Replies to 24/23, 13/9

Best
Nearly Best
Pretty Good
Not So Good
Here are White's best replies after Red opens 24/23, 13/9.

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)   + .537, .144, .006
  − .463, .128, .005
 +.091   RBC
  24/23, 6/5(3)   + .530, .148, .006
  − .470, .137, .005
 +.072   (.019) (.015) (.006) (.032)
  24/23(2), 6/5(2)   + .522, .147, .006
  − .478, .129, .006
 +.062   (.028) (.030) (.024) (.031)
   PLAY W      G     BG     EQUITY VOTES CL DMP GG GS
  24/23, 13/11   + .458, .121, .005
  − .542, .167, .007
 −.131   RBC (.004)
  24/21   + .457, .112, .004
  − .543, .163, .006
 −.139   (.008) (.004) (.022)
  24/23, 24/22   + .452, .111, .004
  − .548, .168, .006
 −.155   (.024) (.013) (.033) (.020)
  13/10   + .447, .119, .005
  − .553, .167, .009
 −.158   (.027) (.022) (.027) (.028)
  13/11, 6/5   + .455, .118, .005
  − .545, .184, .014
 −.165   (.034) (.007) (.014) (.046)
  24/22, 6/5   + .451, .109, .004
  − .549, .183, .010
 −.178   (.047) (.015) (.040) (.052)
   PLAY W      G     BG     EQUITY VOTES CL DMP GG GS
  24/22(2), 6/4(2)   + .545, .155, .005
  − .455, .100, .004
 +.146   RBC (.009) (.031) (.007)
  13/11(2), 6/4(2)   + .549, .166, .007
  − .451, .133, .006
 +.131   (.014) (.001) (.065)
  24/16*   + .549, .144, .007
  − .451, .126, .004
 +.120   (.025) (.043) (.048)
  24/20(2)   + .527, .115, .003
  − .473, .079, .002
 +.091   (.054) (.044) (.145)
   PLAY W      G     BG     EQUITY VOTES CL DMP GG GS
  8/5, 6/5   + .513, .151, .006
  − .487, .144, .006
 +.034   RBC
   PLAY W      G     BG     EQUITY VOTES CL DMP GG GS
  24/22, 13/10   + .465, .126, .005
  − .535, .166, .007
 −.113   C (.003) (.007)
  24/21, 13/11   + .466, .120, .005
  − .534, .164, .007
 −.113   RB (.001) (.008)
  13/11, 13/10   + .457, .130, .005
  − .543, .167, .010
 −.129   (.016) (.019) (.008) (.027)
  13/8   + .453, .120, .005
  − .547, .170, .007
 −.146   (.033) (.026) (.035) (.038)
  24/22, 24/21   + .455, .111, .004
  − .545, .168, .006
 −.149   (.037) (.023) (.049) (.032)
   PLAY W      G     BG     EQUITY VOTES CL DMP GG GS
  24/21(2), 13/10(2)   + .555, .144, .005
  − .445, .089, .003
 +.166   RBC
  24/21(2), 6/3(2)   + .549, .145, .005
  − .451, .092, .003
 +.153   (.013) (.012) (.009) (.018)
   PLAY W      G     BG     EQUITY VOTES CL DMP GG GS
  6/2*/1*   + .466, .125, .005
  − .534, .155, .008
 −.100   RBC
  24/23, 24/20   + .460, .115, .005
  − .540, .160, .007
 −.127   (.027) (.013) (.033) (.023)
  24/23, 13/9   + .460, .116, .005
  − .540, .161, .007
 −.128   (.028) (.013) (.032) (.026)
  24/23, 6/2*   + .455, .117, .005
  − .545, .159, .008
 −.134   (.034) (.022) (.038) (.029)
  13/8   + .454, .117, .005
  − .546, .165, .007
 −.143   (.043) (.025) (.042) (.045)
   PLAY W      G     BG     EQUITY VOTES CL DMP GG GS
  8/4, 6/4   + .497, .148, .006
  − .503, .150, .007
 −.009   RBC
   PLAY W      G     BG     EQUITY VOTES CL DMP GG GS
  24/21, 6/2*   + .470, .122, .005
  − .530, .153, .007
 −.093   BC (.005)
  24/21, 13/9   + .465, .125, .005
  − .535, .161, .007
 −.109   R (.016) (.011) (.009) (.027)
  24/20, 13/10   + .463, .122, .005
  − .537, .158, .007
 −.112   (.019) (.015) (.019) (.025)
  13/10, 13/9   + .458, .136, .006
  − .542, .166, .010
 −.118   (.025) (.024) (.050)
  24/21, 24/20   + .458, .115, .006
  − .542, .164, .006
 −.135   (.041) (.025) (.044) (.047)
   PLAY W      G     BG     EQUITY VOTES CL DMP GG GS
  24/16*, 6/2*(2)   + .609, .212, .013
  − .391, .098, .003
 +.342   RBC (.022)
  24/16*, 13/9(2)   + .605, .176, .009
  − .395, .097, .003
 +.295   (.047) (.008) (.079) (.029)
  24/20(2), 13/9(2)   + .590, .145, .004
  − .410, .068, .002
 +.259   (.082) (.039) (.172)
   PLAY W      G     BG     EQUITY VOTES CL DMP GG GS
  24/23, 13/8   + .469, .124, .005
  − .531, .160, .006
 −.101   RBC
  24/23, 6/1*   + .455, .119, .004
  − .545, .163, .008
 −.137   (.036) (.026) (.035) (.033)
  24/18   + .461, .110, .004
  − .539, .171, .006
 −.140   (.039) (.015) (.041) (.036)
   PLAY W      G     BG     EQUITY VOTES CL DMP GG GS
  24/22, 13/8   + .465, .121, .005
  − .535, .162, .006
 −.113   RBC (.006)
  13/11, 13/8   + .459, .130, .005
  − .541, .166, .008
 −.122   (.009) (.012) (.020)
  24/22, 6/1*   + .456, .118, .004
  − .544, .165, .007
 −.138   (.025) (.018) (.029) (.023)
  13/11, 6/1*   + .453, .126, .005
  − .547, .170, .010
 −.144   (.031) (.024) (.020) (.040)
   PLAY W      G     BG     EQUITY VOTES CL DMP GG GS
  24/16*   + .549, .144, .007
  − .451, .126, .004
 +.120   RBC
   PLAY W      G     BG     EQUITY VOTES CL DMP GG GS
  24/20, 6/1*   + .472, .124, .005
  − .528, .153, .007
 −.087   B (.001) (.000) (.003)
  24/20, 13/8   + .472, .120, .005
  − .528, .151, .005
 −.088   RC (.001) (.002) (.008)
  13/9, 13/8   + .461, .135, .006
  − .539, .162, .008
 −.107   (.020) (.022) (.042)
  24/15   + .473, .110, .005
  − .527, .162, .006
 −.107   (.020) (.026) (.019)
  13/8, 6/2*   + .458, .125, .005
  − .542, .162, .009
 −.125   (.038) (.030) (.026) (.050)
   PLAY W      G     BG     EQUITY VOTES CL DMP GG GS
  8/3(2), 6/1*(2)   + .518, .204, .007
  − .482, .137, .006
 +.103   RBC (.001)
  13/8(2), 6/1*(2)   + .517, .171, .006
  − .483, .136, .005
 +.070   (.033) (.001) (.067)
  13/3(2)   + .512, .171, .007
  − .488, .140, .006
 +.055   (.048) (.011) (.077) (.019)
   PLAY W      G     BG     EQUITY VOTES CL DMP GG GS
  13/7, 8/7   + .494, .136, .005
  − .506, .152, .006
 −.027   RBC
   PLAY W      G     BG     EQUITY VOTES CL DMP GG GS
  24/16*   + .549, .144, .007
  − .451, .126, .004
 +.120   RBC
   PLAY W      G     BG     EQUITY VOTES CL DMP GG GS
  24/15   + .473, .110, .005
  − .527, .162, .006
 −.107   BC (.016)
  24/18, 13/10   + .469, .122, .005
  − .531, .167, .007
 −.109   R (.002) (.007) (.018)
  24/21, 8/2*   + .459, .123, .005
  − .541, .160, .008
 −.122   (.014) (.027) (.017) (.024)
  24/21, 13/7   + .446, .118, .004
  − .554, .164, .008
 −.157   (.050) (.053) (.054) (.057)
   PLAY W      G     BG     EQUITY VOTES CL DMP GG GS
  8/2*, 6/2   + .507, .166, .008
  − .493, .143, .006
 +.039   RBC
   PLAY W      G     BG     EQUITY VOTES CL DMP GG GS
  24/13   + .491, .103, .004
  − .509, .146, .004
 −.061   RBC (.012)
  24/18, 13/8   + .479, .121, .005
  − .521, .160, .005
 −.081   (.020) (.024) (.051)
   PLAY W      G     BG     EQUITY VOTES CL DMP GG GS
  24/18(2), 13/7(2)   + .631, .147, .005
  − .369, .076, .002
 +.336   RBC

Summary

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

(+.344) 24/16*, 6/2*(2) +.342 × 1  =   +.342
(+.338) 24/18(2), 13/7(2) +.336 × 1  =   +.336
(+.168) 24/21(2), 13/10(2) +.166 × 1  =   +.166
(+.148) 24/22(2), 6/4(2) +.146 × 1  =   +.146
(+.122) 24/16* +.120 × 2  =   +.240
(+.122) 24/16* +.120 × 2  =   +.240
(+.105) 8/3(2), 6/1*(2) +.103 × 1  =   +.103
(+.093) 24/22, 6/5(2) +.091 × 1  =   +.091
(+.042) 8/2*, 6/2 +.039 × 2  =   +.079
(+.036) 8/5, 6/5 +.034 × 2  =   +.067
(−.006) 8/4, 6/4 −.009 × 2  =   −.017
(−.025) 13/7, 8/7 −.027 × 2  =   −.055
(−.059) 24/13 −.061 × 2  =   −.122
(−.085) 24/20, 6/1* −.087 × 2  =   −.174
(−.091) 24/21, 6/2* −.093 × 2  =   −.187
(−.098) 6/2*/1* −.100 × 2  =   −.200
(−.099) 24/23, 13/8 −.101 × 2  =   −.201
(−.105) 24/15 −.107 × 2  =   −.215
(−.111) 24/22, 13/10 −.113 × 2  =   −.225
(−.111) 24/22, 13/8 −.113 × 2  =   −.226
(−.129) 24/23, 13/11 −.131 × 2  =   −.262
  ———
  White's Average Equity −.075  ÷  36  =  −.002

 

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