Replies to 24/18, 13/10

Best
Nearly Best
Pretty Good
Not So Good
Here are White's best replies after Red opens 24/18, 13/10.

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)   + .581, .179, .009
  − .419, .111, .005
 +.233   RDBC
  8/7*/5, 6/5   + .570, .180, .009
  − .430, .114, .005
 +.210   (.024) (.022) (.020) (.027)
  24/23, 8/7*, 6/5(2)   + .569, .175, .008
  − .431, .116, .005
 +.199   (.034) (.024) (.032) (.035)
   PLAY W      G     BG     EQUITY VOTES CL DMP GG GS
  13/11, 8/7*   + .470, .135, .006
  − .530, .160, .010
 −.088   RDBC (.017)
  24/22, 8/7*   + .468, .124, .005
  − .532, .149, .007
 −.092   (.004) (.005) (.027)
   PLAY W      G     BG     EQUITY VOTES CL DMP GG GS
  13/11(2), 6/4(2)   + .513, .142, .006
  − .487, .123, .005
 +.046   RBC (.078)
  24/22(2), 6/4(2)   + .502, .120, .004
  − .498, .092, .003
 +.032   (.014) (.023) (.066) (.040)
  24/20(2)   + .495, .093, .002
  − .505, .066, .002
 +.017   D (.029) (.037) (.135)
   PLAY W      G     BG     EQUITY VOTES CL DMP GG GS
  8/5, 6/5   + .480, .129, .005
  − .520, .129, .005
 −.040   RDBC
  24/21, 8/7*   + .471, .126, .005
  − .529, .145, .007
 −.079   (.038) (.019) (.024) (.051)
   PLAY W      G     BG     EQUITY VOTES CL DMP GG GS
  24/22, 24/21   + .437, .103, .004
  − .563, .153, .006
 −.178   (.003) (.012)
  24/21, 13/11   + .436, .108, .004
  − .564, .159, .008
 −.183   (.005) (.005) (.003) (.015)
  24/22, 13/10   + .432, .103, .004
  − .568, .149, .006
 −.184   RB (.006) (.012) (.022) (.001)
  6/1*   + .428, .115, .004
  − .572, .155, .008
 −.188   D (.010) (.020) (.006) (.023)
  24/21, 6/4   + .438, .108, .004
  − .562, .169, .009
 −.190   (.012) (.031)
  13/8   + .430, .109, .004
  − .570, .157, .007
 −.191   C (.013) (.016) (.013) (.022)
  13/10, 6/4   + .432, .112, .004
  − .568, .167, .011
 −.197   (.020) (.012) (.004) (.038)
  13/11, 8/5   + .428, .115, .004
  − .572, .169, .011
 −.206   (.028) (.021) (.007) (.051)
  24/22, 8/5   + .428, .109, .004
  − .572, .167, .008
 −.206   (.028) (.021) (.018) (.046)
  24/22, 6/3   + .424, .106, .004
  − .576, .166, .008
 −.216   (.038) (.029) (.031) (.053)
  24/21, 8/6   + .417, .099, .003
  − .583, .155, .006
 −.224   (.047) (.042) (.061) (.043)
   PLAY W      G     BG     EQUITY VOTES CL DMP GG GS
  13/7*(2)   + .551, .163, .007
  − .449, .116, .004
 +.152   RBC (.031) (.012)
  13/7*, 8/5(2)   + .536, .193, .010
  − .464, .129, .007
 +.140   (.013) (.030) (.068)
  13/7*, 6/3(2)   + .534, .175, .008
  − .466, .125, .006
 +.120   (.032) (.034) (.041) (.064)
  24/21(2), 6/3(2)   + .518, .118, .004
  − .482, .077, .002
 +.078   (.074) (.067) (.188)
   PLAY W      G     BG     EQUITY VOTES CL DMP GG GS
  24/20, 8/7*   + .475, .126, .005
  − .525, .144, .007
 −.070   RB (.024)
  13/9, 8/7*   + .473, .139, .006
  − .527, .162, .010
 −.080   DC (.009) (.002) (.038)
   PLAY W      G     BG     EQUITY VOTES CL DMP GG GS
  13/7*   + .479, .136, .006
  − .521, .147, .007
 −.053   RB (.008)
  8/4, 6/4   + .472, .129, .005
  − .528, .135, .006
 −.064   DC (.011) (.015) (.029)
   PLAY W      G     BG     EQUITY VOTES CL DMP GG GS
  24/21, 13/9   + .439, .112, .005
  − .561, .158, .007
 −.170   RC (.005)
  24/20, 13/10   + .438, .105, .004
  − .562, .154, .007
 −.176   B (.006) (.002) (.016)
  24/21, 24/20   + .431, .104, .005
  − .569, .158, .006
 −.192   (.023) (.016) (.032) (.022)
  8/1*   + .420, .117, .004
  − .580, .162, .009
 −.210   D (.040) (.038) (.028) (.053)
  13/10, 8/4   + .424, .117, .005
  − .576, .173, .012
 −.215   (.045) (.031) (.020) (.067)
  13/6   + .419, .108, .004
  − .581, .161, .008
 −.219   (.049) (.041) (.048) (.054)
   PLAY W      G     BG     EQUITY VOTES CL DMP GG GS
  24/20(2), 13/9(2)   + .553, .114, .003
  − .447, .057, .002
 +.165   RDBC
   PLAY W      G     BG     EQUITY VOTES CL DMP GG GS
  13/7*   + .479, .136, .006
  − .521, .147, .007
 −.053   RB
  8/7*, 6/1*   + .472, .142, .005
  − .528, .159, .009
 −.078   DC (.024) (.015) (.003) (.040)
   PLAY W      G     BG     EQUITY VOTES CL DMP GG GS
  24/22, 6/1*   + .449, .120, .004
  − .551, .145, .007
 −.129   R (.004)
  24/22, 13/8   + .449, .114, .004
  − .551, .143, .006
 −.133   BC (.004) (.013)
  13/8, 6/4   + .438, .112, .004
  − .562, .153, .007
 −.167   D (.038) (.021) (.037) (.041)
   PLAY W      G     BG     EQUITY VOTES CL DMP GG GS
  8/3, 6/3   + .456, .128, .005
  − .544, .145, .007
 −.107   RBC
  24/21, 13/8   + .449, .110, .004
  − .551, .140, .005
 −.133   (.027) (.014) (.051) (.003)
  24/21, 6/1*   + .448, .118, .004
  − .552, .148, .007
 −.137   D (.030) (.016) (.036) (.022)
   PLAY W      G     BG     EQUITY VOTES CL DMP GG GS
  24/15*   + .526, .128, .006
  − .474, .121, .004
 +.060   RDBC
   PLAY W      G     BG     EQUITY VOTES CL DMP GG GS
  8/3(2), 6/1*(2)   + .535, .237, .008
  − .465, .113, .005
 +.197   RDBC (.005) (.010)
  13/8(2), 6/1*(2)   + .537, .209, .007
  − .463, .111, .004
 +.175   (.022) (.053)
   PLAY W      G     BG     EQUITY VOTES CL DMP GG GS
  13/7*, 8/7   + .528, .148, .006
  − .472, .123, .005
 +.083   RDBC
   PLAY W      G     BG     EQUITY VOTES CL DMP GG GS
  24/22, 13/7*   + .491, .137, .006
  − .509, .138, .006
 −.019   DBC (.006)
  13/11, 13/7*   + .488, .144, .007
  − .512, .151, .009
 −.034   R (.016) (.007) (.034)
   PLAY W      G     BG     EQUITY VOTES CL DMP GG GS
  24/15*   + .526, .128, .006
  − .474, .121, .004
 +.060   RDBC
   PLAY W      G     BG     EQUITY VOTES CL DMP GG GS
  24/20, 13/7*   + .498, .138, .006
  − .502, .131, .005
 +.005   RDBC (.007)
  13/9, 13/7*   + .489, .151, .007
  − .511, .152, .009
 −.024   (.029) (.018) (.061)
   PLAY W      G     BG     EQUITY VOTES CL DMP GG GS
  13/7*, 6/1*   + .499, .160, .006
  − .501, .141, .007
 +.017   RDBC
  13/8, 13/7*   + .490, .142, .007
  − .510, .141, .007
 −.020   (.037) (.019) (.055) (.020)
   PLAY W      G     BG     EQUITY VOTES CL DMP GG GS
  24/18(2), 13/7*(2)   + .641, .153, .006
  − .359, .070, .002
 +.369   RDBC (.094)
  13/7*/1*(2)   + .586, .255, .009
  − .414, .106, .004
 +.328   (.042) (.109) (.181)

Summary

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

(+.375) 24/18(2), 13/7*(2) +.369 × 1  =   +.369
(+.239) 8/7*(2), 6/5(2) +.233 × 1  =   +.233
(+.203) 8/3(2), 6/1*(2) +.197 × 1  =   +.197
(+.171) 24/20(2), 13/9(2) +.165 × 1  =   +.165
(+.158) 13/7*(2) +.152 × 1  =   +.152
(+.089) 13/7*, 8/7 +.083 × 2  =   +.166
(+.065) 24/15* +.060 × 2  =   +.120
(+.065) 24/15* +.060 × 2  =   +.120
(+.052) 13/11(2), 6/4(2) +.046 × 1  =   +.046
(+.022) 13/7*, 6/1* +.017 × 2  =   +.033
(+.011) 24/20, 13/7* +.005 × 2  =   +.011
(−.013) 24/22, 13/7* −.019 × 2  =   −.037
(−.035) 8/5, 6/5 −.040 × 2  =   −.081
(−.048) 13/7* −.053 × 2  =   −.107
(−.048) 13/7* −.053 × 2  =   −.107
(−.065) 24/20, 8/7* −.070 × 2  =   −.141
(−.083) 13/11, 8/7* −.088 × 2  =   −.177
(−.101) 8/3, 6/3 −.107 × 2  =   −.214
(−.124) 24/22, 6/1* −.129 × 2  =   −.259
(−.164) 24/21, 13/9 −.170 × 2  =   −.339
(−.172) 24/22, 24/21 −.178 × 2  =   −.355
  ———
  White's Average Equity −.204  ÷  36  =  −.006

 

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