Replies to 24/13

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

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)   + .503, .143, .004
  − .497, .118, .005
 +.029   RDBC (.009)
  24/22, 6/5(2)   + .499, .134, .004
  − .501, .110, .004
 +.022   (.008) (.007) (.025)
  24/23, 6/5(3)   + .492, .136, .004
  − .508, .115, .005
 +.005   (.024) (.020) (.033) (.025)
  24/23, 8/7, 6/5(2)   + .492, .141, .004
  − .508, .128, .006
 −.004   (.033) (.021) (.025) (.049)
  24/23(2), 6/5(2)   + .484, .128, .004
  − .516, .107, .005
 −.012   (.041) (.038) (.067) (.025)
  8/5, 6/5   + .482, .140, .004
  − .518, .120, .006
 −.018   (.047) (.041) (.047) (.055)
   PLAY W      G     BG     EQUITY VOTES CL DMP GG GS
  13/11, 6/5   + .453, .122, .004
  − .547, .150, .009
 −.128   RDBC (.021)
  24/23, 13/11   + .446, .115, .004
  − .554, .133, .006
 −.129   (.001) (.014) (.029)
  24/21   + .432, .099, .003
  − .568, .120, .005
 −.160   (.032) (.043) (.088) (.003)
  13/10   + .433, .111, .004
  − .567, .139, .007
 −.166   (.038) (.040) (.062) (.038)
  24/22, 6/5   + .436, .108, .003
  − .564, .153, .007
 −.176   (.049) (.033) (.062) (.059)
   PLAY W      G     BG     EQUITY VOTES CL DMP GG GS
  13/11(2), 6/4(2)   + .526, .158, .005
  − .474, .118, .006
 +.091   RDBC (.054)
  24/22, 13/11, 6/4(2)   + .512, .149, .005
  − .488, .111, .005
 +.062   (.028) (.027) (.046) (.066)
  24/22(2), 6/4(2)   + .504, .124, .003
  − .496, .079, .003
 +.054   (.037) (.043) (.112) (.018)
  24/20(2)   + .489, .095, .002
  − .511, .054, .002
 +.019   (.072) (.074) (.200)
   PLAY W      G     BG     EQUITY VOTES CL DMP GG GS
  8/5, 6/5   + .482, .140, .004
  − .518, .120, .006
 −.018   RDBC
   PLAY W      G     BG     EQUITY VOTES CL DMP GG GS
  24/21, 13/11   + .451, .113, .004
  − .549, .128, .005
 −.114   RDBC (.011)
  13/11, 13/10   + .444, .124, .004
  − .556, .140, .008
 −.131   (.017) (.015) (.003) (.039)
  24/22, 13/10   + .444, .111, .004
  − .556, .130, .005
 −.134   (.019) (.015) (.031) (.019)
  13/11, 8/5   + .445, .125, .004
  − .555, .152, .009
 −.143   (.029) (.013) (.062)
  13/10, 6/4   + .439, .117, .004
  − .561, .151, .009
 −.163   (.048) (.025) (.028) (.072)
  24/22, 24/21   + .434, .092, .003
  − .566, .123, .005
 −.164   (.049) (.034) (.086) (.024)
   PLAY W      G     BG     EQUITY VOTES CL DMP GG GS
  24/21(2), 13/10(2)   + .529, .123, .003
  − .471, .070, .002
 +.112   BC (.070) (.006)
  24/21(2), 6/3(2)   + .522, .116, .003
  − .478, .060, .002
 +.102   (.010) (.013) (.096)
  8/5(2), 6/3(2)   + .514, .173, .005
  − .486, .104, .005
 +.096   R (.016) (.030) (.105)
  24/21(2), 8/5(2)   + .507, .127, .003
  − .493, .062, .002
 +.079   D (.033) (.043) (.105) (.034)
  13/10(2), 6/3(2)   + .515, .157, .005
  − .485, .116, .005
 +.072   (.039) (.027) (.027) (.125)
   PLAY W      G     BG     EQUITY VOTES CL DMP GG GS
  24/23, 13/9   + .441, .114, .004
  − .559, .132, .006
 −.138   DBC (.004) (.011) (.002)
  13/9, 6/5   + .443, .118, .004
  − .557, .146, .009
 −.147   R (.010) (.027)
  24/23, 24/20   + .433, .096, .003
  − .567, .122, .005
 −.163   (.025) (.021) (.066)
  24/20, 6/5   + .441, .107, .003
  − .559, .148, .007
 −.163   (.026) (.004) (.027) (.035)
  13/8   + .429, .103, .003
  − .571, .136, .006
 −.179   (.041) (.028) (.059) (.036)
   PLAY W      G     BG     EQUITY VOTES CL DMP GG GS
  8/4, 6/4   + .472, .136, .004
  − .528, .121, .006
 −.043   RDBC
   PLAY W      G     BG     EQUITY VOTES CL DMP GG GS
  24/21, 13/9   + .448, .114, .004
  − .552, .124, .005
 −.115   RDB (.011)
  13/10, 13/9   + .443, .124, .004
  − .557, .132, .007
 −.125   (.010) (.010) (.026)
  24/20, 13/10   + .447, .110, .004
  − .553, .130, .005
 −.127   C (.012) (.002) (.020) (.014)
  24/21, 24/20   + .443, .095, .003
  − .557, .122, .004
 −.143   (.027) (.011) (.060) (.007)
   PLAY W      G     BG     EQUITY VOTES CL DMP GG GS
  24/20(2), 13/9(2)   + .564, .131, .003
  − .436, .048, .002
 +.211   RDBC
   PLAY W      G     BG     EQUITY VOTES CL DMP GG GS
  24/23, 13/8   + .440, .108, .003
  − .560, .125, .005
 −.138   C (.012)
  13/8, 6/5   + .440, .115, .003
  − .560, .138, .008
 −.148   RB (.010) (.001) (.027)
  24/18   + .437, .094, .003
  − .563, .133, .005
 −.166   D (.028) (.006) (.045) (.022)
  13/7   + .427, .111, .003
  − .573, .138, .007
 −.176   (.038) (.027) (.032) (.052)
   PLAY W      G     BG     EQUITY VOTES CL DMP GG GS
  13/11, 13/8   + .446, .118, .004
  − .554, .138, .007
 −.131   RDB (.027)
  24/22, 13/8   + .443, .104, .003
  − .557, .122, .004
 −.133   C (.002) (.006) (.034)
  13/8, 6/4   + .435, .112, .004
  − .565, .143, .007
 −.166   (.034) (.022) (.034) (.059)
  24/22, 6/1*   + .427, .106, .003
  − .573, .130, .006
 −.174   (.043) (.039) (.062) (.050)
  13/11, 6/1*   + .427, .115, .003
  − .573, .143, .008
 −.178   (.047) (.038) (.042) (.074)
   PLAY W      G     BG     EQUITY VOTES CL DMP GG GS
  8/3, 6/3   + .459, .130, .004
  − .541, .127, .006
 −.081   RBC (.011)
  24/21, 13/8   + .453, .106, .003
  − .547, .115, .004
 −.104   (.023) (.012) (.060)
  13/10, 13/8   + .444, .119, .004
  − .556, .133, .006
 −.129   (.048) (.030) (.052) (.054)
   PLAY W      G     BG     EQUITY VOTES CL DMP GG GS
  24/20, 13/8   + .453, .106, .004
  − .547, .121, .004
 −.109   RBC
  13/9, 13/8   + .441, .117, .004
  − .559, .128, .006
 −.133   (.024) (.025) (.003) (.040)
  24/20, 6/1*   + .443, .107, .003
  − .557, .124, .006
 −.133   D (.024) (.019) (.017) (.026)
  24/15   + .443, .096, .003
  − .557, .136, .005
 −.155   (.047) (.020) (.040) (.050)
   PLAY W      G     BG     EQUITY VOTES CL DMP GG GS
  8/3(2), 6/1*(2)   + .526, .209, .004
  − .474, .098, .004
 +.162   RDBC
   PLAY W      G     BG     EQUITY VOTES CL DMP GG GS
  13/7, 8/7   + .469, .120, .004
  − .531, .122, .005
 −.065   RDBC
   PLAY W      G     BG     EQUITY VOTES CL DMP GG GS
  24/18, 13/11   + .453, .104, .003
  − .547, .130, .005
 −.122   RDBC (.012)
  13/5   + .438, .118, .004
  − .562, .136, .007
 −.145   (.023) (.029) (.013) (.041)
  13/11, 13/7   + .439, .123, .004
  − .561, .149, .009
 −.152   (.030) (.027) (.065)
  24/22, 13/7   + .437, .113, .004
  − .563, .137, .006
 −.152   (.030) (.032) (.026) (.045)
  24/16   + .439, .096, .003
  − .561, .134, .005
 −.162   (.039) (.027) (.056) (.034)
   PLAY W      G     BG     EQUITY VOTES CL DMP GG GS
  24/18, 13/10   + .451, .104, .003
  − .549, .131, .005
 −.127   RDBC (.009)
  24/21, 13/7   + .443, .114, .004
  − .557, .132, .006
 −.134   (.007) (.015) (.003) (.018)
  24/15   + .443, .096, .003
  − .557, .136, .005
 −.155   (.028) (.015) (.039) (.026)
  13/10, 13/7   + .435, .123, .004
  − .565, .146, .009
 −.157   (.030) (.030) (.062)
  13/4   + .433, .116, .004
  − .567, .142, .008
 −.164   (.037) (.036) (.020) (.058)
   PLAY W      G     BG     EQUITY VOTES CL DMP GG GS
  8/2, 6/2   + .446, .128, .004
  − .554, .129, .006
 −.112   C (.013) (.020)
  24/18, 13/9   + .452, .106, .004
  − .548, .126, .005
 −.116   RDB (.004) (.031)
  24/20, 13/7   + .441, .114, .004
  − .559, .132, .006
 −.139   (.027) (.023) (.038) (.037)
  24/14   + .447, .095, .003
  − .553, .133, .005
 −.146   (.034) (.012) (.065) (.025)
   PLAY W      G     BG     EQUITY VOTES CL DMP GG GS
  24/13   + .464, .090, .002
  − .536, .115, .003
 −.098   RDBC (.010)
  24/18, 13/8   + .458, .101, .003
  − .542, .125, .004
 −.109   (.011) (.012) (.032)
  13/8, 13/7   + .437, .119, .004
  − .563, .132, .006
 −.142   (.044) (.054) (.005) (.089)
   PLAY W      G     BG     EQUITY VOTES CL DMP GG GS
  24/18(2), 13/7(2)   + .620, .131, .003
  − .380, .049, .002
 +.324   RDBC

Summary

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

(+.383) 24/18(2), 13/7(2) +.324 × 1  =   +.324
(+.271) 24/20(2), 13/9(2) +.211 × 1  =   +.211
(+.222) 8/3(2), 6/1*(2) +.162 × 1  =   +.162
(+.171) 24/21(2), 13/10(2) +.112 × 1  =   +.112
(+.150) 13/11(2), 6/4(2) +.091 × 1  =   +.091
(+.089) 8/7(2), 6/5(2) +.029 × 1  =   +.029
(+.042) 8/5, 6/5 −.018 × 2  =   −.036
(+.017) 8/4, 6/4 −.043 × 2  =   −.085
(−.005) 13/7, 8/7 −.065 × 2  =   −.129
(−.021) 8/3, 6/3 −.081 × 2  =   −.161
(−.038) 24/13 −.098 × 2  =   −.196
(−.049) 24/20, 13/8 −.109 × 2  =   −.218
(−.052) 8/2, 6/2 −.112 × 2  =   −.224
(−.055) 24/21, 13/11 −.114 × 2  =   −.229
(−.056) 24/21, 13/9 −.115 × 2  =   −.230
(−.063) 24/18, 13/11 −.122 × 2  =   −.245
(−.068) 24/18, 13/10 −.127 × 2  =   −.254
(−.068) 13/11, 6/5 −.128 × 2  =   −.255
(−.072) 13/11, 13/8 −.131 × 2  =   −.262
(−.078) 24/23, 13/9 −.138 × 2  =   −.275
(−.079) 24/23, 13/8 −.138 × 2  =   −.276
  ———
  White's Average Equity −2.147  ÷  36  =  −.060

 

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