Replies to 13/9, 13/8

Best
Nearly Best
Pretty Good
Not So Good
Here are White's best replies after Red opens 13/9, 13/8.

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).
      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)   + .566, .172, .008
  − .434, .133, .007
 +.172   RDB
   PLAY W      G     BG     EQUITY VOTES CL DMP GG GS
  13/11, 6/5   + .475, .133, .005
  − .525, .174, .012
 −.099   RDB
  24/23, 13/11   + .458, .125, .005
  − .542, .177, .008
 −.138   (.039) (.034) (.048) (.039)
   PLAY W      G     BG     EQUITY VOTES CL DMP GG GS
  24/22(2), 6/4(2)   + .557, .163, .006
  − .443, .104, .004
 +.174   RB (.010)
  13/11(2), 6/4(2)   + .552, .172, .008
  − .448, .141, .007
 +.136   (.038) (.009) (.084)
   PLAY W      G     BG     EQUITY VOTES CL DMP GG GS
  8/5, 6/5   + .520, .161, .007
  − .480, .148, .007
 +.052   RDB
   PLAY W      G     BG     EQUITY VOTES CL DMP GG GS
  13/11, 13/10   + .460, .136, .006
  − .540, .171, .011
 −.120   RDB (.009) (.009)
  24/21, 13/11   + .464, .122, .005
  − .536, .171, .008
 −.123   (.003) (.019)
  13/11, 8/5   + .460, .135, .006
  − .540, .180, .013
 −.132   (.012) (.009) (.002) (.026)
  24/22, 13/10   + .460, .124, .005
  − .540, .175, .008
 −.132   (.013) (.008) (.024) (.015)
  13/10, 6/4   + .457, .128, .005
  − .543, .180, .012
 −.147   (.027) (.016) (.024) (.033)
   PLAY W      G     BG     EQUITY VOTES CL DMP GG GS
  24/21(2), 6/3(2)   + .557, .154, .006
  − .443, .094, .003
 +.178   B (.002) (.077) (.006)
  24/21(2), 13/10(2)   + .558, .148, .005
  − .442, .091, .003
 +.175   R (.003) (.089)
  24/21(2), 8/5(2)   + .550, .166, .005
  − .450, .093, .003
 +.175   D (.003) (.016) (.069) (.020)
  8/5(2), 6/3(2)   + .555, .195, .010
  − .445, .137, .007
 +.171   (.007) (.006) (.098)
   PLAY W      G     BG     EQUITY VOTES CL DMP GG GS
  13/9, 6/5   + .471, .133, .005
  − .529, .176, .013
 −.108   RDB
  24/20, 6/5   + .467, .123, .006
  − .533, .181, .009
 −.127   (.019) (.007) (.028) (.018)
  24/23, 13/9   + .456, .129, .006
  − .544, .180, .008
 −.141   (.033) (.029) (.038) (.038)
  24/23, 24/20   + .453, .112, .005
  − .547, .172, .006
 −.156   (.048) (.036) (.079) (.029)
   PLAY W      G     BG     EQUITY VOTES CL DMP GG GS
  8/4, 6/4   + .499, .155, .007
  − .501, .158, .008
 −.006   RDB
   PLAY W      G     BG     EQUITY VOTES CL DMP GG GS
  13/10, 13/9   + .464, .141, .006
  − .536, .170, .011
 −.105   RDB
  24/21, 13/9   + .462, .125, .005
  − .538, .172, .008
 −.125   (.019) (.004) (.036) (.007)
  24/20, 13/10   + .460, .128, .006
  − .540, .172, .008
 −.126   (.020) (.009) (.034) (.013)
  13/9, 8/5   + .454, .133, .006
  − .546, .181, .014
 −.149   (.044) (.022) (.037) (.045)
   PLAY W      G     BG     EQUITY VOTES CL DMP GG GS
  24/16*, 13/9(2)   + .609, .176, .010
  − .391, .102, .004
 +.299   RB (.037)
  24/20(2), 13/9(2)   + .592, .154, .005
  − .408, .066, .002
 +.275   D (.024) (.033) (.078)
   PLAY W      G     BG     EQUITY VOTES CL DMP GG GS
  13/8, 6/5   + .466, .130, .005
  − .534, .169, .010
 −.113   RDB
  24/23, 13/8   + .455, .122, .005
  − .545, .174, .007
 −.144   (.031) (.022) (.036) (.032)
   PLAY W      G     BG     EQUITY VOTES CL DMP GG GS
  13/11, 13/8   + .457, .132, .006
  − .543, .175, .009
 −.131   RB
  13/8, 6/4   + .452, .125, .005
  − .548, .174, .010
 −.150   D (.019) (.011) (.025) (.009)
  24/22, 13/8   + .453, .118, .005
  − .547, .174, .006
 −.153   (.021) (.009) (.037) (.008)
   PLAY W      G     BG     EQUITY VOTES CL DMP GG GS
  24/16*   + .546, .142, .007
  − .454, .129, .005
 +.107   RDB
   PLAY W      G     BG     EQUITY VOTES CL DMP GG GS
  13/9, 13/8   + .462, .139, .006
  − .538, .170, .009
 −.111   DB (.013) (.013)
  24/20, 13/8   + .463, .119, .005
  − .537, .165, .006
 −.121   (.011) (.011) (.038) (.001)
  24/15   + .468, .113, .005
  − .532, .170, .006
 −.122   R (.011) (.039)
  13/4   + .447, .129, .005
  − .553, .176, .010
 −.158   (.047) (.044) (.050) (.055)
   PLAY W      G     BG     EQUITY VOTES CL DMP GG GS
  13/3(2)   + .499, .157, .008
  − .501, .157, .007
 −.000   RDB
   PLAY W      G     BG     EQUITY VOTES CL DMP GG GS
  13/7, 8/7   + .497, .140, .006
  − .503, .157, .007
 −.025   RDB
   PLAY W      G     BG     EQUITY VOTES CL DMP GG GS
  24/16*   + .546, .142, .007
  − .454, .129, .005
 +.107   RDB
   PLAY W      G     BG     EQUITY VOTES CL DMP GG GS
  24/15   + .468, .113, .005
  − .532, .170, .006
 −.122   RDB (.010)
  24/18, 13/10   + .466, .120, .005
  − .534, .176, .008
 −.126   (.003) (.004) (.015)
  13/4   + .447, .129, .005
  − .553, .176, .010
 −.158   (.036) (.044) (.021) (.055)
   PLAY W      G     BG     EQUITY VOTES CL DMP GG GS
  24/14   + .472, .112, .005
  − .528, .167, .006
 −.112   RDB (.022)
  24/18, 13/9   + .469, .126, .006
  − .531, .180, .008
 −.118   (.006) (.006) (.032)
  8/2, 6/2   + .452, .141, .006
  − .548, .177, .009
 −.134   (.023) (.041) (.004) (.060)
   PLAY W      G     BG     EQUITY VOTES CL DMP GG GS
  24/13   + .485, .104, .004
  − .515, .154, .005
 −.080   RDB
  24/18, 13/8   + .469, .117, .005
  − .531, .170, .006
 −.114   (.034) (.031) (.005) (.063)
   PLAY W      G     BG     EQUITY VOTES CL DMP GG GS
  24/18(2), 13/7(2)   + .628, .148, .006
  − .372, .082, .002
 +.325   RDB

Summary

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

(+.341) 24/18(2), 13/7(2) +.325 × 1  =   +.325
(+.315) 24/16*, 13/9(2) +.299 × 1  =   +.299
(+.194) 24/21(2), 6/3(2) +.178 × 1  =   +.178
(+.191) 24/22(2), 6/4(2) +.174 × 1  =   +.174
(+.189) 8/7(2), 6/5(2) +.172 × 1  =   +.172
(+.123) 24/16* +.107 × 2  =   +.213
(+.123) 24/16* +.107 × 2  =   +.213
(+.068) 8/5, 6/5 +.052 × 2  =   +.104
(+.016) 13/3(2) −.000 × 1  =   −.000
(+.010) 8/4, 6/4 −.006 × 2  =   −.012
(−.009) 13/7, 8/7 −.025 × 2  =   −.051
(−.064) 24/13 −.080 × 2  =   −.160
(−.082) 13/11, 6/5 −.099 × 2  =   −.198
(−.089) 13/10, 13/9 −.105 × 2  =   −.211
(−.092) 13/9, 6/5 −.108 × 2  =   −.216
(−.094) 13/9, 13/8 −.111 × 2  =   −.221
(−.096) 24/14 −.112 × 2  =   −.224
(−.096) 13/8, 6/5 −.113 × 2  =   −.225
(−.104) 13/11, 13/10 −.120 × 2  =   −.240
(−.106) 24/15 −.122 × 2  =   −.244
(−.115) 13/11, 13/8 −.131 × 2  =   −.263
  ———
  White's Average Equity −.586  ÷  36  =  −.016

 

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