Replies to 24/21, 13/11

Best
Nearly Best
Pretty Good
Not So Good
Here are White's best replies after Red opens 24/21, 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
  6/4*(2)   + .549, .165, .008
  − .451, .117, .005
 +.150   RBC
  6/4*, 6/5(2)   + .543, .162, .007
  − .457, .132, .007
 +.117   (.033) (.013) (.019) (.043)
   PLAY W      G     BG     EQUITY VOTES CL DMP GG GS
  24/23, 6/4*   + .469, .125, .005
  − .531, .156, .008
 −.097   RBC
  6/4*/3   + .458, .120, .005
  − .542, .160, .009
 −.128   (.030) (.022) (.031) (.029)
  24/21   + .457, .102, .004
  − .543, .145, .005
 −.131   (.034) (.025) (.069) (.002)
  24/23, 13/11   + .454, .111, .004
  − .546, .153, .007
 −.136   (.039) (.029) (.056) (.023)
   PLAY W      G     BG     EQUITY VOTES CL DMP GG GS
  13/11(2), 6/4*(2)   + .596, .202, .011
  − .404, .105, .005
 +.296   RBC
  24/22, 13/11, 6/4*(2)   + .587, .191, .010
  − .413, .105, .005
 +.265   (.030) (.019) (.041) (.017)
   PLAY W      G     BG     EQUITY VOTES CL DMP GG GS
  8/5, 6/5   + .508, .140, .006
  − .492, .131, .006
 +.025   RBC
   PLAY W      G     BG     EQUITY VOTES CL DMP GG GS
  13/10, 6/4*   + .481, .137, .006
  − .519, .163, .011
 −.069   B (.022)
  24/21, 6/4*   + .477, .125, .005
  − .523, .148, .008
 −.071   R (.001) (.007) (.031)
  6/4*/1*   + .469, .130, .004
  − .531, .151, .007
 −.086   C (.017) (.024) (.038) (.024)
  24/21, 13/11   + .460, .108, .004
  − .540, .145, .006
 −.118   (.049) (.041) (.098) (.028)
   PLAY W      G     BG     EQUITY VOTES CL DMP GG GS
  24/21(2), 13/10(2)   + .550, .129, .005
  − .450, .086, .003
 +.144   RBC (.019)
  24/21(2), 6/3(2)   + .530, .122, .004
  − .470, .087, .003
 +.096   (.048) (.039) (.072) (.041)
  13/10(2), 6/3(2)   + .531, .157, .007
  − .469, .125, .006
 +.095   (.049) (.037) (.115)
   PLAY W      G     BG     EQUITY VOTES CL DMP GG GS
  24/23, 8/4*   + .457, .126, .005
  − .543, .161, .009
 −.126   RBC (.007)
  24/23, 24/20   + .449, .103, .004
  − .551, .150, .006
 −.149   (.024) (.014) (.059)
  8/4*/3   + .448, .123, .005
  − .552, .169, .009
 −.154   (.028) (.017) (.022) (.041)
  13/8   + .445, .110, .004
  − .555, .159, .007
 −.162   (.036) (.024) (.056) (.027)
  8/4*, 6/5   + .451, .119, .005
  − .549, .185, .015
 −.174   (.049) (.012) (.026) (.067)
   PLAY W      G     BG     EQUITY VOTES CL DMP GG GS
  8/4*, 6/4   + .546, .176, .008
  − .454, .118, .005
 +.154   RBC
   PLAY W      G     BG     EQUITY VOTES CL DMP GG GS
  24/21, 8/4*   + .468, .127, .005
  − .532, .153, .008
 −.093   R (.002) (.027)
  13/10, 8/4*   + .469, .140, .006
  − .531, .166, .011
 −.095   BC (.001) (.025)
  8/4*/1*   + .460, .133, .005
  − .540, .158, .007
 −.107   (.014) (.017) (.030) (.026)
  24/21, 24/20   + .457, .109, .005
  − .543, .153, .006
 −.130   (.037) (.023) (.085) (.021)
   PLAY W      G     BG     EQUITY VOTES CL DMP GG GS
  24/20(2), 8/4*(2)   + .601, .189, .008
  − .399, .076, .003
 +.321   RBC (.017)
  8/4*(2), 6/2(2)   + .574, .225, .013
  − .426, .112, .005
 +.269   (.052) (.054) (.126)
   PLAY W      G     BG     EQUITY VOTES CL DMP GG GS
  24/23, 13/8   + .462, .110, .004
  − .538, .143, .005
 −.110   RBC
  24/18   + .455, .104, .004
  − .545, .164, .006
 −.152   (.042) (.015) (.027) (.056)
  24/23, 6/1*   + .445, .111, .003
  − .555, .157, .007
 −.160   (.050) (.034) (.033) (.062)
   PLAY W      G     BG     EQUITY VOTES CL DMP GG GS
  13/8, 6/4*   + .476, .131, .005
  − .524, .146, .007
 −.065   RBC
  24/22, 13/8   + .466, .113, .004
  − .534, .151, .005
 −.108   (.043) (.021) (.057) (.032)
   PLAY W      G     BG     EQUITY VOTES CL DMP GG GS
  8/3, 6/3   + .470, .132, .005
  − .530, .149, .007
 −.078   RBC (.004) (.031)
  24/21, 13/8   + .473, .108, .004
  − .527, .136, .005
 −.084   (.007) (.044)
   PLAY W      G     BG     EQUITY VOTES CL DMP GG GS
  13/4*   + .474, .137, .006
  − .526, .149, .008
 −.067   RBC
  24/20, 13/8   + .466, .115, .005
  − .534, .148, .005
 −.103   (.036) (.017) (.060) (.015)
  24/15   + .467, .112, .005
  − .533, .159, .006
 −.114   (.048) (.014) (.063) (.034)
   PLAY W      G     BG     EQUITY VOTES CL DMP GG GS
  8/3(2), 6/1*(2)   + .514, .193, .006
  − .486, .127, .005
 +.094   RBC
  13/8(2), 6/1*(2)   + .510, .155, .004
  − .490, .125, .004
 +.050   (.044) (.008) (.082) (.005)
   PLAY W      G     BG     EQUITY VOTES CL DMP GG GS
  13/7, 8/7   + .479, .122, .005
  − .521, .140, .005
 −.060   RBC
   PLAY W      G     BG     EQUITY VOTES CL DMP GG GS
  24/18, 13/11   + .463, .111, .005
  − .537, .161, .007
 −.125   C (.001) (.022)
  13/7, 6/4*   + .459, .126, .005
  − .541, .169, .012
 −.131   RB (.006) (.008) (.024)
  24/18, 6/4*   + .463, .115, .005
  − .537, .171, .009
 −.133   (.008) (.014) (.021)
  24/16   + .455, .103, .004
  − .545, .159, .006
 −.149   (.023) (.018) (.055) (.014)
  24/22, 24/18   + .452, .109, .005
  − .548, .173, .006
 −.161   (.035) (.023) (.049) (.046)
  13/5   + .444, .114, .004
  − .556, .160, .009
 −.163   (.037) (.039) (.055) (.037)
  24/22, 13/7   + .442, .113, .004
  − .558, .157, .007
 −.164   (.038) (.044) (.062) (.036)
   PLAY W      G     BG     EQUITY VOTES CL DMP GG GS
  13/4*   + .474, .137, .006
  − .526, .149, .008
 −.067   RBC
  24/15   + .467, .112, .005
  − .533, .159, .006
 −.114   (.048) (.014) (.063) (.034)
   PLAY W      G     BG     EQUITY VOTES CL DMP GG GS
  24/14*   + .540, .130, .006
  − .460, .123, .004
 +.089   RBC
   PLAY W      G     BG     EQUITY VOTES CL DMP GG GS
  24/13   + .486, .095, .004
  − .514, .138, .004
 −.070   RBC
  24/18, 13/8   + .470, .110, .005
  − .530, .153, .005
 −.104   (.034) (.033) (.003) (.064)
   PLAY W      G     BG     EQUITY VOTES CL DMP GG GS
  24/18(2), 13/7(2)   + .612, .119, .004
  − .388, .067, .002
 +.277   RBC

Summary

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

(+.327) 24/20(2), 8/4*(2) +.321 × 1  =   +.321
(+.302) 13/11(2), 6/4*(2) +.296 × 1  =   +.296
(+.284) 24/18(2), 13/7(2) +.277 × 1  =   +.277
(+.160) 8/4*, 6/4 +.154 × 2  =   +.308
(+.157) 6/4*(2) +.150 × 1  =   +.150
(+.150) 24/21(2), 13/10(2) +.144 × 1  =   +.144
(+.100) 8/3(2), 6/1*(2) +.094 × 1  =   +.094
(+.095) 24/14* +.089 × 2  =   +.178
(+.031) 8/5, 6/5 +.025 × 2  =   +.050
(−.053) 13/7, 8/7 −.060 × 2  =   −.120
(−.058) 13/8, 6/4* −.065 × 2  =   −.130
(−.060) 13/4* −.067 × 2  =   −.133
(−.060) 13/4* −.067 × 2  =   −.133
(−.063) 13/10, 6/4* −.069 × 2  =   −.138
(−.064) 24/13 −.070 × 2  =   −.141
(−.071) 8/3, 6/3 −.078 × 2  =   −.155
(−.087) 24/21, 8/4* −.093 × 2  =   −.187
(−.091) 24/23, 6/4* −.097 × 2  =   −.194
(−.103) 24/23, 13/8 −.110 × 2  =   −.220
(−.119) 24/18, 13/11 −.125 × 2  =   −.251
(−.119) 24/23, 8/4* −.126 × 2  =   −.251
  ———
  White's Average Equity −.236  ÷  36  =  −.007

 

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