Replies to 24/18, 13/11

Best
Nearly Best
Pretty Good
Not So Good
Here are White's best replies after Red opens 24/18, 13/11.

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)   + .577, .177, .008
  − .423, .110, .005
 +.224   RDBC
  8/7*/5, 6/5   + .565, .179, .008
  − .435, .113, .005
 +.199   (.025) (.025) (.019) (.031)
  24/23, 8/7*, 6/5(2)   + .566, .177, .008
  − .434, .116, .005
 +.196   (.029) (.022) (.022) (.034)
   PLAY W      G     BG     EQUITY VOTES CL DMP GG GS
  13/11, 8/7*   + .473, .134, .006
  − .527, .157, .009
 −.081   RDBC (.006)
  24/22, 8/7*   + .468, .127, .005
  − .532, .149, .007
 −.088   (.007) (.010) (.024)
   PLAY W      G     BG     EQUITY VOTES CL DMP GG GS
  13/11(2), 6/4(2)   + .512, .142, .006
  − .488, .119, .005
 +.049   RDBC (.088)
  24/20(2)   + .502, .097, .003
  − .498, .065, .002
 +.037   (.011) (.020) (.110)
  24/22(2), 6/4(2)   + .501, .121, .004
  − .499, .090, .003
 +.034   (.014) (.022) (.065) (.051)
  24/20, 6/4(2)   + .495, .125, .005
  − .505, .115, .004
 +.000   (.049) (.035) (.070) (.114)
   PLAY W      G     BG     EQUITY VOTES CL DMP GG GS
  8/5, 6/5   + .480, .129, .005
  − .520, .124, .005
 −.036   RDBC
  24/21, 8/7*   + .474, .125, .005
  − .526, .139, .007
 −.067   (.031) (.011) (.019) (.040)
   PLAY W      G     BG     EQUITY VOTES CL DMP GG GS
  24/21, 6/4   + .443, .108, .004
  − .557, .152, .008
 −.162   (.019)
  24/22, 24/21   + .441, .099, .004
  − .559, .141, .006
 −.162   DB (.001) (.004) (.023)
  24/21, 13/11   + .438, .107, .004
  − .562, .149, .007
 −.170   RC (.008) (.011) (.013) (.022)
  13/8   + .433, .112, .004
  − .567, .154, .007
 −.179   (.017) (.019) (.012) (.041)
  24/22, 13/10   + .433, .105, .004
  − .567, .148, .007
 −.179   (.018) (.019) (.026) (.029)
  6/1*   + .430, .116, .004
  − .570, .152, .008
 −.181   (.019) (.026) (.012) (.044)
  13/11, 8/5   + .431, .117, .004
  − .569, .162, .010
 −.190   (.028) (.024) (.007) (.063)
  13/10, 6/4   + .433, .112, .004
  − .567, .163, .011
 −.191   (.029) (.019) (.011) (.059)
  24/21, 8/6   + .426, .099, .003
  − .574, .142, .006
 −.194   (.032) (.034) (.053) (.032)
  24/22, 8/5   + .429, .107, .004
  − .571, .163, .008
 −.202   (.040) (.028) (.031) (.067)
  24/22, 6/3   + .425, .104, .004
  − .575, .160, .007
 −.209   (.047) (.035) (.043) (.068)
   PLAY W      G     BG     EQUITY VOTES CL DMP GG GS
  13/7*(2)   + .549, .164, .008
  − .451, .116, .004
 +.149   RBC (.020) (.026)
  13/7*, 8/5(2)   + .534, .189, .009
  − .466, .128, .007
 +.132   (.017) (.030) (.078)
  13/7*, 6/3(2)   + .535, .178, .009
  − .465, .124, .006
 +.126   (.023) (.028) (.021) (.070)
  24/21(2), 6/3(2)   + .522, .118, .004
  − .478, .077, .002
 +.087   (.062) (.054) (.167)
   PLAY W      G     BG     EQUITY VOTES CL DMP GG GS
  24/20, 8/7*   + .475, .127, .005
  − .525, .138, .006
 −.062   RDB (.025)
  13/9, 8/7*   + .474, .140, .006
  − .526, .156, .009
 −.071   C (.008) (.001) (.036)
   PLAY W      G     BG     EQUITY VOTES CL DMP GG GS
  13/7*   + .481, .135, .006
  − .519, .145, .007
 −.049   RBC (.014)
  8/4, 6/4   + .473, .130, .005
  − .527, .131, .006
 −.055   D (.005) (.015) (.025)
   PLAY W      G     BG     EQUITY VOTES CL DMP GG GS
  24/21, 13/9   + .445, .114, .004
  − .555, .149, .007
 −.148   RDBC (.024)
  24/21, 24/20   + .444, .099, .004
  − .556, .136, .005
 −.150   (.002) (.002) (.032)
  24/20, 13/10   + .436, .105, .004
  − .564, .150, .007
 −.178   (.030) (.019) (.037) (.046)
  24/21, 8/4   + .432, .109, .004
  − .568, .158, .008
 −.190   (.042) (.026) (.037) (.068)
   PLAY W      G     BG     EQUITY VOTES CL DMP GG GS
  24/20(2), 13/9(2)   + .560, .120, .003
  − .440, .058, .002
 +.184   RDBC
   PLAY W      G     BG     EQUITY VOTES CL DMP GG GS
  13/7*   + .481, .135, .006
  − .519, .145, .007
 −.049   RB
  8/7*, 6/1*   + .472, .143, .005
  − .528, .156, .008
 −.072   DC (.023) (.018) (.002) (.040)
   PLAY W      G     BG     EQUITY VOTES CL DMP GG GS
  24/22, 6/1*   + .446, .121, .004
  − .554, .142, .006
 −.131   RB (.003) (.006)
  24/22, 13/8   + .447, .111, .004
  − .553, .140, .005
 −.135   C (.005) (.018)
  13/8, 6/4   + .440, .115, .004
  − .560, .151, .007
 −.158   D (.028) (.015) (.023) (.037)
   PLAY W      G     BG     EQUITY VOTES CL DMP GG GS
  8/3, 6/3   + .458, .128, .005
  − .542, .141, .006
 −.098   RBC (.002) (.025)
  24/21, 13/8   + .459, .111, .004
  − .541, .129, .005
 −.102   (.004) (.033)
  24/21, 6/1*   + .452, .119, .004
  − .548, .135, .006
 −.114   D (.016) (.014) (.029) (.025)
  13/5   + .444, .121, .004
  − .556, .147, .008
 −.141   (.044) (.029) (.042) (.066)
   PLAY W      G     BG     EQUITY VOTES CL DMP GG GS
  24/20, 6/1*   + .460, .119, .004
  − .540, .142, .006
 −.105   RDBC (.003)
  24/20, 13/8   + .454, .111, .004
  − .546, .134, .005
 −.117   (.012) (.013) (.029)
   PLAY W      G     BG     EQUITY VOTES CL DMP GG GS
  8/3(2), 6/1*(2)   + .535, .240, .008
  − .465, .114, .005
 +.199   RDBC (.003) (.014)
  13/8(2), 6/1*(2)   + .536, .204, .007
  − .464, .108, .004
 +.171   (.028) (.069)
   PLAY W      G     BG     EQUITY VOTES CL DMP GG GS
  13/7*, 8/7   + .527, .149, .006
  − .473, .122, .004
 +.083   RDBC
   PLAY W      G     BG     EQUITY VOTES CL DMP GG GS
  24/22, 13/7*   + .489, .138, .006
  − .511, .138, .006
 −.021   BC (.013)
  13/11, 13/7*   + .489, .146, .007
  − .512, .149, .008
 −.028   RD (.007) (.002) (.024)
  13/7*/5   + .477, .136, .006
  − .523, .148, .008
 −.061   (.040) (.025) (.043) (.045)
   PLAY W      G     BG     EQUITY VOTES CL DMP GG GS
  24/21, 13/7*   + .496, .140, .006
  − .504, .131, .006
 +.001   RBC
  13/10, 13/7*   + .486, .146, .007
  − .514, .150, .009
 −.034   D (.035) (.021) (.007) (.058)
   PLAY W      G     BG     EQUITY VOTES CL DMP GG GS
  24/14*   + .532, .128, .006
  − .468, .118, .004
 +.076   RDBC
   PLAY W      G     BG     EQUITY VOTES CL DMP GG GS
  13/7*, 6/1*   + .500, .162, .006
  − .500, .138, .007
 +.022   RDBC
  13/8, 13/7*   + .491, .143, .007
  − .509, .140, .007
 −.014   (.036) (.017) (.054) (.020)
   PLAY W      G     BG     EQUITY VOTES CL DMP GG GS
  24/18(2), 13/7*(2)   + .635, .165, .006
  − .365, .073, .002
 +.367   RDBC (.071)
  13/7*/1*(2)   + .582, .254, .009
  − .418, .106, .004
 +.316   (.051) (.108) (.174)

Summary

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

(+.377) 24/18(2), 13/7*(2) +.367 × 1  =   +.367
(+.234) 8/7*(2), 6/5(2) +.224 × 1  =   +.224
(+.209) 8/3(2), 6/1*(2) +.199 × 1  =   +.199
(+.194) 24/20(2), 13/9(2) +.184 × 1  =   +.184
(+.158) 13/7*(2) +.149 × 1  =   +.149
(+.093) 13/7*, 8/7 +.083 × 2  =   +.166
(+.085) 24/14* +.076 × 2  =   +.151
(+.058) 13/11(2), 6/4(2) +.049 × 1  =   +.049
(+.032) 13/7*, 6/1* +.022 × 2  =   +.044
(+.011) 24/21, 13/7* +.001 × 2  =   +.003
(−.011) 24/22, 13/7* −.021 × 2  =   −.041
(−.027) 8/5, 6/5 −.036 × 2  =   −.073
(−.040) 13/7* −.049 × 2  =   −.099
(−.040) 13/7* −.049 × 2  =   −.099
(−.053) 24/20, 8/7* −.062 × 2  =   −.125
(−.071) 13/11, 8/7* −.081 × 2  =   −.162
(−.088) 8/3, 6/3 −.098 × 2  =   −.196
(−.095) 24/20, 6/1* −.105 × 2  =   −.209
(−.121) 24/22, 6/1* −.131 × 2  =   −.261
(−.138) 24/21, 13/9 −.148 × 2  =   −.296
(−.152) 24/21, 6/4 −.162 × 2  =   −.323
  ———
  White's Average Equity −.347  ÷  36  =  −.010

 

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