Replies to 8/3, 6/3

Best
Nearly Best
Pretty Good
Not So Good
Here are White's best replies after Red opens 8/3, 6/3.

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
  8/7(2), 6/5(2)   + .546, .167, .007
  − .454, .141, .008
 +.118   RBC
   PLAY W      G     BG     EQUITY VOTES CL DMP GG GS
  24/23, 13/11   + .460, .123, .005
  − .540, .174, .008
 −.134   RBC (.002)
  24/21   + .454, .114, .005
  − .546, .174, .007
 −.155   (.020) (.012) (.033) (.012)
  13/11, 6/5   + .458, .126, .005
  − .542, .189, .015
 −.157   (.023) (.004) (.034)
  13/10   + .445, .126, .005
  − .555, .177, .010
 −.165   (.031) (.029) (.026) (.035)
   PLAY W      G     BG     EQUITY VOTES CL DMP GG GS
  13/11(2), 6/4(2)   + .548, .176, .008
  − .452, .143, .007
 +.130   RBC
   PLAY W      G     BG     EQUITY VOTES CL DMP GG GS
  8/5, 6/5   + .513, .159, .007
  − .487, .151, .008
 +.033   RBC
   PLAY W      G     BG     EQUITY VOTES CL DMP GG GS
  24/21, 13/11   + .462, .122, .005
  − .538, .175, .008
 −.132   B (.004)
  13/11, 13/10   + .451, .135, .006
  − .549, .179, .011
 −.147   RC (.016) (.022) (.030)
  13/8   + .445, .124, .005
  − .555, .183, .009
 −.173   (.041) (.034) (.034) (.051)
   PLAY W      G     BG     EQUITY VOTES CL DMP GG GS
  24/21(2), 13/10(2)   + .551, .148, .005
  − .449, .091, .003
 +.161   RBC (.066)
  24/21(2), 8/5(2)   + .539, .160, .006
  − .461, .097, .003
 +.144   (.017) (.023) (.066) (.034)
  24/21(2), 6/3(2)   + .542, .146, .005
  − .458, .097, .003
 +.136   (.025) (.018) (.087) (.028)
  8/5(2), 6/3(2)   + .537, .195, .009
  − .463, .141, .008
 +.130   (.031) (.027) (.125)
   PLAY W      G     BG     EQUITY VOTES CL DMP GG GS
  24/23, 13/9   + .458, .128, .005
  − .542, .184, .009
 −.143   RBC (.002)
  24/23, 24/20   + .454, .115, .005
  − .546, .178, .007
 −.157   (.014) (.008) (.034)
  13/8   + .445, .124, .005
  − .555, .183, .009
 −.173   (.029) (.027) (.033) (.028)
  13/9, 6/5   + .452, .125, .005
  − .548, .197, .017
 −.181   (.037) (.013) (.019) (.042)
   PLAY W      G     BG     EQUITY VOTES CL DMP GG GS
  8/4, 6/4   + .494, .154, .007
  − .506, .159, .009
 −.018   RBC
   PLAY W      G     BG     EQUITY VOTES CL DMP GG GS
  24/21, 13/9   + .459, .125, .005
  − .541, .176, .008
 −.135   (.016)
  13/10, 13/9   + .455, .138, .006
  − .545, .179, .012
 −.137   RBC (.002) (.009) (.015)
  24/21, 24/20   + .459, .115, .006
  − .541, .176, .007
 −.144   (.010) (.001) (.037) (.002)
  24/20, 13/10   + .455, .122, .006
  − .545, .176, .008
 −.145   (.011) (.007) (.030) (.008)
   PLAY W      G     BG     EQUITY VOTES CL DMP GG GS
  24/20(2), 13/9(2)   + .581, .153, .005
  − .419, .072, .002
 +.247   RBC
   PLAY W      G     BG     EQUITY VOTES CL DMP GG GS
  24/23, 13/8   + .462, .125, .005
  − .538, .172, .007
 −.125   RBC
  13/8, 6/5   + .450, .123, .005
  − .550, .178, .011
 −.161   (.036) (.023) (.026) (.036)
   PLAY W      G     BG     EQUITY VOTES CL DMP GG GS
  13/11, 13/8   + .454, .132, .006
  − .546, .177, .009
 −.141   RBC
  13/8, 6/4   + .445, .124, .005
  − .555, .183, .011
 −.174   (.033) (.017) (.033) (.028)
   PLAY W      G     BG     EQUITY VOTES CL DMP GG GS
  8/3, 6/3   + .471, .148, .007
  − .529, .170, .009
 −.082   RBC
  24/21, 13/8   + .467, .126, .006
  − .533, .172, .007
 −.112   (.031) (.009) (.053) (.012)
   PLAY W      G     BG     EQUITY VOTES CL DMP GG GS
  24/20, 13/8   + .466, .122, .005
  − .534, .167, .007
 −.114   RBC (.017)
  13/9, 13/8   + .457, .140, .007
  − .544, .178, .010
 −.128   (.014) (.019) (.042)
   PLAY W      G     BG     EQUITY VOTES CL DMP GG GS
  13/3(2)   + .498, .161, .010
  − .502, .163, .007
 −.003   RBC
   PLAY W      G     BG     EQUITY VOTES CL DMP GG GS
  13/7, 8/7   + .491, .139, .006
  − .509, .156, .007
 −.035   RBC
   PLAY W      G     BG     EQUITY VOTES CL DMP GG GS
  24/18, 13/11   + .458, .116, .005
  − .542, .191, .009
 −.163   RBC (.001)
  13/5   + .446, .127, .005
  − .554, .179, .011
 −.166   (.003) (.024) (.002)
  24/16   + .449, .104, .004
  − .551, .183, .007
 −.186   (.022) (.019) (.043) (.004)
  13/11, 13/7   + .438, .126, .005
  − .562, .195, .015
 −.203   (.040) (.041) (.020) (.050)
   PLAY W      G     BG     EQUITY VOTES CL DMP GG GS
  24/18, 13/10   + .458, .117, .005
  − .542, .196, .009
 −.166   R (.014)
  24/15   + .452, .106, .005
  − .548, .182, .007
 −.176   BC (.010) (.012) (.035)
  13/4   + .442, .128, .006
  − .558, .185, .011
 −.178   (.012) (.033) (.010) (.025)
  24/21, 13/7   + .442, .118, .005
  − .558, .191, .010
 −.193   (.027) (.032) (.030) (.035)
   PLAY W      G     BG     EQUITY VOTES CL DMP GG GS
  8/2, 6/2   + .454, .145, .007
  − .546, .182, .010
 −.131   BC (.004) (.012)
  24/14   + .456, .104, .004
  − .544, .178, .007
 −.163   (.032) (.077)
  24/18, 13/9   + .455, .123, .006
  − .545, .200, .010
 −.172   R (.041) (.003) (.043) (.047)
   PLAY W      G     BG     EQUITY VOTES CL DMP GG GS
  24/13   + .478, .104, .005
  − .522, .161, .005
 −.101   RBC (.005)
  24/18, 13/8   + .464, .120, .005
  − .536, .188, .007
 −.142   (.041) (.028) (.084)
   PLAY W      G     BG     EQUITY VOTES CL DMP GG GS
  24/18(2), 13/7(2)   + .621, .148, .006
  − .379, .081, .002
 +.313   RBC

Summary

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

(+.374) 24/18(2), 13/7(2) +.313 × 1  =   +.313
(+.308) 24/20(2), 13/9(2) +.247 × 1  =   +.247
(+.222) 24/21(2), 13/10(2) +.161 × 1  =   +.161
(+.191) 13/11(2), 6/4(2) +.130 × 1  =   +.130
(+.180) 8/7(2), 6/5(2) +.118 × 1  =   +.118
(+.094) 8/5, 6/5 +.033 × 2  =   +.066
(+.059) 13/3(2) −.003 × 1  =   −.003
(+.043) 8/4, 6/4 −.018 × 2  =   −.037
(+.026) 13/7, 8/7 −.035 × 2  =   −.071
(−.020) 8/3, 6/3 −.082 × 2  =   −.163
(−.040) 24/13 −.101 × 2  =   −.203
(−.053) 24/20, 13/8 −.114 × 2  =   −.228
(−.063) 24/23, 13/8 −.125 × 2  =   −.249
(−.070) 8/2, 6/2 −.131 × 2  =   −.262
(−.070) 24/21, 13/11 −.132 × 2  =   −.263
(−.073) 24/23, 13/11 −.134 × 2  =   −.269
(−.073) 24/21, 13/9 −.135 × 2  =   −.269
(−.080) 13/11, 13/8 −.141 × 2  =   −.283
(−.082) 24/23, 13/9 −.143 × 2  =   −.286
(−.102) 24/18, 13/11 −.163 × 2  =   −.327
(−.104) 24/18, 13/10 −.166 × 2  =   −.332
  ———
  White's Average Equity −2.209  ÷  36  =  −.061

 

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