Replies to 13/9, 6/5

Best
Nearly Best
Pretty Good
Not So Good
Here are White's best replies after Red opens 13/9, 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
  24/20*   + .535, .171, .012
  − .465, .121, .004
 +.128  
  8/7(2), 6/5(2)   + .533, .162, .009
  − .467, .146, .007
 +.082   RDB (.046) (.005) (.023) (.056)
   PLAY W      G     BG     EQUITY VOTES CL DMP GG GS
  13/11, 6/5   + .443, .127, .006
  − .557, .188, .013
 −.183   RDB (.011)
  24/23, 13/11   + .438, .118, .005
  − .562, .178, .008
 −.186   (.003) (.010) (.027)
  24/21   + .430, .107, .005
  − .570, .179, .007
 −.214   (.031) (.026) (.065) (.017)
  24/22, 6/5   + .437, .114, .005
  − .563, .201, .011
 −.219   (.036) (.011) (.037) (.048)
  24/23, 24/22   + .427, .109, .005
  − .573, .190, .008
 −.229   (.046) (.033) (.067) (.046)
   PLAY W      G     BG     EQUITY VOTES CL DMP GG GS
  24/20*, 6/4(2)   + .604, .219, .020
  − .396, .090, .003
 +.354   RDB
  24/20*/16*   + .589, .210, .017
  − .411, .097, .003
 +.305   (.049) (.030) (.048) (.044)
   PLAY W      G     BG     EQUITY VOTES CL DMP GG GS
  24/20*   + .535, .171, .012
  − .465, .121, .004
 +.128   RDB
   PLAY W      G     BG     EQUITY VOTES CL DMP GG GS
  24/21, 13/11   + .443, .116, .005
  − .557, .175, .008
 −.176   RDB
  24/22, 13/10   + .436, .117, .005
  − .564, .185, .009
 −.198   (.023) (.014) (.011) (.033)
  24/22, 24/21   + .435, .106, .005
  − .565, .179, .007
 −.205   (.030) (.017) (.036) (.025)
  13/11, 13/10   + .429, .129, .006
  − .571, .186, .011
 −.206   (.030) (.030) (.004) (.052)
  13/11, 8/5   + .428, .127, .006
  − .572, .198, .015
 −.223   (.048) (.031) (.009) (.076)
   PLAY W      G     BG     EQUITY VOTES CL DMP GG GS
  24/21(2), 8/5(2)   + .533, .158, .006
  − .467, .098, .004
 +.128   DB (.005) (.032) (.004)
  24/21(2), 6/3(2)   + .535, .146, .006
  − .465, .101, .004
 +.117   (.011) (.051) (.005)
  24/21(2), 13/10(2)   + .533, .137, .005
  − .467, .097, .003
 +.108   R (.020) (.004) (.073)
  8/5(2), 6/3(2)   + .521, .185, .011
  − .479, .152, .008
 +.078   (.049) (.028) (.134)
   PLAY W      G     BG     EQUITY VOTES CL DMP GG GS
  24/23, 24/20*   + .538, .168, .011
  − .462, .116, .004
 +.135   RDB
   PLAY W      G     BG     EQUITY VOTES CL DMP GG GS
  24/20*, 13/11   + .542, .185, .015
  − .458, .118, .005
 +.162   RDB
  24/22, 24/20*   + .541, .165, .011
  − .459, .116, .004
 +.137   (.025) (.004) (.044) (.001)
   PLAY W      G     BG     EQUITY VOTES CL DMP GG GS
  24/21, 24/20*   + .550, .167, .012
  − .450, .116, .004
 +.157   B (.012)
  24/20*, 13/10   + .540, .183, .014
  − .460, .118, .005
 +.154   RD (.003) (.019) (.022)
   PLAY W      G     BG     EQUITY VOTES CL DMP GG GS
  24/20*/16*, 8/4(2)   + .618, .281, .034
  − .382, .082, .003
 +.465   DB (.016) (.027)
  24/20*/16*, 13/9(2)   + .626, .255, .025
  − .374, .077, .003
 +.453   R (.012) (.035)
   PLAY W      G     BG     EQUITY VOTES CL DMP GG GS
  24/23, 13/8   + .437, .118, .005
  − .563, .176, .007
 −.184   DB (.004) (.015)
  13/8, 6/5   + .439, .124, .006
  − .561, .183, .010
 −.185   R (.000) (.010)
  24/18   + .431, .106, .005
  − .569, .191, .007
 −.226   (.041) (.017) (.053) (.043)
   PLAY W      G     BG     EQUITY VOTES CL DMP GG GS
  24/22, 13/8   + .433, .116, .005
  − .567, .184, .007
 −.204   B
  13/11, 13/8   + .425, .121, .006
  − .575, .188, .009
 −.221   D (.016) (.016) (.006) (.023)
  13/8, 6/4   + .425, .119, .005
  − .575, .186, .009
 −.221   R (.016) (.015) (.010) (.019)
   PLAY W      G     BG     EQUITY VOTES CL DMP GG GS
  24/16*   + .529, .152, .009
  − .471, .134, .005
 +.081   RDB
   PLAY W      G     BG     EQUITY VOTES CL DMP GG GS
  24/20*, 13/8   + .546, .183, .014
  − .454, .115, .004
 +.170   RB
  24/20*/15   + .542, .158, .010
  − .458, .124, .005
 +.123   D (.047) (.009) (.059) (.026)
   PLAY W      G     BG     EQUITY VOTES CL DMP GG GS
  13/3(2)   + .453, .147, .009
  − .547, .172, .007
 −.116   RDB
   PLAY W      G     BG     EQUITY VOTES CL DMP GG GS
  13/7, 8/7   + .465, .130, .006
  − .535, .170, .007
 −.110   RDB
   PLAY W      G     BG     EQUITY VOTES CL DMP GG GS
  24/16*   + .529, .152, .009
  − .471, .134, .005
 +.081   RDB
   PLAY W      G     BG     EQUITY VOTES CL DMP GG GS
  24/15   + .441, .103, .005
  − .559, .178, .007
 −.195   RDB (.021)
  24/18, 13/10   + .440, .115, .006
  − .560, .191, .009
 −.200   (.006) (.003) (.031)
  24/21, 13/7   + .421, .113, .005
  − .579, .188, .010
 −.236   (.042) (.040) (.039) (.061)
   PLAY W      G     BG     EQUITY VOTES CL DMP GG GS
  24/20*/14   + .548, .159, .010
  − .452, .122, .004
 +.139   RDB
  24/20*, 13/7   + .528, .172, .012
  − .472, .119, .005
 +.116   (.023) (.041) (.015) (.035)
  24/20*, 24/18   + .535, .161, .011
  − .465, .125, .005
 +.114   (.026) (.026) (.022) (.032)
   PLAY W      G     BG     EQUITY VOTES CL DMP GG GS
  24/13   + .469, .106, .005
  − .531, .165, .005
 −.121   RDB
   PLAY W      G     BG     EQUITY VOTES CL DMP GG GS
  24/18(2), 13/7(2)   + .613, .142, .005
  − .387, .084, .002
 +.285   RDB

Summary

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

(+.437) 24/20*/16*, 8/4(2) +.465 × 1  =   +.465
(+.326) 24/20*, 6/4(2) +.354 × 1  =   +.354
(+.257) 24/18(2), 13/7(2) +.285 × 1  =   +.285
(+.142) 24/20*, 13/8 +.170 × 2  =   +.340
(+.134) 24/20*, 13/11 +.162 × 2  =   +.324
(+.129) 24/21, 24/20* +.157 × 2  =   +.314
(+.112) 24/20*/14 +.139 × 2  =   +.279
(+.107) 24/23, 24/20* +.135 × 2  =   +.269
(+.100) 24/20* +.128 × 2  =   +.256
(+.100) 24/20* +.128 × 1  =   +.128
(+.100) 24/21(2), 8/5(2) +.128 × 1  =   +.128
(+.053) 24/16* +.081 × 2  =   +.161
(+.053) 24/16* +.081 × 2  =   +.161
(−.138) 13/7, 8/7 −.110 × 2  =   −.221
(−.144) 13/3(2) −.116 × 1  =   −.116
(−.149) 24/13 −.121 × 2  =   −.242
(−.203) 24/21, 13/11 −.176 × 2  =   −.351
(−.211) 13/11, 6/5 −.183 × 2  =   −.366
(−.212) 24/23, 13/8 −.184 × 2  =   −.369
(−.222) 24/15 −.195 × 2  =   −.389
(−.232) 24/22, 13/8 −.204 × 2  =   −.409
  ———
  White's Average Equity +1.002  ÷  36  =  +.028

 

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