Replies to 13/8, 6/5

Best
Nearly Best
Pretty Good
Not So Good
Here are White's best replies after Red opens 13/8, 6/5.

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:

      D = Joe Dwek, in Backgammon for Profit (1975).
      R = Bill Robertie, in Inside Backgammon, Volume 8 (1998).
      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)   + .553, .169, .009
  − .447, .133, .006
 +.144   RDB (.004)
  24/20*   + .535, .149, .008
  − .465, .113, .004
 +.110   (.034) (.035) (.074)
   PLAY W      G     BG     EQUITY VOTES CL DMP GG GS
  13/11, 6/5   + .451, .124, .005
  − .549, .175, .012
 −.158   RB (.001)
  24/23, 13/11   + .444, .117, .004
  − .556, .169, .007
 −.166   D (.009) (.012) (.026)
  13/10   + .439, .121, .005
  − .561, .172, .009
 −.177   (.020) (.024) (.028) (.018)
  24/21   + .441, .107, .004
  − .559, .166, .007
 −.179   (.021) (.019) (.052) (.000)
  24/23, 6/4   + .441, .118, .005
  − .559, .185, .009
 −.189   (.031) (.019) (.031) (.039)
  24/23, 24/22   + .437, .107, .004
  − .563, .169, .006
 −.190   (.032) (.027) (.060) (.015)
  24/22, 6/5   + .436, .108, .004
  − .564, .179, .009
 −.203   (.045) (.029) (.059) (.036)
   PLAY W      G     BG     EQUITY VOTES CL DMP GG GS
  24/20*, 6/4(2)   + .602, .191, .013
  − .398, .087, .003
 +.318   RDB
   PLAY W      G     BG     EQUITY VOTES CL DMP GG GS
  24/20*   + .535, .149, .008
  − .465, .113, .004
 +.110   RB
   PLAY W      G     BG     EQUITY VOTES CL DMP GG GS
  24/21, 13/11   + .453, .113, .005
  − .547, .160, .007
 −.144   (.020)
  24/22, 13/10   + .451, .116, .005
  − .549, .161, .007
 −.145   (.000) (.003) (.017) (.004)
  13/10, 6/4   + .451, .124, .005
  − .549, .172, .012
 −.152   RDB (.008) (.003) (.026)
  13/11, 13/10   + .446, .128, .005
  − .554, .167, .010
 −.152   (.008) (.015) (.004) (.027)
  24/22, 24/21   + .448, .105, .004
  − .552, .164, .006
 −.166   (.022) (.011) (.046) (.019)
  24/21, 6/4   + .445, .113, .005
  − .555, .176, .009
 −.176   (.032) (.016) (.034) (.047)
  13/11, 8/5   + .435, .121, .005
  − .565, .177, .012
 −.193   (.049) (.035) (.038) (.069)
   PLAY W      G     BG     EQUITY VOTES CL DMP GG GS
  24/21(2), 8/5(2)   + .540, .158, .005
  − .460, .092, .003
 +.149   DB (.000) (.067)
  8/5(2), 6/3(2)   + .540, .191, .010
  − .460, .142, .007
 +.133   (.016) (.099)
  24/21(2), 13/10(2)   + .535, .135, .004
  − .465, .089, .003
 +.118   R (.031) (.011) (.123) (.005)
  24/21(2), 6/3(2)   + .532, .140, .005
  − .468, .092, .003
 +.114   (.035) (.017) (.119) (.016)
   PLAY W      G     BG     EQUITY VOTES CL DMP GG GS
  24/23, 24/20*   + .532, .148, .008
  − .468, .114, .004
 +.103   RDB
   PLAY W      G     BG     EQUITY VOTES CL DMP GG GS
  24/20*, 13/11   + .543, .162, .009
  − .457, .112, .004
 +.141   RDB
  24/22, 24/20*   + .538, .152, .008
  − .462, .115, .004
 +.117   (.024) (.010) (.031) (.015)
   PLAY W      G     BG     EQUITY VOTES CL DMP GG GS
  24/20*, 13/10   + .543, .162, .009
  − .457, .110, .004
 +.143   RDB
  24/21, 24/20*   + .540, .151, .009
  − .460, .111, .004
 +.126   (.017) (.006) (.027) (.007)
   PLAY W      G     BG     EQUITY VOTES CL DMP GG GS
  24/20*(2), 13/9(2)   + .632, .176, .008
  − .368, .068, .002
 +.378   RB
  24/20*(2), 8/4(2)   + .610, .189, .011
  − .390, .076, .002
 +.342   D (.036) (.043) (.016) (.060)
   PLAY W      G     BG     EQUITY VOTES CL DMP GG GS
  24/23, 13/8   + .446, .118, .005
  − .554, .168, .006
 −.159   B (.002)
  13/8, 6/5   + .446, .118, .005
  − .554, .167, .009
 −.160   R (.001) (.000)
  13/7   + .433, .118, .005
  − .567, .174, .009
 −.195   (.036) (.028) (.027) (.042)
   PLAY W      G     BG     EQUITY VOTES CL DMP GG GS
  13/8, 6/4   + .447, .125, .005
  − .553, .169, .008
 −.153   RDB (.002) (.014)
  24/22, 13/8   + .448, .115, .005
  − .552, .163, .006
 −.153   (.000) (.018)
  13/11, 13/8   + .444, .127, .005
  − .556, .174, .009
 −.161   (.009) (.008) (.002) (.029)
   PLAY W      G     BG     EQUITY VOTES CL DMP GG GS
  8/3, 6/3   + .461, .138, .006
  − .539, .166, .008
 −.107   RB (.006)
  24/21, 13/8   + .456, .117, .005
  − .544, .158, .006
 −.131   (.024) (.010) (.054)
  13/10, 13/8   + .444, .130, .006
  − .556, .172, .009
 −.156   D (.049) (.034) (.050) (.050)
   PLAY W      G     BG     EQUITY VOTES CL DMP GG GS
  24/20*, 13/8   + .548, .161, .009
  − .452, .110, .004
 +.153   RB (.002)
  24/20*/15   + .549, .151, .008
  − .451, .119, .004
 +.134   D (.019) (.018) (.017)
   PLAY W      G     BG     EQUITY VOTES CL DMP GG GS
  13/3(2)   + .482, .155, .009
  − .518, .160, .006
 −.040   RDB
   PLAY W      G     BG     EQUITY VOTES CL DMP GG GS
  13/7, 8/7   + .484, .134, .006
  − .516, .155, .006
 −.053   RDB
   PLAY W      G     BG     EQUITY VOTES CL DMP GG GS
  24/16   + .453, .104, .004
  − .547, .171, .006
 −.164   DB (.011)
  13/5   + .441, .122, .005
  − .559, .169, .009
 −.169   (.006) (.024) (.019)
  24/18, 13/11   + .449, .110, .005
  − .551, .180, .008
 −.175   R (.011) (.008) (.007) (.024)
  13/7, 6/4   + .441, .121, .005
  − .559, .181, .013
 −.187   (.023) (.024) (.002) (.044)
  13/11, 13/7   + .435, .125, .005
  − .565, .181, .011
 −.192   (.028) (.035) (.005) (.054)
  24/22, 13/7   + .435, .115, .004
  − .565, .175, .008
 −.193   (.029) (.035) (.024) (.042)
  24/22, 24/18   + .437, .100, .004
  − .563, .185, .006
 −.213   (.049) (.031) (.050) (.058)
   PLAY W      G     BG     EQUITY VOTES CL DMP GG GS
  24/15   + .459, .106, .004
  − .541, .171, .006
 −.148   DB (.025)
  13/4   + .445, .132, .006
  − .555, .174, .009
 −.155   (.007) (.028) (.035)
  24/18, 13/10   + .448, .112, .005
  − .552, .176, .008
 −.170   R (.022) (.022) (.034) (.032)
  24/21, 13/7   + .440, .115, .005
  − .560, .172, .008
 −.182   (.034) (.039) (.046) (.043)
  13/10, 13/7   + .433, .127, .005
  − .567, .183, .012
 −.197   (.049) (.053) (.036) (.077)
   PLAY W      G     BG     EQUITY VOTES CL DMP GG GS
  24/20*/14   + .550, .147, .008
  − .450, .118, .004
 +.134   RDB
  24/20*, 13/7   + .527, .155, .009
  − .473, .111, .004
 +.102   (.032) (.048) (.032) (.035)
  24/20*, 24/18   + .537, .140, .007
  − .463, .123, .004
 +.095   (.039) (.027) (.042) (.036)
   PLAY W      G     BG     EQUITY VOTES CL DMP GG GS
  24/13   + .481, .106, .005
  − .520, .158, .005
 −.091   RDB
   PLAY W      G     BG     EQUITY VOTES CL DMP GG GS
  24/18(2), 13/7(2)   + .621, .144, .005
  − .379, .079, .002
 +.310   RDB

Summary

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

(+.365) 24/20*(2), 13/9(2) +.378 × 1  =   +.378
(+.305) 24/20*, 6/4(2) +.318 × 1  =   +.318
(+.297) 24/18(2), 13/7(2) +.310 × 1  =   +.310
(+.140) 24/20*, 13/8 +.153 × 2  =   +.306
(+.136) 24/21(2), 8/5(2) +.149 × 1  =   +.149
(+.131) 8/7(2), 6/5(2) +.144 × 1  =   +.144
(+.130) 24/20*, 13/10 +.143 × 2  =   +.286
(+.128) 24/20*, 13/11 +.141 × 2  =   +.282
(+.121) 24/20*/14 +.134 × 2  =   +.268
(+.097) 24/20* +.110 × 2  =   +.220
(+.090) 24/23, 24/20* +.103 × 2  =   +.207
(−.053) 13/3(2) −.040 × 1  =   −.040
(−.066) 13/7, 8/7 −.053 × 2  =   −.106
(−.104) 24/13 −.091 × 2  =   −.182
(−.121) 8/3, 6/3 −.107 × 2  =   −.215
(−.157) 24/21, 13/11 −.144 × 2  =   −.288
(−.161) 24/15 −.148 × 2  =   −.295
(−.166) 13/8, 6/4 −.153 × 2  =   −.305
(−.171) 13/11, 6/5 −.158 × 2  =   −.315
(−.172) 24/23, 13/8 −.159 × 2  =   −.317
(−.177) 24/16 −.164 × 2  =   −.327
  ———
  White's Average Equity +.479  ÷  36  =  +.013

 

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