Replies to 8/2, 6/2

Best
Nearly Best
Pretty Good
Not So Good
Here are White's best replies after Red opens 8/2, 6/2.

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).
      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)   + .567, .177, .008
  − .433, .137, .008
 +.174   RB
   PLAY W      G     BG     EQUITY VOTES CL DMP GG GS
  13/11, 6/5   + .480, .135, .005
  − .520, .183, .014
 −.098   RB (.005)
  13/10   + .469, .134, .005
  − .531, .170, .009
 −.101   (.004) (.020) (.022)
  24/21   + .469, .120, .005
  − .532, .170, .006
 −.114   (.016) (.022) (.052) (.001)
   PLAY W      G     BG     EQUITY VOTES CL DMP GG GS
  24/22(2), 6/4(2)   + .564, .166, .006
  − .436, .102, .004
 +.196   R (.010) (.041)
  13/11(2), 6/4(2)   + .569, .182, .009
  − .431, .136, .007
 +.186   B (.009) (.058)
   PLAY W      G     BG     EQUITY VOTES CL DMP GG GS
  8/5, 6/5   + .536, .168, .007
  − .464, .145, .008
 +.094   RB
   PLAY W      G     BG     EQUITY VOTES CL DMP GG GS
  13/11, 13/10   + .479, .144, .006
  − .521, .172, .011
 −.075   RB
  24/22, 13/10   + .478, .132, .006
  − .522, .175, .007
 −.089   (.014) (.002) (.027) (.008)
  24/21, 13/11   + .478, .129, .006
  − .522, .174, .008
 −.090   (.015) (.001) (.031) (.006)
  13/8   + .466, .131, .005
  − .534, .173, .009
 −.113   (.038) (.026) (.052) (.028)
  24/22, 24/21   + .469, .119, .005
  − .531, .176, .006
 −.120   (.045) (.020) (.071) (.028)
   PLAY W      G     BG     EQUITY VOTES CL DMP GG GS
  24/21(2), 13/10(2)   + .564, .152, .006
  − .436, .091, .003
 +.192   RB (.094)
  8/5(2), 6/3(2)   + .558, .205, .009
  − .442, .136, .008
 +.187   (.005) (.011) (.101)
  24/21(2), 6/3(2)   + .555, .154, .006
  − .445, .096, .003
 +.171   (.021) (.017) (.107) (.028)
  24/21(2), 8/5(2)   + .550, .167, .006
  − .450, .099, .003
 +.171   (.022) (.029) (.092) (.044)
  13/10(2), 6/3(2)   + .554, .187, .009
  − .446, .138, .007
 +.159   (.033) (.020) (.045) (.115)
   PLAY W      G     BG     EQUITY VOTES CL DMP GG GS
  13/8   + .466, .131, .005
  − .534, .173, .009
 −.113   B (.016) (.019)
  13/9, 6/5   + .474, .133, .005
  − .526, .191, .016
 −.121   R (.008) (.020)
   PLAY W      G     BG     EQUITY VOTES CL DMP GG GS
  8/4, 6/4   + .515, .164, .007
  − .485, .153, .008
 +.039   RB
   PLAY W      G     BG     EQUITY VOTES CL DMP GG GS
  13/10, 13/9   + .479, .147, .007
  − .521, .173, .011
 −.074   RB
  24/21, 13/9   + .476, .133, .006
  − .524, .176, .008
 −.094   (.020) (.006) (.034) (.012)
  24/20, 13/10   + .472, .129, .006
  − .528, .178, .008
 −.108   (.034) (.013) (.049) (.024)
   PLAY W      G     BG     EQUITY VOTES CL DMP GG GS
  24/20(2), 13/9(2)   + .587, .155, .005
  − .413, .069, .002
 +.263   RB
   PLAY W      G     BG     EQUITY VOTES CL DMP GG GS
  13/8, 6/5   + .472, .132, .005
  − .528, .170, .010
 −.100   RB
  13/7   + .457, .128, .005
  − .543, .179, .011
 −.143   (.043) (.030) (.037) (.047)
   PLAY W      G     BG     EQUITY VOTES CL DMP GG GS
  24/22, 13/8   + .483, .129, .005
  − .517, .167, .005
 −.071   (.011)
  13/11, 13/8   + .478, .140, .006
  − .522, .170, .009
 −.077   RB (.005) (.010) (.016)
   PLAY W      G     BG     EQUITY VOTES CL DMP GG GS
  8/3, 6/3   + .491, .155, .007
  − .509, .163, .009
 −.028   RB
  24/21, 13/8   + .485, .130, .006
  − .515, .164, .005
 −.063   (.034) (.011) (.060) (.012)
  13/10, 13/8   + .478, .142, .006
  − .522, .168, .009
 −.073   (.044) (.026) (.053) (.035)
   PLAY W      G     BG     EQUITY VOTES CL DMP GG GS
  13/9, 13/8   + .481, .147, .007
  − .519, .168, .009
 −.061   RB (.001)
  24/20, 13/8   + .481, .129, .006
  − .519, .167, .006
 −.078   (.017) (.001) (.037)
   PLAY W      G     BG     EQUITY VOTES CL DMP GG GS
  13/3(2)   + .523, .171, .010
  − .477, .155, .007
 +.066   RB
   PLAY W      G     BG     EQUITY VOTES CL DMP GG GS
  13/7, 8/7   + .512, .149, .006
  − .488, .153, .007
 +.020   RB
   PLAY W      G     BG     EQUITY VOTES CL DMP GG GS
  13/5   + .467, .135, .005
  − .533, .174, .010
 −.110   B (.014)
  24/18, 13/11   + .474, .123, .006
  − .526, .190, .008
 −.122   R (.012) (.011) (.017)
  24/16   + .466, .111, .005
  − .534, .184, .007
 −.143   (.033) (.016) (.049) (.022)
  13/11, 13/7   + .460, .134, .006
  − .540, .190, .014
 −.144   (.034) (.028) (.017) (.045)
  24/22, 13/7   + .458, .125, .005
  − .542, .186, .009
 −.149   (.039) (.033) (.039) (.042)
   PLAY W      G     BG     EQUITY VOTES CL DMP GG GS
  24/18, 13/10   + .472, .125, .006
  − .528, .192, .009
 −.126   RB (.017)
  13/4   + .461, .134, .005
  − .539, .177, .011
 −.127   (.000) (.022) (.002) (.010)
  24/15   + .469, .111, .005
  − .531, .180, .006
 −.134   (.007) (.006) (.034)
  24/21, 13/7   + .457, .125, .005
  − .543, .188, .009
 −.151   (.025) (.029) (.028) (.038)
  13/10, 13/7   + .456, .135, .006
  − .544, .194, .015
 −.157   (.031) (.032) (.012) (.053)
   PLAY W      G     BG     EQUITY VOTES CL DMP GG GS
  8/2, 6/2   + .475, .152, .007
  − .525, .172, .009
 −.072   RB
   PLAY W      G     BG     EQUITY VOTES CL DMP GG GS
  24/13   + .495, .110, .005
  − .505, .163, .004
 −.063   RB
  24/18, 13/8   + .478, .126, .006
  − .522, .181, .006
 −.100   (.037) (.033) (.002) (.070)
   PLAY W      G     BG     EQUITY VOTES CL DMP GG GS
  24/18(2), 13/7(2)   + .635, .157, .006
  − .365, .076, .002
 +.356   RB

Summary

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

(+.368) 24/18(2), 13/7(2) +.356 × 1  =   +.356
(+.275) 24/20(2), 13/9(2) +.263 × 1  =   +.263
(+.208) 24/22(2), 6/4(2) +.196 × 1  =   +.196
(+.204) 24/21(2), 13/10(2) +.192 × 1  =   +.192
(+.186) 8/7(2), 6/5(2) +.174 × 1  =   +.174
(+.106) 8/5, 6/5 +.094 × 2  =   +.188
(+.078) 13/3(2) +.066 × 1  =   +.066
(+.051) 8/4, 6/4 +.039 × 2  =   +.078
(+.032) 13/7, 8/7 +.020 × 2  =   +.040
(−.016) 8/3, 6/3 −.028 × 2  =   −.057
(−.049) 13/9, 13/8 −.061 × 2  =   −.123
(−.051) 24/13 −.063 × 2  =   −.125
(−.059) 24/22, 13/8 −.071 × 2  =   −.143
(−.060) 8/2, 6/2 −.072 × 2  =   −.144
(−.062) 13/10, 13/9 −.074 × 2  =   −.147
(−.063) 13/11, 13/10 −.075 × 2  =   −.151
(−.086) 13/11, 6/5 −.098 × 2  =   −.195
(−.088) 13/8, 6/5 −.100 × 2  =   −.199
(−.098) 13/5 −.110 × 2  =   −.220
(−.101) 13/8 −.113 × 2  =   −.226
(−.114) 24/18, 13/10 −.126 × 2  =   −.253
  ———
  White's Average Equity −.431  ÷  36  =  −.012

 

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