Replies to 24/15

Best
Nearly Best
Pretty Good
Not So Good
Here are White's best replies after Red opens 24/15.

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
  24/22, 6/5(2)   + .517, .142, .005
  − .483, .110, .004
 +.066   (.009)
  8/7(2), 6/5(2)   + .514, .149, .005
  − .486, .120, .006
 +.056   RB (.010) (.005) (.026)
  24/23, 6/5(3)   + .505, .139, .004
  − .495, .112, .005
 +.037   (.029) (.023) (.037) (.028)
  24/23, 8/7, 6/5(2)   + .502, .147, .005
  − .498, .127, .006
 +.024   (.042) (.029) (.027) (.062)
  24/23(2), 6/5(2)   + .500, .134, .004
  − .500, .110, .005
 +.023   (.042) (.034) (.059) (.033)
   PLAY W      G     BG     EQUITY VOTES CL DMP GG GS
  13/10*   + .508, .142, .006
  − .492, .131, .006
 +.027   RB
   PLAY W      G     BG     EQUITY VOTES CL DMP GG GS
  13/11(2), 6/4(2)   + .528, .157, .006
  − .472, .118, .006
 +.096   RB (.067)
  24/22(2), 6/4(2)   + .516, .133, .004
  − .484, .086, .003
 +.080   (.016) (.023) (.073) (.027)
  24/20(2)   + .505, .104, .002
  − .495, .061, .002
 +.053   (.042) (.046) (.152)
   PLAY W      G     BG     EQUITY VOTES CL DMP GG GS
  24/23, 13/10*   + .512, .143, .005
  − .488, .123, .005
 +.046   RB (.005)
  13/10*/9   + .510, .149, .006
  − .490, .132, .006
 +.036   (.009) (.005) (.024)
  8/5, 6/5   + .494, .144, .005
  − .506, .119, .006
 +.013   (.033) (.036) (.040) (.029)
   PLAY W      G     BG     EQUITY VOTES CL DMP GG GS
  24/22, 13/10*   + .519, .143, .005
  − .481, .121, .005
 +.061   RB (.015)
  13/11, 13/10*   + .517, .152, .007
  − .483, .132, .007
 +.054   (.007) (.005) (.027)
  13/10*/8   + .507, .137, .006
  − .493, .132, .005
 +.021   (.040) (.023) (.049) (.045)
   PLAY W      G     BG     EQUITY VOTES CL DMP GG GS
  13/10*(2), 6/3(2)   + .594, .200, .010
  − .406, .103, .004
 +.291   RB (.021)
  13/10*(2), 8/5(2)   + .583, .209, .009
  − .417, .108, .005
 +.271   (.020) (.024) (.006) (.053)
  24/21(2), 13/10*(2)   + .584, .162, .006
  − .416, .083, .003
 +.252   (.040) (.020) (.097)
  13/10*, 8/5(3)   + .572, .206, .009
  − .428, .111, .005
 +.243   (.049) (.045) (.034) (.082)
   PLAY W      G     BG     EQUITY VOTES CL DMP GG GS
  24/23, 13/9   + .450, .119, .004
  − .550, .133, .006
 −.117   RB (.002) (.010) (.004)
  13/9, 6/5   + .451, .123, .004
  − .549, .149, .010
 −.130   (.013) (.034)
  24/23, 24/20   + .442, .102, .004
  − .558, .123, .005
 −.139   (.022) (.019) (.061)
  24/20, 6/5   + .447, .112, .004
  − .553, .150, .007
 −.148   (.032) (.009) (.030) (.045)
  13/8   + .435, .110, .004
  − .565, .143, .007
 −.166   (.050) (.032) (.058) (.053)
   PLAY W      G     BG     EQUITY VOTES CL DMP GG GS
  8/4, 6/4   + .484, .141, .005
  − .516, .123, .006
 −.016   RB
   PLAY W      G     BG     EQUITY VOTES CL DMP GG GS
  24/20, 13/10*   + .523, .140, .006
  − .477, .115, .004
 +.071   R (.037)
  13/10*, 13/9   + .520, .162, .007
  − .480, .131, .007
 +.070   B (.002) (.006) (.038)
   PLAY W      G     BG     EQUITY VOTES CL DMP GG GS
  24/20(2), 13/9(2)   + .573, .136, .003
  − .427, .051, .002
 +.232   RB
   PLAY W      G     BG     EQUITY VOTES CL DMP GG GS
  24/23, 13/8   + .451, .114, .004
  − .549, .128, .005
 −.114   RB
  13/8, 6/5   + .447, .117, .004
  − .553, .143, .008
 −.136   (.022) (.009) (.001) (.038)
  24/18   + .446, .096, .003
  − .554, .128, .005
 −.142   (.029) (.011) (.046) (.011)
  13/7   + .435, .117, .004
  − .565, .141, .007
 −.158   (.044) (.033) (.025) (.058)
   PLAY W      G     BG     EQUITY VOTES CL DMP GG GS
  24/22, 13/8   + .456, .113, .004
  − .544, .129, .005
 −.106   RB
  24/22, 6/1*   + .437, .111, .003
  − .563, .128, .006
 −.147   (.041) (.038) (.042) (.036)
  13/8, 6/4   + .440, .117, .004
  − .560, .147, .008
 −.154   (.047) (.031) (.022) (.067)
   PLAY W      G     BG     EQUITY VOTES CL DMP GG GS
  13/10*, 13/8   + .517, .150, .006
  − .483, .127, .005
 +.058   RB
  13/10*, 6/1*   + .499, .156, .005
  − .501, .138, .007
 +.014   (.044) (.035) (.024) (.059)
   PLAY W      G     BG     EQUITY VOTES CL DMP GG GS
  24/20, 13/8   + .458, .113, .005
  − .542, .126, .005
 −.098   R (.005)
  24/20, 6/1*   + .452, .114, .003
  − .548, .131, .006
 −.115   B (.017) (.011) (.012) (.021)
  13/9, 13/8   + .449, .124, .004
  − .551, .135, .007
 −.116   (.018) (.018) (.036)
   PLAY W      G     BG     EQUITY VOTES CL DMP GG GS
  8/3(2), 6/1*(2)   + .544, .235, .006
  − .456, .099, .004
 +.225   RB
   PLAY W      G     BG     EQUITY VOTES CL DMP GG GS
  13/7, 8/7   + .474, .126, .004
  − .526, .128, .005
 −.056   RB
   PLAY W      G     BG     EQUITY VOTES CL DMP GG GS
  13/5   + .446, .124, .004
  − .554, .142, .008
 −.128   B (.009) (.019)
  24/22, 13/7   + .444, .119, .004
  − .556, .138, .006
 −.134   (.006) (.014) (.015) (.017)
  24/18, 13/11   + .451, .103, .003
  − .549, .137, .006
 −.135   R (.007) (.034)
  24/22, 24/18   + .447, .098, .004
  − .553, .141, .005
 −.150   (.022) (.007) (.052) (.015)
  24/18, 8/6   + .437, .096, .003
  − .563, .137, .005
 −.168   (.040) (.027) (.075) (.027)
  24/16   + .437, .103, .003
  − .563, .148, .006
 −.174   (.046) (.028) (.061) (.050)
  13/7, 6/4   + .434, .118, .004
  − .566, .155, .010
 −.175   (.048) (.033) (.038) (.071)
   PLAY W      G     BG     EQUITY VOTES CL DMP GG GS
  24/18, 13/10*   + .519, .130, .005
  − .481, .125, .005
 +.044   RB
  13/10*, 13/7   + .498, .149, .006
  − .502, .139, .007
 +.005   (.038) (.041) (.004) (.069)
   PLAY W      G     BG     EQUITY VOTES CL DMP GG GS
  24/18, 13/9   + .465, .114, .004
  − .535, .131, .006
 −.088   RB (.017)
  8/2, 6/2   + .452, .135, .004
  − .548, .136, .006
 −.099   (.011) (.026) (.037)
  24/20, 13/7   + .447, .119, .004
  − .553, .133, .006
 −.121   (.034) (.036) (.042) (.041)
   PLAY W      G     BG     EQUITY VOTES CL DMP GG GS
  24/13   + .475, .098, .003
  − .525, .117, .003
 −.071   RB (.008)
  24/18, 13/8   + .468, .108, .004
  − .532, .124, .004
 −.081   (.010) (.013) (.027)
   PLAY W      G     BG     EQUITY VOTES CL DMP GG GS
  24/18(2), 13/7(2)   + .619, .136, .003
  − .381, .056, .002
 +.319   RB

Summary

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

(+.312) 24/18(2), 13/7(2) +.319 × 1  =   +.319
(+.284) 13/10*(2), 6/3(2) +.291 × 1  =   +.291
(+.225) 24/20(2), 13/9(2) +.232 × 1  =   +.232
(+.218) 8/3(2), 6/1*(2) +.225 × 1  =   +.225
(+.089) 13/11(2), 6/4(2) +.096 × 1  =   +.096
(+.064) 24/20, 13/10* +.071 × 2  =   +.143
(+.059) 24/22, 6/5(2) +.066 × 1  =   +.066
(+.054) 24/22, 13/10* +.061 × 2  =   +.122
(+.051) 13/10*, 13/8 +.058 × 2  =   +.116
(+.038) 24/23, 13/10* +.046 × 2  =   +.091
(+.036) 24/18, 13/10* +.044 × 2  =   +.087
(+.020) 13/10* +.027 × 2  =   +.054
(−.023) 8/4, 6/4 −.016 × 2  =   −.032
(−.063) 13/7, 8/7 −.056 × 2  =   −.112
(−.078) 24/13 −.071 × 2  =   −.142
(−.095) 24/18, 13/9 −.088 × 2  =   −.175
(−.105) 24/20, 13/8 −.098 × 2  =   −.196
(−.113) 24/22, 13/8 −.106 × 2  =   −.212
(−.121) 24/23, 13/8 −.114 × 2  =   −.227
(−.124) 24/23, 13/9 −.117 × 2  =   −.233
(−.135) 13/5 −.128 × 2  =   −.256
  ———
  White's Average Equity +.256  ÷  36  =  +.007

 

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