Replies to 8/5, 6/5

Best
Nearly Best
Pretty Good
Not So Good
Here are White's best replies after Red opens 8/5, 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).
      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
  24/22, 6/5(2)   + .502, .134, .005
  − .498, .138, .005
 +.001   (.021)
  8/7(2), 6/5(2)   + .502, .145, .006
  − .498, .153, .008
 −.005   RDBC (.006) (.001) (.030)
  24/23, 6/5(3)   + .488, .135, .005
  − .512, .154, .007
 −.044   (.045) (.028) (.048) (.061)
   PLAY W      G     BG     EQUITY VOTES CL DMP GG GS
  24/23, 13/11   + .421, .110, .004
  − .579, .188, .009
 −.239   RBC
  24/23, 24/22   + .417, .101, .004
  − .583, .188, .007
 −.255   (.016) (.008) (.026) (.007)
  24/21   + .414, .101, .004
  − .586, .187, .008
 −.261   (.022) (.016) (.033) (.012)
  13/10   + .405, .111, .005
  − .595, .191, .010
 −.275   (.036) (.032) (.031) (.037)
  13/11, 6/5   + .410, .107, .004
  − .590, .205, .015
 −.289   D (.050) (.023) (.029) (.056)
   PLAY W      G     BG     EQUITY VOTES CL DMP GG GS
  24/22(2), 6/4(2)   + .494, .132, .005
  − .506, .113, .004
 +.008   RDBC (.014) (.065)
  13/11(2), 6/4(2)   + .502, .158, .007
  − .498, .156, .007
 +.005   (.003) (.071)
  24/22, 13/11, 6/4(2)   + .488, .141, .006
  − .512, .150, .007
 −.033   (.041) (.027) (.060) (.086)
   PLAY W      G     BG     EQUITY VOTES CL DMP GG GS
  8/5, 6/5   + .474, .138, .006
  − .526, .161, .008
 −.077   RDBC
   PLAY W      G     BG     EQUITY VOTES CL DMP GG GS
  24/22, 13/10   + .422, .110, .005
  − .578, .186, .008
 −.234   RB
  24/21, 13/11   + .419, .107, .005
  − .581, .186, .009
 −.245   DC (.011) (.007) (.012) (.009)
  24/22, 24/21   + .420, .103, .005
  − .580, .193, .007
 −.252   (.018) (.005) (.018) (.020)
  13/11, 13/10   + .406, .117, .005
  − .594, .194, .012
 −.271   (.037) (.032) (.018) (.049)
  13/8   + .407, .110, .005
  − .593, .196, .009
 −.276   (.041) (.031) (.031) (.052)
   PLAY W      G     BG     EQUITY VOTES CL DMP GG GS
  24/21(2), 13/10(2)   + .519, .125, .004
  − .481, .091, .003
 +.074   RBC (.002) (.045)
  24/21(2), 6/3(2)   + .512, .126, .004
  − .488, .093, .003
 +.058   (.015) (.017) (.056) (.019)
  24/21(2), 8/5(2)   + .506, .136, .004
  − .494, .098, .004
 +.050   D (.023) (.030) (.051) (.041)
  24/18(2)   + .520, .107, .003
  − .479, .103, .003
 +.045   (.028) (.078) (.022)
  8/5(2), 6/3(2)   + .496, .171, .008
  − .504, .155, .008
 +.008   (.065) (.049) (.174)
   PLAY W      G     BG     EQUITY VOTES CL DMP GG GS
  24/23, 13/9   + .421, .113, .005
  − .579, .189, .009
 −.237   RBC
  13/8   + .407, .110, .005
  − .593, .196, .009
 −.276   (.039) (.029) (.034) (.043)
   PLAY W      G     BG     EQUITY VOTES CL DMP GG GS
  8/4, 6/4   + .456, .136, .006
  − .544, .171, .008
 −.126   RDBC
   PLAY W      G     BG     EQUITY VOTES CL DMP GG GS
  24/21, 13/9   + .420, .111, .005
  − .580, .185, .009
 −.239   RDBC
  13/10, 13/9   + .410, .120, .005
  − .590, .196, .013
 −.263   (.024) (.020) (.001) (.042)
   PLAY W      G     BG     EQUITY VOTES CL DMP GG GS
  13/5(2)   + .492, .162, .008
  − .508, .156, .007
 −.009   RDBC
   PLAY W      G     BG     EQUITY VOTES CL DMP GG GS
  24/23, 13/8   + .425, .115, .005
  − .575, .185, .007
 −.222   RBC
  24/18   + .420, .099, .004
  − .580, .196, .007
 −.260   (.038) (.010) (.042) (.032)
   PLAY W      G     BG     EQUITY VOTES CL DMP GG GS
  24/22, 13/8   + .428, .111, .005
  − .572, .179, .007
 −.213   RBC
  13/11, 13/8   + .410, .117, .005
  − .590, .194, .010
 −.261   D (.048) (.036) (.024) (.066)
   PLAY W      G     BG     EQUITY VOTES CL DMP GG GS
  8/3, 6/3   + .433, .131, .006
  − .567, .185, .009
 −.190   RBC
  24/21, 13/8   + .426, .111, .005
  − .574, .182, .007
 −.223   D (.033) (.015) (.055) (.010)
   PLAY W      G     BG     EQUITY VOTES CL DMP GG GS
  13/9, 13/8   + .414, .122, .006
  − .586, .188, .010
 −.241   RDB
   PLAY W      G     BG     EQUITY VOTES CL DMP GG GS
  13/3(2)   + .446, .145, .009
  − .554, .179, .008
 −.141   RDBC
   PLAY W      G     BG     EQUITY VOTES CL DMP GG GS
  13/7, 8/7   + .449, .122, .005
  − .551, .168, .007
 −.149   RDBC
   PLAY W      G     BG     EQUITY VOTES CL DMP GG GS
  24/18, 13/11   + .430, .105, .005
  − .570, .196, .009
 −.236   RB
  24/16   + .423, .099, .004
  − .577, .194, .007
 −.253   C (.017) (.014) (.026) (.009)
  24/22, 24/18   + .418, .098, .004
  − .582, .210, .008
 −.279   (.043) (.024) (.037) (.051)
   PLAY W      G     BG     EQUITY VOTES CL DMP GG GS
  24/18, 13/10   + .425, .106, .005
  − .575, .197, .009
 −.247   R (.010)
  24/15   + .422, .097, .004
  − .578, .190, .007
 −.251   DBC (.005) (.005) (.022)
   PLAY W      G     BG     EQUITY VOTES CL DMP GG GS
  24/14   + .431, .098, .004
  − .569, .184, .007
 −.226   DBC (.021)
  8/2, 6/2   + .413, .127, .006
  − .587, .197, .009
 −.248   (.022) (.037) (.063)
  24/18, 13/9   + .424, .108, .005
  − .576, .201, .009
 −.250   R (.024) (.015) (.016) (.049)
   PLAY W      G     BG     EQUITY VOTES CL DMP GG GS
  24/13   + .463, .104, .005
  − .537, .171, .005
 −.141   RDBC
   PLAY W      G     BG     EQUITY VOTES CL DMP GG GS
  24/18(2), 13/7(2)   + .612, .141, .005
  − .388, .081, .002
 +.287   RDBC

Summary

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

(+.448) 24/18(2), 13/7(2) +.287 × 1  =   +.287
(+.235) 24/21(2), 13/10(2) +.074 × 1  =   +.074
(+.169) 24/22(2), 6/4(2) +.008 × 1  =   +.008
(+.163) 24/22, 6/5(2) +.001 × 1  =   +.001
(+.153) 13/5(2) −.009 × 1  =   −.009
(+.085) 8/5, 6/5 −.077 × 2  =   −.153
(+.036) 8/4, 6/4 −.126 × 2  =   −.251
(+.021) 24/13 −.141 × 2  =   −.282
(+.020) 13/3(2) −.141 × 1  =   −.141
(+.012) 13/7, 8/7 −.149 × 2  =   −.299
(−.029) 8/3, 6/3 −.190 × 2  =   −.380
(−.052) 24/22, 13/8 −.213 × 2  =   −.426
(−.061) 24/23, 13/8 −.222 × 2  =   −.444
(−.064) 24/14 −.226 × 2  =   −.452
(−.073) 24/22, 13/10 −.234 × 2  =   −.469
(−.075) 24/18, 13/11 −.236 × 2  =   −.472
(−.075) 24/23, 13/9 −.237 × 2  =   −.474
(−.077) 24/21, 13/9 −.239 × 2  =   −.478
(−.078) 24/23, 13/11 −.239 × 2  =   −.479
(−.079) 13/9, 13/8 −.241 × 2  =   −.482
(−.085) 24/18, 13/10 −.247 × 2  =   −.494
  ———
  White's Average Equity −5.815  ÷  36  =  −.162

 

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