Replies to 8/4, 6/4

Best
Nearly Best
Pretty Good
Not So Good
Here are White's best replies after Red opens 8/4, 6/4.

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)   + .518, .154, .007
  − .482, .151, .008
 +.039   RDBC (.013)
  24/22, 6/5(2)   + .516, .143, .006
  − .484, .143, .005
 +.033   (.006) (.004) (.027)
  24/23, 6/5(3)   + .509, .144, .006
  − .491, .153, .006
 +.010   (.029) (.018) (.038) (.035)
  24/23(2), 6/5(2)   + .499, .146, .006
  − .501, .138, .006
 +.005   (.034) (.038) (.056) (.026)
   PLAY W      G     BG     EQUITY VOTES CL DMP GG GS
  24/23, 13/11   + .439, .116, .005
  − .561, .180, .008
 −.190   RBC
  24/23, 24/22   + .430, .105, .004
  − .570, .183, .007
 −.220   (.030) (.017) (.038) (.023)
  13/10   + .423, .116, .005
  − .577, .185, .010
 −.227   (.038) (.031) (.032) (.040)
  13/11, 6/5   + .432, .114, .004
  − .568, .197, .015
 −.229   D (.039) (.013) (.016) (.047)
   PLAY W      G     BG     EQUITY VOTES CL DMP GG GS
  24/22(2), 6/4(2)   + .519, .142, .005
  − .481, .110, .004
 +.071   RB (.006) (.047) (.049)
  13/11(2), 6/4(2)   + .522, .163, .008
  − .478, .152, .008
 +.055   C (.017) (.127)
  24/20(2)   + .513, .105, .003
  − .487, .080, .002
 +.052   D (.019) (.017) (.133)
   PLAY W      G     BG     EQUITY VOTES CL DMP GG GS
  8/5, 6/5   + .490, .148, .006
  − .510, .160, .008
 −.035   RDBC
   PLAY W      G     BG     EQUITY VOTES CL DMP GG GS
  24/22, 13/10   + .436, .113, .005
  − .564, .185, .009
 −.203   RBC (.005)
  13/11, 13/10   + .428, .124, .005
  − .572, .187, .012
 −.214   D (.011) (.017) (.020)
  13/8   + .424, .116, .005
  − .576, .192, .009
 −.233   (.030) (.025) (.024) (.039)
   PLAY W      G     BG     EQUITY VOTES CL DMP GG GS
  8/5(2), 6/3(2)   + .516, .183, .009
  − .484, .148, .008
 +.068   RDBC
  13/10(2), 6/3(2)   + .505, .168, .009
  − .495, .154, .008
 +.025   (.044) (.023) (.053) (.035)
   PLAY W      G     BG     EQUITY VOTES CL DMP GG GS
  24/23, 13/9   + .438, .121, .005
  − .562, .190, .009
 −.198   RBC (.008)
  24/23, 24/20   + .432, .106, .005
  − .568, .181, .007
 −.213   (.014) (.010) (.040)
  13/8   + .424, .116, .005
  − .576, .192, .009
 −.233   (.035) (.028) (.037) (.040)
   PLAY W      G     BG     EQUITY VOTES CL DMP GG GS
  8/4, 6/4   + .471, .143, .007
  − .529, .167, .008
 −.083   RDBC
   PLAY W      G     BG     EQUITY VOTES CL DMP GG GS
  24/20, 13/10   + .435, .112, .005
  − .565, .177, .008
 −.197   RDC (.026)
  13/10, 13/9   + .431, .130, .006
  − .569, .188, .012
 −.202   B (.005) (.009) (.030)
   PLAY W      G     BG     EQUITY VOTES CL DMP GG GS
  24/20(2), 13/9(2)   + .574, .148, .005
  − .426, .072, .002
 +.227   RDBC
   PLAY W      G     BG     EQUITY VOTES CL DMP GG GS
  24/23, 13/8   + .444, .119, .005
  − .556, .179, .007
 −.174   RBC
  13/8, 6/5   + .428, .115, .004
  − .572, .187, .011
 −.224   D (.049) (.031) (.040) (.048)
   PLAY W      G     BG     EQUITY VOTES CL DMP GG GS
  24/22, 13/8   + .446, .116, .005
  − .554, .181, .006
 −.176   RBC
  13/11, 13/8   + .429, .123, .006
  − .571, .187, .009
 −.210   D (.034) (.032) (.018) (.045)
   PLAY W      G     BG     EQUITY VOTES CL DMP GG GS
  8/3, 6/3   + .450, .139, .007
  − .550, .180, .009
 −.145   RBC
   PLAY W      G     BG     EQUITY VOTES CL DMP GG GS
  24/20, 13/8   + .447, .113, .005
  − .553, .169, .007
 −.164   RDBC
  13/9, 13/8   + .428, .129, .007
  − .572, .187, .010
 −.204   (.041) (.037) (.005) (.073)
   PLAY W      G     BG     EQUITY VOTES CL DMP GG GS
  13/3(2)   + .468, .151, .010
  − .532, .173, .007
 −.084   RDBC
   PLAY W      G     BG     EQUITY VOTES CL DMP GG GS
  13/7, 8/7   + .466, .128, .005
  − .534, .165, .007
 −.107   RDBC
   PLAY W      G     BG     EQUITY VOTES CL DMP GG GS
  24/18, 13/11   + .440, .109, .005
  − .560, .198, .010
 −.214   RBC (.002)
  24/16   + .432, .099, .004
  − .568, .190, .007
 −.229   (.015) (.014) (.034)
  13/5   + .423, .119, .005
  − .577, .189, .012
 −.231   D (.017) (.032) (.013) (.018)
   PLAY W      G     BG     EQUITY VOTES CL DMP GG GS
  24/15   + .436, .098, .004
  − .564, .184, .007
 −.217   DC (.004) (.032)
  24/18, 13/10   + .438, .112, .005
  − .562, .201, .010
 −.217   RB (.000) (.030)
  13/4   + .417, .118, .005
  − .583, .196, .012
 −.251   (.034) (.042) (.029) (.063)
   PLAY W      G     BG     EQUITY VOTES CL DMP GG GS
  8/2, 6/2   + .431, .136, .007
  − .569, .190, .010
 −.195   C (.018) (.029)
  24/14   + .440, .101, .004
  − .560, .185, .007
 −.206   DB (.011) (.053)
  24/18, 13/9   + .436, .115, .005
  − .564, .202, .010
 −.220   R (.025) (.009) (.034) (.043)
   PLAY W      G     BG     EQUITY VOTES CL DMP GG GS
  24/13   + .470, .102, .005
  − .530, .169, .005
 −.127   RDBC
   PLAY W      G     BG     EQUITY VOTES CL DMP GG GS
  24/18(2), 13/7(2)   + .614, .144, .005
  − .386, .081, .002
 +.293   RDBC

Summary

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

(+.411) 24/18(2), 13/7(2) +.293 × 1  =   +.293
(+.344) 24/20(2), 13/9(2) +.227 × 1  =   +.227
(+.189) 24/22(2), 6/4(2) +.071 × 1  =   +.071
(+.186) 8/5(2), 6/3(2) +.068 × 1  =   +.068
(+.156) 8/7(2), 6/5(2) +.039 × 1  =   +.039
(+.083) 8/5, 6/5 −.035 × 2  =   −.070
(+.034) 8/4, 6/4 −.083 × 2  =   −.166
(+.033) 13/3(2) −.084 × 1  =   −.084
(+.011) 13/7, 8/7 −.107 × 2  =   −.214
(−.009) 24/13 −.127 × 2  =   −.254
(−.027) 8/3, 6/3 −.145 × 2  =   −.290
(−.046) 24/20, 13/8 −.164 × 2  =   −.327
(−.057) 24/23, 13/8 −.174 × 2  =   −.349
(−.058) 24/22, 13/8 −.176 × 2  =   −.351
(−.072) 24/23, 13/11 −.190 × 2  =   −.380
(−.077) 8/2, 6/2 −.195 × 2  =   −.389
(−.080) 24/20, 13/10 −.197 × 2  =   −.395
(−.081) 24/23, 13/9 −.198 × 2  =   −.396
(−.085) 24/22, 13/10 −.203 × 2  =   −.406
(−.097) 24/18, 13/11 −.214 × 2  =   −.428
(−.099) 24/15 −.217 × 2  =   −.434
  ———
  White's Average Equity −4.235  ÷  36  =  −.118

 

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