Replies to 13/11, 6/5

Best
Nearly Best
Pretty Good
Not So Good
Here are White's best replies after Red opens 13/11, 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*   + .525, .154, .010
  − .475, .119, .005
 +.091   (.012) (.016)
  8/7(2), 6/5(2)   + .531, .156, .008
  − .469, .139, .007
 +.082   RDB (.009) (.027)
  24/22, 6/5(2)   + .526, .142, .007
  − .474, .134, .005
 +.062   (.029) (.011) (.039) (.029)
   PLAY W      G     BG     EQUITY VOTES CL DMP GG GS
  24/23, 13/11   + .443, .119, .005
  − .557, .173, .007
 −.172   DB (.006)
  13/11, 6/5   + .442, .123, .005
  − .558, .182, .012
 −.183   R (.011) (.002) (.020)
  24/21   + .437, .108, .005
  − .563, .174, .007
 −.194   (.022) (.011) (.039) (.012)
  24/23, 24/22   + .433, .108, .004
  − .567, .174, .007
 −.204   (.032) (.020) (.048) (.022)
  13/10   + .429, .121, .005
  − .571, .181, .009
 −.206   (.034) (.027) (.028) (.042)
   PLAY W      G     BG     EQUITY VOTES CL DMP GG GS
  24/20*, 6/4(2)   + .597, .215, .019
  − .403, .090, .003
 +.334   RDB
   PLAY W      G     BG     EQUITY VOTES CL DMP GG GS
  24/20*   + .525, .154, .010
  − .475, .119, .005
 +.091   RDB
   PLAY W      G     BG     EQUITY VOTES CL DMP GG GS
  24/21, 13/11   + .449, .117, .005
  − .551, .174, .008
 −.162   RD (.010)
  24/22, 13/10   + .442, .120, .005
  − .558, .174, .008
 −.173   (.011) (.014) (.018) (.015)
  13/11, 13/10   + .437, .134, .006
  − .563, .181, .011
 −.178   (.016) (.023) (.039)
  24/22, 24/21   + .443, .110, .005
  − .557, .173, .007
 −.179   B (.017) (.012) (.036) (.011)
  13/10, 6/4   + .436, .125, .006
  − .564, .187, .012
 −.197   (.036) (.026) (.020) (.053)
   PLAY W      G     BG     EQUITY VOTES CL DMP GG GS
  24/21(2), 8/5(2)   + .538, .156, .006
  − .462, .096, .003
 +.139   DB (.046)
  24/21(2), 13/10(2)   + .533, .134, .005
  − .467, .094, .003
 +.107   R (.032) (.011) (.101) (.007)
  8/5(2), 6/3(2)   + .532, .186, .011
  − .468, .148, .008
 +.104   (.035) (.013) (.118)
  24/21(2), 6/3(2)   + .528, .137, .005
  − .472, .095, .003
 +.100   (.039) (.021) (.104) (.019)
   PLAY W      G     BG     EQUITY VOTES CL DMP GG GS
  24/23, 24/20*   + .527, .162, .011
  − .473, .119, .004
 +.104   RDB
   PLAY W      G     BG     EQUITY VOTES CL DMP GG GS
  24/20*, 13/11   + .537, .171, .012
  − .463, .118, .005
 +.134   RDB
  24/22, 24/20*   + .530, .162, .010
  − .470, .121, .004
 +.108   (.025) (.013) (.031) (.018)
  24/20*/18   + .531, .156, .010
  − .469, .126, .005
 +.098   (.035) (.011) (.041) (.026)
   PLAY W      G     BG     EQUITY VOTES CL DMP GG GS
  24/21, 24/20*   + .537, .164, .011
  − .463, .114, .004
 +.131   (.005)
  24/20*, 13/10   + .532, .172, .012
  − .468, .118, .005
 +.124   RDB (.007) (.012) (.020)
   PLAY W      G     BG     EQUITY VOTES CL DMP GG GS
  24/20*(2), 13/9(2)   + .630, .205, .013
  − .370, .068, .002
 +.409   RB
  24/20*(2), 8/4(2)   + .611, .218, .018
  − .389, .077, .002
 +.378   D (.031) (.040) (.014) (.056)
   PLAY W      G     BG     EQUITY VOTES CL DMP GG GS
  24/23, 13/8   + .443, .119, .005
  − .557, .176, .007
 −.173   DB
  13/8, 6/5   + .436, .118, .005
  − .564, .179, .010
 −.195   R (.022) (.014) (.016) (.021)
  13/7   + .427, .121, .005
  − .573, .181, .010
 −.210   (.037) (.030) (.027) (.041)
  24/18   + .432, .105, .005
  − .568, .185, .007
 −.219   (.046) (.021) (.049) (.040)
   PLAY W      G     BG     EQUITY VOTES CL DMP GG GS
  24/22, 13/8   + .440, .116, .005
  − .560, .175, .007
 −.180   RDB (.014)
  13/11, 13/8   + .436, .127, .006
  − .564, .183, .009
 −.187   (.006) (.007) (.024)
  13/8, 6/4   + .433, .120, .005
  − .567, .179, .009
 −.195   (.015) (.013) (.018) (.021)
   PLAY W      G     BG     EQUITY VOTES CL DMP GG GS
  8/3, 6/3   + .455, .139, .007
  − .545, .177, .008
 −.129   RB (.004)
  24/21, 13/8   + .451, .118, .006
  − .549, .171, .006
 −.152   D (.022) (.008) (.050)
   PLAY W      G     BG     EQUITY VOTES CL DMP GG GS
  24/20*, 13/8   + .537, .172, .012
  − .463, .117, .004
 +.136   RB
  24/20*/15   + .536, .156, .010
  − .464, .125, .005
 +.109   D (.028) (.001) (.032) (.018)
   PLAY W      G     BG     EQUITY VOTES CL DMP GG GS
  13/3(2)   + .465, .150, .010
  − .535, .170, .007
 −.088   RDB
   PLAY W      G     BG     EQUITY VOTES CL DMP GG GS
  13/7, 8/7   + .466, .131, .006
  − .534, .161, .007
 −.099   RDB
   PLAY W      G     BG     EQUITY VOTES CL DMP GG GS
  24/22, 13/7   + .435, .119, .005
  − .565, .179, .008
 −.193   RB (.013) (.002)
  24/18, 13/11   + .442, .113, .005
  − .558, .189, .008
 −.195   D (.001) (.005)
  13/5   + .429, .123, .005
  − .571, .180, .010
 −.204   (.010) (.025) (.006) (.014)
  24/16   + .435, .105, .005
  − .565, .185, .007
 −.212   (.019) (.013) (.029) (.011)
  13/11, 13/7   + .429, .124, .006
  − .571, .189, .012
 −.213   (.020) (.026) (.006) (.031)
  24/22, 24/18   + .433, .105, .005
  − .567, .188, .007
 −.219   (.025) (.018) (.034) (.022)
   PLAY W      G     BG     EQUITY VOTES CL DMP GG GS
  24/15   + .450, .107, .005
  − .550, .179, .006
 −.173   DB (.013)
  24/21, 13/7   + .442, .121, .006
  − .558, .180, .009
 −.177   R (.004) (.016) (.018)
  24/21, 24/18   + .444, .105, .005
  − .556, .181, .007
 −.191   (.018) (.013) (.030) (.017)
  24/18, 13/10   + .439, .115, .005
  − .561, .184, .009
 −.195   (.022) (.023) (.019) (.034)
  13/4   + .429, .124, .006
  − .571, .184, .009
 −.205   (.031) (.042) (.020) (.052)
  13/10, 13/7   + .425, .126, .006
  − .575, .189, .013
 −.221   (.047) (.050) (.026) (.071)
   PLAY W      G     BG     EQUITY VOTES CL DMP GG GS
  24/20*/14*   + .594, .210, .017
  − .406, .093, .003
 +.319   RDB
   PLAY W      G     BG     EQUITY VOTES CL DMP GG GS
  24/13   + .476, .109, .005
  − .524, .163, .005
 −.103   RDB
   PLAY W      G     BG     EQUITY VOTES CL DMP GG GS
  24/18(2), 13/7(2)   + .615, .146, .005
  − .385, .081, .002
 +.298   RDB

Summary

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

(+.402) 24/20*(2), 13/9(2) +.409 × 1  =   +.409
(+.327) 24/20*, 6/4(2) +.334 × 1  =   +.334
(+.313) 24/20*/14* +.319 × 2  =   +.639
(+.292) 24/18(2), 13/7(2) +.298 × 1  =   +.298
(+.133) 24/21(2), 8/5(2) +.139 × 1  =   +.139
(+.130) 24/20*, 13/8 +.136 × 2  =   +.273
(+.127) 24/20*, 13/11 +.134 × 2  =   +.268
(+.124) 24/21, 24/20* +.131 × 2  =   +.262
(+.097) 24/23, 24/20* +.104 × 2  =   +.207
(+.084) 24/20* +.091 × 1  =   +.091
(+.084) 24/20* +.091 × 2  =   +.182
(−.095) 13/3(2) −.088 × 1  =   −.088
(−.106) 13/7, 8/7 −.099 × 2  =   −.199
(−.110) 24/13 −.103 × 2  =   −.206
(−.136) 8/3, 6/3 −.129 × 2  =   −.259
(−.168) 24/21, 13/11 −.162 × 2  =   −.323
(−.179) 24/23, 13/11 −.172 × 2  =   −.344
(−.180) 24/23, 13/8 −.173 × 2  =   −.346
(−.180) 24/15 −.173 × 2  =   −.347
(−.187) 24/22, 13/8 −.180 × 2  =   −.361
(−.200) 24/22, 13/7 −.193 × 2  =   −.386
  ———
  White's Average Equity +.242  ÷  36  =  +.007

 

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