Opening Reply 4-1

Best Nearly Best Pretty Good Not So Good Here are the best ways to play a roll of    after each of Red's possible opening rolls. 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 in each of the following situations: Cubeless (CL): Cubeless money play. Double Match Point (DMP): In a match with just one game to go. Gammon-Go (GG): When aggressively going for a gammon win. Gammon-Save (GS): When aggressively avoiding a gammon loss.

After played 24/23, 13/11		Reply    PLAY W      G     BG     EQUITY VOTES CL DMP GG GS   6/2*/1*   + .469, .130, .004   − .531, .151, .007 −.086   RBC   24/23, 13/9   + .462, .126, .005   − .538, .157, .007 −.110   (.024) (.014) (.023) (.025)   24/23, 24/20   + .462, .112, .004   − .538, .146, .005 −.111   (.025) (.014) (.050) (.003)   13/8   + .460, .118, .005   − .540, .158, .006 −.122   (.036) (.019) (.042) (.032)   24/23, 6/2*   + .455, .115, .004   − .545, .154, .007 −.132   (.045) (.028) (.058) (.032)
After played 13/11, 6/5		Reply    PLAY W      G     BG     EQUITY VOTES CL DMP GG GS   24/23, 24/20*   + .527, .162, .011   − .473, .119, .004 +.104   RDB
After played 8/5, 6/5		Reply    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)
After played 24/21, 13/11		Reply    PLAY W      G     BG     EQUITY VOTES CL DMP GG GS   24/23, 8/4*   + .457, .126, .005   − .543, .161, .009 −.126   RBC (.007)   24/23, 24/20   + .449, .103, .004   − .551, .150, .006 −.149   (.024) (.014) (.059)   8/4*/3   + .448, .123, .005   − .552, .169, .009 −.154   (.028) (.017) (.022) (.041)   13/8   + .445, .110, .004   − .555, .159, .007 −.162   (.036) (.024) (.056) (.027)   8/4*, 6/5   + .451, .119, .005   − .549, .185, .015 −.174   (.049) (.012) (.026) (.067)
After played 13/11, 13/10		Reply    PLAY W      G     BG     EQUITY VOTES CL DMP GG GS   24/23, 13/9   + .462, .133, .007   − .538, .171, .008 −.115   RDB (.010) (.008)   13/9, 6/5   + .467, .133, .007   − .533, .182, .013 −.123   (.007) (.012)
After played 24/23, 13/9		Reply    PLAY W      G     BG     EQUITY VOTES CL DMP GG GS   6/2*/1*   + .466, .125, .005   − .534, .155, .008 −.100   RBC   24/23, 24/20   + .460, .115, .005   − .540, .160, .007 −.127   (.027) (.013) (.033) (.023)   24/23, 13/9   + .460, .116, .005   − .540, .161, .007 −.128   (.028) (.013) (.032) (.026)   24/23, 6/2*   + .455, .117, .005   − .545, .159, .008 −.134   (.034) (.022) (.038) (.029)   13/8   + .454, .117, .005   − .546, .165, .007 −.143   (.043) (.025) (.042) (.045)
After played 24/20, 6/5		Reply    PLAY W      G     BG     EQUITY VOTES CL DMP GG GS   24/20*, 6/5*   + .565, .164, .009   − .435, .098, .004 +.200   R
After played 13/9, 6/5		Reply    PLAY W      G     BG     EQUITY VOTES CL DMP GG GS   24/23, 24/20*   + .538, .168, .011   − .462, .116, .004 +.135   RDB
After played 8/4, 6/4		Reply    PLAY W      G     BG     EQUITY VOTES CL DMP GG GS   24/23, 13/9   + .438, .121, .005   − .562, .190, .009 −.198   RBC (.008)   24/23, 24/20   + .432, .106, .005   − .568, .181, .007 −.213   (.014) (.010) (.040)   13/8   + .424, .116, .005   − .576, .192, .009 −.233   (.035) (.028) (.037) (.040)
After played 24/21, 24/20		Reply    PLAY W      G     BG     EQUITY VOTES CL DMP GG GS   8/4*, 6/5*   + .494, .143, .005   − .506, .153, .010 −.026   R (.020)   24/20, 6/5*   + .484, .115, .004   − .516, .132, .006 −.052   (.026) (.020) (.077)
After played 24/21, 13/9		Reply    PLAY W      G     BG     EQUITY VOTES CL DMP GG GS   24/23, 8/4*   + .460, .126, .005   − .540, .166, .009 −.123   RBC   24/23, 24/20   + .448, .106, .004   − .552, .162, .006 −.161   (.038) (.024) (.063) (.018)
After played 24/20, 13/10		Reply    PLAY W      G     BG     EQUITY VOTES CL DMP GG GS   24/20, 6/5*   + .483, .123, .005   − .516, .150, .007 −.061   RB (.014)   13/9, 6/5*   + .479, .134, .006   − .521, .166, .012 −.079   (.018) (.008) (.041)   6/5*/1*   + .469, .129, .005   − .531, .153, .007 −.088   (.027) (.029) (.031) (.036)
After played 13/10, 13/9		Reply    PLAY W      G     BG     EQUITY VOTES CL DMP GG GS   13/9, 6/5   + .465, .133, .006   − .535, .183, .014 −.127   RB   24/23, 13/9   + .454, .128, .006   − .546, .179, .008 −.146   D (.019) (.023) (.032) (.016)
After played 24/23, 13/8		Reply    PLAY W      G     BG     EQUITY VOTES CL DMP GG GS   6/2*/1*   + .465, .128, .004   − .535, .155, .007 −.100   RBC (.016)   13/8   + .463, .120, .004   − .537, .153, .006 −.110   (.009) (.004) (.020) (.018)   24/23, 24/20   + .461, .105, .004   − .539, .142, .005 −.117   (.017) (.009) (.054)   24/23, 13/9   + .454, .122, .004   − .546, .160, .007 −.132   (.031) (.022) (.032) (.048)   24/23, 6/2*   + .453, .113, .004   − .547, .157, .007 −.142   (.041) (.025) (.053) (.045)
After played 24/18		Reply    PLAY W      G     BG     EQUITY VOTES CL DMP GG GS   24/20, 8/7*   + .487, .127, .005   − .513, .127, .005 −.028   R (.003) (.036)   13/9, 8/7*   + .488, .144, .006   − .512, .146, .008 −.029   (.001) (.036)
After played 13/8, 6/5		Reply    PLAY W      G     BG     EQUITY VOTES CL DMP GG GS   24/23, 24/20*   + .532, .148, .008   − .468, .114, .004 +.103   RDB
After played 24/22, 13/8		Reply    PLAY W      G     BG     EQUITY VOTES CL DMP GG GS   13/8   + .460, .116, .004   − .540, .152, .007 −.119   B (.013)   24/23, 24/20   + .459, .105, .004   − .541, .145, .005 −.123   R (.003) (.001) (.022)   8/3*   + .447, .121, .004   − .553, .169, .010 −.160   (.040) (.026) (.016) (.072)   24/23, 13/9   + .444, .115, .004   − .556, .163, .007 −.164   (.044) (.032) (.033) (.067)
After played 13/8, 6/4		Reply    PLAY W      G     BG     EQUITY VOTES CL DMP GG GS   13/9, 6/5   + .473, .134, .006   − .527, .169, .012 −.096   R (.013)   24/20, 6/5   + .471, .118, .004   − .529, .161, .008 −.105   (.010) (.005) (.037)   24/23, 13/9   + .461, .130, .005   − .539, .163, .007 −.112   (.017) (.023) (.030) (.024)   24/23, 24/20   + .454, .110, .004   − .546, .156, .006 −.140   (.045) (.039) (.086) (.025)
After played 13/11, 13/8		Reply    PLAY W      G     BG     EQUITY VOTES CL DMP GG GS   13/9, 6/5   + .471, .132, .006   − .529, .171, .012 −.103   DB   24/23, 13/9   + .463, .133, .006   − .537, .165, .008 −.109   RC (.006) (.016) (.015) (.005)   24/23, 24/20   + .460, .116, .005   − .540, .162, .006 −.128   (.026) (.023) (.056) (.006)   13/8   + .453, .122, .005   − .547, .164, .007 −.137   (.035) (.036) (.056) (.022)
After played 8/3, 6/3		Reply    PLAY W      G     BG     EQUITY VOTES CL DMP GG GS   24/23, 13/9   + .458, .128, .005   − .542, .184, .009 −.143   RBC (.002)   24/23, 24/20   + .454, .115, .005   − .546, .178, .007 −.157   (.014) (.008) (.034)   13/8   + .445, .124, .005   − .555, .183, .009 −.173   (.029) (.027) (.033) (.028)   13/9, 6/5   + .452, .125, .005   − .548, .197, .017 −.181   (.037) (.013) (.019) (.042)
After played 13/10, 13/8		Reply    PLAY W      G     BG     EQUITY VOTES CL DMP GG GS   13/9, 6/5   + .472, .133, .006   − .528, .173, .012 −.102   D   24/23, 13/9   + .462, .131, .006   − .538, .170, .008 −.117   R (.015) (.020) (.025) (.015)
After played 24/20, 13/8		Reply    PLAY W      G     BG     EQUITY VOTES CL DMP GG GS   13/9, 6/5*   + .480, .136, .005   − .520, .164, .011 −.074   BC (.022)   24/20, 6/5*   + .474, .118, .004   − .526, .147, .007 −.083   R (.009) (.012) (.047)   6/5*/1*   + .465, .128, .004   − .535, .155, .007 −.100   (.026) (.030) (.047) (.034)
After played 13/9, 13/8		Reply    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)
After played 13/7, 8/7		Reply    PLAY W      G     BG     EQUITY VOTES CL DMP GG GS   24/23, 13/9   + .445, .122, .004   − .555, .176, .008 −.167   RDBC (.025)   24/23, 24/20   + .441, .103, .004   − .559, .159, .006 −.176   (.009) (.009) (.047)   13/9, 6/5   + .438, .116, .004   − .562, .179, .012 −.194   (.028) (.014) (.024) (.046)   13/8   + .428, .113, .004   − .572, .170, .008 −.207   (.040) (.035) (.054) (.050)   24/20, 6/5   + .437, .105, .004   − .563, .184, .010 −.211   (.044) (.017) (.051) (.058)
After played 24/18, 13/11		Reply    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)
After played 24/16		Reply    PLAY W      G     BG     EQUITY VOTES CL DMP GG GS   24/23, 13/9*   + .517, .151, .006   − .483, .125, .005 +.060   RB   13/9*/8   + .507, .137, .006   − .493, .132, .005 +.021   (.038) (.018) (.046) (.031)
After played 13/5		Reply    PLAY W      G     BG     EQUITY VOTES CL DMP GG GS   24/23, 24/20*   + .539, .146, .007   − .461, .116, .004 +.113   R
After played 24/18, 13/10		Reply    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)
After played 24/15		Reply    PLAY W      G     BG     EQUITY VOTES CL DMP GG GS   24/23, 13/9   + .450, .119, .004   − .550, .133, .006 −.117   RB (.002) (.010) (.004)   13/9, 6/5   + .451, .123, .004   − .549, .149, .010 −.130   (.013) (.034)   24/23, 24/20   + .442, .102, .004   − .558, .123, .005 −.139   (.022) (.019) (.061)   24/20, 6/5   + .447, .112, .004   − .553, .150, .007 −.148   (.032) (.009) (.030) (.045)   13/8   + .435, .110, .004   − .565, .143, .007 −.166   (.050) (.032) (.058) (.053)
After played 8/2, 6/2		Reply    PLAY W      G     BG     EQUITY VOTES CL DMP GG GS   13/8   + .466, .131, .005   − .534, .173, .009 −.113   B (.016) (.019)   13/9, 6/5   + .474, .133, .005   − .526, .191, .016 −.121   R (.008) (.020)
After played 24/18, 13/9		Reply    PLAY W      G     BG     EQUITY VOTES CL DMP GG GS   24/20, 8/7*   + .475, .131, .006   − .525, .152, .007 −.072   RB (.012)   13/9, 8/7*   + .472, .140, .006   − .528, .166, .011 −.086   D (.014) (.006) (.034)
After played 24/14		Reply    PLAY W      G     BG     EQUITY VOTES CL DMP GG GS   13/9, 6/5   + .451, .123, .004   − .549, .154, .010 −.137   R (.039)   24/23, 13/9   + .441, .115, .004   − .559, .133, .006 −.137   C (.000) (.019) (.033) (.015)   24/20, 6/5   + .449, .112, .004   − .551, .149, .008 −.142   B (.005) (.003) (.024) (.031)   24/23, 24/20   + .439, .099, .003   − .561, .124, .005 −.147   (.010) (.022) (.069)   13/8   + .431, .107, .003   − .569, .143, .007 −.176   (.039) (.038) (.070) (.054)
After played 24/13		Reply    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)

Summary

Opening Play   Reply 24/23, 13/9 13/9, 6/5 24/23, 24/20 24/20, 8/7 6/2/1 24/23, 8/4 24/20, 6/5 13/8 13/9, 8/7 8/4, 6/5   24/23, 13/11         *2, 1             13/11, 6/5     *20                 8/5, 6/5                     24/21, 13/11           *4           13/11, 13/10                     24/23, 13/9         *2, 1             24/20, 6/5             *20, 5         13/9, 6/5     *20                 8/4, 6/4                     24/21, 24/20                   *4, 5   24/21, 13/9           *4           24/20, 13/10             *5         13/10, 13/9                     24/23, 13/8         *2, 1             24/18       *7         *7     13/8, 6/5     *20                 24/22, 13/8                     13/8, 6/4                     13/11, 13/8                     8/3, 6/3                     13/10, 13/8                     24/20, 13/8   *5                   13/9, 13/8                     13/7, 8/7                     24/18, 13/11       *7               24/16 *9                     13/5     *20                 24/18, 13/10       *7               24/15                     8/2, 6/2                     24/18, 13/9       *7               24/14                   24/13                     24/23, 13/9 13/9, 6/5 24/23, 24/20 24/20, 8/7 6/2/1 24/23, 8/4 24/20, 6/5 13/8 13/9, 8/7 8/4, 6/5

 

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