8/4, 6/4 +.014 × 2 =   +.027
(−.005) 13/7, 8/7 −.007 × 2 =   −.014
(−.044) 24/21, 13/8 −.046 × 2 =   −.093
(−.046) 24/13 −.048 × 2 =   −.097
(−.069) 24/23, 13/8 −.071 × 2 =   −.143
(−.073) 24/20, 13/8 −.075 × 2 =   −.151
(−.075) 24/18, 13/11 −.078 × 2 =   −.156
(−.078) 24/21, 13/9 −.080 × 2 =   −.161
(−.079) 24/21, 13/11 −.082 × 2 =   −.164
(−.081) 24/18, 13/10 −.084 × 2 =   −.168
(−.083) 24/22, 13/8 −.085 × 2 =   −.171
(−.084) 6/2*/1* −.086 × 2 =   −.172
(−.099) 24/21 −.102 × 2 =   −.204
———
White's Average Equity −.092 ÷ 36 = −.003

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