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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