Replies to 13/10, 13/9

Best
Nearly Best
Pretty Good
Not So Good
Here are White's best replies after Red opens 13/10, 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:

      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)   + .557, .170, .009
  − .443, .143, .007
 +.143   RDB
   PLAY W      G     BG     EQUITY VOTES CL DMP GG GS
  13/11, 6/5   + .469, .133, .006
  − .531, .183, .013
 −.119   RB
  24/23, 13/11   + .454, .123, .005
  − .546, .179, .008
 −.150   D (.031) (.030) (.049) (.023)
   PLAY W      G     BG     EQUITY VOTES CL DMP GG GS
  24/22(2), 6/4(2)   + .541, .159, .007
  − .459, .112, .004
 +.131   RB (.000) (.018) (.032)
  13/11(2), 6/4(2)   + .541, .167, .008
  − .459, .149, .007
 +.103   (.029) (.105)
  24/16*   + .540, .154, .010
  − .460, .137, .005
 +.101   (.030) (.003) (.029) (.084)
  24/20(2)   + .530, .123, .004
  − .470, .085, .002
 +.100   D (.031) (.023) (.111)
   PLAY W      G     BG     EQUITY VOTES CL DMP GG GS
  8/5, 6/5   + .525, .154, .008
  − .475, .146, .007
 +.060   RDB
   PLAY W      G     BG     EQUITY VOTES CL DMP GG GS
  24/22, 13/10   + .461, .124, .006
  − .539, .178, .008
 −.135   RB (.011)
  13/11, 13/10   + .453, .137, .007
  − .547, .181, .011
 −.143   (.008) (.016) (.022)
  24/21, 13/11   + .451, .121, .006
  − .549, .188, .009
 −.167   (.032) (.019) (.034) (.038)
  13/11, 8/5   + .449, .132, .006
  − .551, .191, .015
 −.170   (.035) (.023) (.018) (.050)
  13/10, 6/4   + .450, .127, .006
  − .550, .194, .014
 −.175   D (.039) (.021) (.025) (.053)
   PLAY W      G     BG     EQUITY VOTES CL DMP GG GS
  24/21(2), 8/5(2)   + .556, .169, .007
  − .444, .095, .004
 +.190   DB (.015) (.026)
  24/21(2), 6/3(2)   + .553, .154, .006
  − .447, .093, .003
 +.170   (.020) (.021) (.064) (.002)
  24/15*, 13/10   + .561, .166, .011
  − .439, .127, .005
 +.166   R (.025) (.006) (.025) (.055)
  24/21(2), 13/10(2)   + .553, .150, .006
  − .447, .096, .003
 +.164   (.026) (.021) (.071) (.007)
  24/15*, 24/21   + .564, .157, .011
  − .436, .126, .005
 +.164   (.027) (.036) (.048)
  8/5(2), 6/3(2)   + .546, .193, .012
  − .454, .145, .007
 +.145   (.046) (.034) (.119)
   PLAY W      G     BG     EQUITY VOTES CL DMP GG GS
  13/9, 6/5   + .465, .133, .006
  − .535, .183, .014
 −.127   RB
  24/23, 13/9   + .454, .128, .006
  − .546, .179, .008
 −.146   D (.019) (.023) (.032) (.016)
   PLAY W      G     BG     EQUITY VOTES CL DMP GG GS
  8/4, 6/4   + .493, .150, .007
  − .507, .165, .008
 −.031   RDB
   PLAY W      G     BG     EQUITY VOTES CL DMP GG GS
  13/10, 13/9   + .458, .142, .007
  − .542, .178, .011
 −.123   RDB
  24/21, 13/9   + .454, .126, .006
  − .546, .186, .009
 −.155   (.032) (.008) (.041) (.025)
  24/20, 13/10   + .449, .117, .005
  − .551, .178, .008
 −.166   (.043) (.018) (.068) (.019)
   PLAY W      G     BG     EQUITY VOTES CL DMP GG GS
  24/16*, 13/9(2)   + .599, .186, .013
  − .401, .105, .004
 +.287   RB (.011) (.061)
  24/20(2), 13/9(2)   + .594, .159, .006
  − .406, .071, .002
 +.280   D (.006) (.019) (.062)
  24/16*(2)   + .604, .146, .008
  − .396, .102, .003
 +.257   (.029) (.069) (.043)
   PLAY W      G     BG     EQUITY VOTES CL DMP GG GS
  13/8, 6/5   + .455, .127, .006
  − .545, .179, .011
 −.147   RB
  24/23, 13/8   + .450, .122, .005
  − .550, .177, .007
 −.156   D (.009) (.010) (.020) (.005)
  24/18   + .453, .111, .005
  − .547, .179, .007
 −.164   (.016) (.005) (.035) (.004)
   PLAY W      G     BG     EQUITY VOTES CL DMP GG GS
  24/22, 13/8   + .453, .118, .005
  − .547, .177, .006
 −.154   RB (.004)
  13/11, 13/8   + .445, .128, .006
  − .555, .186, .010
 −.171   (.018) (.015) (.034)
  13/8, 6/4   + .445, .122, .006
  − .555, .187, .010
 −.180   D (.026) (.016) (.013) (.036)
   PLAY W      G     BG     EQUITY VOTES CL DMP GG GS
  24/16*   + .540, .154, .010
  − .460, .137, .005
 +.101   RDB
   PLAY W      G     BG     EQUITY VOTES CL DMP GG GS
  24/15*   + .545, .155, .010
  − .455, .134, .005
 +.115   RDB
   PLAY W      G     BG     EQUITY VOTES CL DMP GG GS
  13/3(2)   + .481, .154, .010
  − .519, .170, .007
 −.052   RDB
   PLAY W      G     BG     EQUITY VOTES CL DMP GG GS
  13/7, 8/7   + .488, .136, .006
  − .512, .166, .007
 −.054   RDB
   PLAY W      G     BG     EQUITY VOTES CL DMP GG GS
  24/16*   + .540, .154, .010
  − .460, .137, .005
 +.101   RDB
   PLAY W      G     BG     EQUITY VOTES CL DMP GG GS
  24/15*   + .545, .155, .010
  − .455, .134, .005
 +.115   RDB
   PLAY W      G     BG     EQUITY VOTES CL DMP GG GS
  24/14   + .472, .113, .006
  − .528, .175, .006
 −.118   RDB (.022)
  24/18, 13/9   + .466, .130, .007
  − .534, .181, .009
 −.121   (.003) (.012) (.024)
  8/2, 6/2   + .443, .137, .007
  − .557, .187, .009
 −.168   (.050) (.059) (.034) (.084)
   PLAY W      G     BG     EQUITY VOTES CL DMP GG GS
  24/13   + .482, .106, .005
  − .518, .165, .005
 −.095   RDB
  24/18, 13/8   + .466, .121, .006
  − .534, .174, .006
 −.122   (.027) (.033) (.003) (.050)
   PLAY W      G     BG     EQUITY VOTES CL DMP GG GS
  24/18(2), 13/7(2)   + .626, .148, .006
  − .374, .083, .003
 +.319   RDB

Summary

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

(+.325) 24/18(2), 13/7(2) +.319 × 1  =   +.319
(+.292) 24/16*, 13/9(2) +.287 × 1  =   +.287
(+.196) 24/21(2), 8/5(2) +.190 × 1  =   +.190
(+.149) 8/7(2), 6/5(2) +.143 × 1  =   +.143
(+.137) 24/22(2), 6/4(2) +.131 × 1  =   +.131
(+.120) 24/15* +.115 × 2  =   +.230
(+.120) 24/15* +.115 × 2  =   +.230
(+.107) 24/16* +.101 × 2  =   +.202
(+.107) 24/16* +.101 × 2  =   +.202
(+.066) 8/5, 6/5 +.060 × 2  =   +.121
(−.025) 8/4, 6/4 −.031 × 2  =   −.061
(−.046) 13/3(2) −.052 × 1  =   −.052
(−.049) 13/7, 8/7 −.054 × 2  =   −.109
(−.090) 24/13 −.095 × 2  =   −.191
(−.112) 24/14 −.118 × 2  =   −.236
(−.114) 13/11, 6/5 −.119 × 2  =   −.238
(−.118) 13/10, 13/9 −.123 × 2  =   −.247
(−.121) 13/9, 6/5 −.127 × 2  =   −.254
(−.130) 24/22, 13/10 −.135 × 2  =   −.270
(−.142) 13/8, 6/5 −.147 × 2  =   −.295
(−.148) 24/22, 13/8 −.154 × 2  =   −.307
  ———
  White's Average Equity −.205  ÷  36  =  −.006

 

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