Replies to 13/11, 13/8

Best
Nearly Best
Pretty Good
Not So Good
Here are White's best replies after Red opens 13/11, 13/8.

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).
      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)   + .569, .173, .008
  − .431, .127, .006
 +.184   RDBC
   PLAY W      G     BG     EQUITY VOTES CL DMP GG GS
  13/11, 6/5   + .477, .136, .005
  − .523, .169, .011
 −.085   RDBC
  24/23, 13/11   + .465, .129, .005
  − .535, .164, .007
 −.109   (.024) (.024) (.039) (.016)
  13/10   + .460, .131, .005
  − .540, .162, .009
 −.115   (.030) (.034) (.044) (.021)
  24/21   + .462, .115, .004
  − .538, .155, .006
 −.119   (.034) (.030) (.073) (.004)
   PLAY W      G     BG     EQUITY VOTES CL DMP GG GS
  13/11(2), 6/4(2)   + .561, .176, .008
  − .439, .131, .006
 +.170   RBC (.054)
  24/22(2), 6/4(2)   + .552, .158, .006
  − .448, .101, .004
 +.164   (.006) (.018) (.055) (.012)
  13/9, 6/4(2)   + .543, .172, .008
  − .457, .134, .007
 +.124   (.046) (.037) (.045) (.098)
  24/20(2)   + .536, .128, .004
  − .464, .079, .002
 +.123   D (.047) (.049) (.146)
   PLAY W      G     BG     EQUITY VOTES CL DMP GG GS
  8/5, 6/5   + .531, .166, .007
  − .469, .140, .007
 +.088   RDBC
   PLAY W      G     BG     EQUITY VOTES CL DMP GG GS
  13/11, 13/10   + .473, .143, .006
  − .527, .162, .010
 −.076   RBC (.004)
  24/21, 13/11   + .473, .129, .006
  − .527, .160, .007
 −.087   D (.011) (.000) (.030)
  24/22, 13/10   + .464, .128, .006
  − .536, .164, .007
 −.110   (.034) (.017) (.049) (.026)
  13/10, 6/4   + .465, .131, .005
  − .536, .170, .011
 −.116   (.040) (.017) (.041) (.038)
  13/11, 8/5   + .462, .138, .006
  − .538, .174, .012
 −.119   (.043) (.022) (.033) (.050)
   PLAY W      G     BG     EQUITY VOTES CL DMP GG GS
  8/5(2), 6/3(2)   + .560, .201, .010
  − .440, .128, .007
 +.196   BC (.074)
  24/21(2), 8/5(2)   + .555, .166, .006
  − .445, .090, .003
 +.187   D (.009) (.011) (.081) (.010)
  24/21(2), 13/10(2)   + .556, .147, .005
  − .444, .086, .003
 +.174   R (.022) (.009) (.116)
  24/21(2), 6/3(2)   + .553, .148, .005
  − .447, .088, .003
 +.168   (.028) (.014) (.118) (.009)
   PLAY W      G     BG     EQUITY VOTES CL DMP GG GS
  13/9, 6/5   + .471, .132, .006
  − .529, .171, .012
 −.103   DB
  24/23, 13/9   + .463, .133, .006
  − .537, .165, .008
 −.109   RC (.006) (.016) (.015) (.005)
  24/23, 24/20   + .460, .116, .005
  − .540, .162, .006
 −.128   (.026) (.023) (.056) (.006)
  13/8   + .453, .122, .005
  − .547, .164, .007
 −.137   (.035) (.036) (.056) (.022)
   PLAY W      G     BG     EQUITY VOTES CL DMP GG GS
  8/4, 6/4   + .507, .160, .007
  − .493, .148, .007
 +.024   RDBC
   PLAY W      G     BG     EQUITY VOTES CL DMP GG GS
  13/10, 13/9   + .475, .147, .007
  − .525, .159, .009
 −.064   RBC
  24/21, 13/9   + .473, .131, .006
  − .527, .159, .007
 −.083   D (.020) (.005) (.037) (.006)
  24/20, 13/10   + .466, .129, .006
  − .534, .172, .008
 −.112   (.049) (.018) (.055) (.046)
   PLAY W      G     BG     EQUITY VOTES CL DMP GG GS
  24/20(2), 13/9(2)   + .601, .161, .005
  − .399, .067, .002
 +.299   RDBC
   PLAY W      G     BG     EQUITY VOTES CL DMP GG GS
  13/8, 6/5   + .469, .130, .005
  − .531, .160, .009
 −.096   RDBC
  24/23, 13/8   + .463, .126, .005
  − .537, .161, .006
 −.110   (.014) (.013) (.020) (.013)
  13/7   + .452, .127, .005
  − .548, .164, .009
 −.137   (.040) (.034) (.039) (.042)
  24/18   + .460, .114, .005
  − .540, .172, .007
 −.140   (.044) (.019) (.050) (.042)
   PLAY W      G     BG     EQUITY VOTES CL DMP GG GS
  13/11, 13/8   + .467, .137, .006
  − .533, .163, .008
 −.095   RB
  24/22, 13/8   + .464, .123, .005
  − .536, .162, .006
 −.111   C (.016) (.006) (.032) (.004)
  13/8, 6/4   + .460, .127, .005
  − .540, .160, .009
 −.118   D (.024) (.015) (.035) (.010)
   PLAY W      G     BG     EQUITY VOTES CL DMP GG GS
  8/3, 6/3   + .483, .151, .007
  − .517, .157, .007
 −.040   RBC
  24/21, 13/8   + .476, .125, .005
  − .524, .151, .005
 −.074   (.034) (.014) (.068) (.003)
  13/10, 13/8   + .468, .138, .006
  − .532, .159, .008
 −.087   D (.048) (.032) (.058) (.035)
   PLAY W      G     BG     EQUITY VOTES CL DMP GG GS
  13/9, 13/8   + .470, .143, .006
  − .530, .160, .008
 −.080   RDBC (.008) (.007)
  24/20, 13/8   + .473, .126, .006
  − .527, .164, .006
 −.093   (.014) (.002) (.028) (.010)
  24/15   + .474, .114, .005
  − .526, .160, .006
 −.100   (.021) (.050)
  13/4   + .455, .132, .005
  − .545, .163, .009
 −.125   (.046) (.038) (.052) (.043)
   PLAY W      G     BG     EQUITY VOTES CL DMP GG GS
  13/3(2)   + .510, .169, .009
  − .490, .147, .006
 +.045   RDBC
   PLAY W      G     BG     EQUITY VOTES CL DMP GG GS
  13/7, 8/7   + .505, .145, .006
  − .495, .147, .006
 +.008   RDBC
   PLAY W      G     BG     EQUITY VOTES CL DMP GG GS
  24/18, 13/11   + .474, .124, .006
  − .526, .170, .007
 −.100   RBC (.003)
  13/5   + .464, .136, .006
  − .536, .163, .009
 −.103   D (.004) (.021) (.006)
  13/11, 13/7   + .460, .136, .006
  − .540, .171, .011
 −.121   (.021) (.029) (.008) (.030)
  24/16   + .467, .117, .005
  − .533, .171, .007
 −.122   (.022) (.015) (.032) (.016)
   PLAY W      G     BG     EQUITY VOTES CL DMP GG GS
  24/15   + .474, .114, .005
  − .526, .160, .006
 −.100   DC (.017)
  24/18, 13/10   + .472, .125, .006
  − .528, .168, .008
 −.102   RB (.001) (.004) (.019)
  13/4   + .455, .132, .005
  − .545, .163, .009
 −.125   (.025) (.038) (.020) (.043)
  13/10, 13/7   + .457, .137, .006
  − .543, .172, .011
 −.127   (.026) (.033) (.005) (.057)
  24/21, 24/18   + .465, .110, .005
  − .535, .169, .006
 −.130   (.029) (.017) (.042) (.034)
  24/21, 13/7   + .456, .125, .006
  − .544, .167, .008
 −.132   (.032) (.035) (.031) (.049)
   PLAY W      G     BG     EQUITY VOTES CL DMP GG GS
  24/14*   + .549, .139, .007
  − .451, .124, .004
 +.116   RDBC
   PLAY W      G     BG     EQUITY VOTES CL DMP GG GS
  24/13   + .489, .111, .004
  − .511, .148, .005
 −.059   RDBC
  24/18, 13/8   + .475, .123, .006
  − .525, .165, .006
 −.092   (.033) (.028) (.004) (.062)
   PLAY W      G     BG     EQUITY VOTES CL DMP GG GS
  24/18(2), 13/7(2)   + .631, .153, .006
  − .369, .080, .002
 +.337   RDBC

Summary

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

(+.340) 24/18(2), 13/7(2) +.337 × 1  =   +.337
(+.301) 24/20(2), 13/9(2) +.299 × 1  =   +.299
(+.199) 8/5(2), 6/3(2) +.196 × 1  =   +.196
(+.187) 8/7(2), 6/5(2) +.184 × 1  =   +.184
(+.172) 13/11(2), 6/4(2) +.170 × 1  =   +.170
(+.118) 24/14* +.116 × 2  =   +.231
(+.090) 8/5, 6/5 +.088 × 2  =   +.175
(+.048) 13/3(2) +.045 × 1  =   +.045
(+.027) 8/4, 6/4 +.024 × 2  =   +.049
(+.011) 13/7, 8/7 +.008 × 2  =   +.017
(−.037) 8/3, 6/3 −.040 × 2  =   −.080
(−.057) 24/13 −.059 × 2  =   −.119
(−.061) 13/10, 13/9 −.064 × 2  =   −.127
(−.074) 13/11, 13/10 −.076 × 2  =   −.152
(−.077) 13/9, 13/8 −.080 × 2  =   −.159
(−.082) 13/11, 6/5 −.085 × 2  =   −.170
(−.092) 13/11, 13/8 −.095 × 2  =   −.189
(−.094) 13/8, 6/5 −.096 × 2  =   −.192
(−.097) 24/18, 13/11 −.100 × 2  =   −.199
(−.098) 24/15 −.100 × 2  =   −.200
(−.100) 13/9, 6/5 −.103 × 2  =   −.205
  ———
  White's Average Equity −.091  ÷  36  =  −.003

 

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