Replies to 13/11, 13/10

Best Nearly Best Pretty Good Not So Good Here are White's best replies after Red opens 13/11, 13/10. 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)   + .562, .172, .009   − .438, .137, .007 +.163   RDB   24/22, 6/5(2)   + .551, .157, .008   − .449, .135, .005 +.127   (.036) (.023) (.053) (.021)
	PLAY W      G     BG     EQUITY VOTES CL DMP GG GS   24/23, 13/11   + .462, .128, .006   − .538, .170, .007 −.120   D (.011) (.018)   13/11, 6/5   + .468, .131, .006   − .532, .180, .012 −.120   RB (.001) (.009)   13/10   + .451, .128, .006   − .549, .174, .009 −.147   (.027) (.033) (.040) (.029)   24/23, 24/22   + .455, .119, .006   − .545, .176, .007 −.149   (.029) (.026) (.050) (.027)   24/21   + .452, .118, .006   − .548, .176, .007 −.155   (.036) (.031) (.057) (.032)
	PLAY W      G     BG     EQUITY VOTES CL DMP GG GS   13/11(2), 6/4(2)   + .547, .174, .010   − .453, .143, .007 +.128   RB (.101)   24/20(2)   + .539, .132, .005   − .461, .084, .003 +.128   D (.000) (.017) (.100)   24/22(2), 6/4(2)   + .541, .153, .007   − .459, .112, .004 +.125   (.004) (.013) (.055) (.052)   24/22, 13/11, 6/4(2)   + .540, .162, .009   − .460, .139, .006 +.105   (.024) (.015) (.039) (.109)   13/9, 6/4(2)   + .533, .171, .009   − .467, .144, .007 +.094   (.034) (.029) (.035) (.132)
	PLAY W      G     BG     EQUITY VOTES CL DMP GG GS   8/5, 6/5   + .526, .163, .008   − .474, .149, .007 +.066   RDB
	PLAY W      G     BG     EQUITY VOTES CL DMP GG GS   13/11, 13/10   + .462, .140, .007   − .538, .173, .010 −.112   RD (.006) (.011)   24/22, 13/10   + .464, .127, .006   − .536, .169, .007 −.116   B (.004) (.002) (.022)   24/21, 13/11   + .465, .127, .006   − .535, .176, .008 −.120   (.008) (.020) (.011)   24/22, 24/21   + .458, .119, .007   − .542, .180, .007 −.145   (.033) (.014) (.050) (.034)   13/10, 6/4   + .455, .128, .006   − .545, .186, .013 −.154   (.042) (.020) (.037) (.051)   13/11, 8/5   + .451, .132, .006   − .549, .186, .013 −.158   (.046) (.028) (.038) (.058)
	PLAY W      G     BG     EQUITY VOTES CL DMP GG GS   24/21(2), 8/5(2)   + .559, .171, .007   − .441, .095, .003 +.199   DB (.001) (.053)   8/5(2), 6/3(2)   + .560, .197, .012   − .440, .140, .007 +.182   (.017) (.090)   24/21(2), 6/3(2)   + .556, .155, .007   − .444, .094, .003 +.176   (.023) (.008) (.092) (.007)   24/21(2), 13/10(2)   + .554, .151, .006   − .446, .095, .003 +.165   R (.034) (.013) (.104) (.014)
	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)
	PLAY W      G     BG     EQUITY VOTES CL DMP GG GS   8/4, 6/4   + .502, .156, .008   − .498, .158, .007 +.003   RDB
	PLAY W      G     BG     EQUITY VOTES CL DMP GG GS   13/10, 13/9   + .465, .145, .007   − .535, .170, .010 −.097   RDB (.005)   24/21, 13/9   + .468, .135, .007   − .532, .174, .008 −.105   (.008) (.016) (.004)
	PLAY W      G     BG     EQUITY VOTES CL DMP GG GS   24/20(2), 13/9(2)   + .603, .165, .006   − .397, .071, .002 +.304   RDB
	PLAY W      G     BG     EQUITY VOTES CL DMP GG GS   24/23, 13/8   + .462, .127, .006   − .538, .171, .006 −.122   D   13/8, 6/5   + .460, .127, .006   − .540, .174, .010 −.131   RB (.009) (.002) (.002) (.009)   24/18   + .459, .116, .005   − .541, .173, .007 −.141   (.019) (.005) (.027) (.009)   13/7   + .449, .125, .006   − .551, .168, .009 −.148   (.026) (.025) (.028) (.018)
	PLAY W      G     BG     EQUITY VOTES CL DMP GG GS   24/22, 13/8   + .463, .123, .006   − .537, .169, .006 −.120   RB (.002)   13/11, 13/8   + .455, .133, .006   − .545, .177, .009 −.138   (.017) (.016) (.032)   13/8, 6/4   + .451, .125, .006   − .549, .177, .009 −.155   D (.035) (.024) (.023) (.040)
	PLAY W      G     BG     EQUITY VOTES CL DMP GG GS   8/3, 6/3   + .478, .150, .008   − .522, .171, .008 −.065   RDB
	PLAY W      G     BG     EQUITY VOTES CL DMP GG GS   24/15*   + .538, .151, .009   − .462, .135, .005 +.097   RDB
	PLAY W      G     BG     EQUITY VOTES CL DMP GG GS   13/3(2)   + .492, .161, .010   − .508, .163, .007 −.015   RDB
	PLAY W      G     BG     EQUITY VOTES CL DMP GG GS   13/7, 8/7   + .492, .141, .007   − .507, .160, .007 −.035   RDB
	PLAY W      G     BG     EQUITY VOTES CL DMP GG GS   24/18, 13/11   + .471, .126, .006   − .529, .175, .008 −.109   RB   24/16   + .463, .120, .006   − .537, .176, .007 −.131   (.022) (.016) (.029) (.017)   24/22, 24/18   + .463, .118, .006   − .537, .181, .007 −.138   (.029) (.015) (.033) (.028)   13/11, 13/7   + .454, .133, .006   − .546, .175, .011 −.139   (.031) (.034) (.021) (.034)   24/22, 13/7   + .453, .127, .006   − .547, .173, .008 −.142   (.033) (.035) (.035) (.031)   13/5   + .453, .130, .006   − .547, .176, .010 −.144   D (.035) (.035) (.029) (.037)
	PLAY W      G     BG     EQUITY VOTES CL DMP GG GS   24/15*   + .538, .151, .009   − .462, .135, .005 +.097   RDB
	PLAY W      G     BG     EQUITY VOTES CL DMP GG GS   24/14*   + .551, .151, .009   − .449, .129, .005 +.128   RDB
	PLAY W      G     BG     EQUITY VOTES CL DMP GG GS   24/13   + .487, .111, .005   − .513, .159, .005 −.073   RDB (.002)   24/18, 13/8   + .474, .125, .006   − .526, .168, .006 −.095   (.021) (.026) (.045)
	PLAY W      G     BG     EQUITY VOTES CL DMP GG GS   24/18(2), 13/7(2)   + .632, .154, .007   − .368, .082, .003 +.339   RDB
Summary Rolls in order from luckiest to unluckiest, and calculation of average equity. (+.341) 24/18(2), 13/7(2) +.339 × 1  =   +.339 (+.306) 24/20(2), 13/9(2) +.304 × 1  =   +.304 (+.200) 24/21(2), 8/5(2) +.199 × 1  =   +.199 (+.164) 8/7(2), 6/5(2) +.163 × 1  =   +.163 (+.129) 13/11(2), 6/4(2) +.128 × 1  =   +.128 (+.129) 24/14* +.128 × 2  =   +.256 (+.098) 24/15* +.097 × 2  =   +.193 (+.098) 24/15* +.097 × 2  =   +.193 (+.067) 8/5, 6/5 +.066 × 2  =   +.132 (+.004) 8/4, 6/4 +.003 × 2  =   +.006 (−.014) 13/3(2) −.015 × 1  =   −.015 (−.034) 13/7, 8/7 −.035 × 2  =   −.069 (−.064) 8/3, 6/3 −.065 × 2  =   −.130 (−.072) 24/13 −.073 × 2  =   −.147 (−.096) 13/10, 13/9 −.097 × 2  =   −.195 (−.108) 24/18, 13/11 −.109 × 2  =   −.218 (−.111) 13/11, 13/10 −.112 × 2  =   −.224 (−.114) 24/23, 13/9 −.115 × 2  =   −.231 (−.119) 24/23, 13/11 −.120 × 2  =   −.239 (−.119) 24/22, 13/8 −.120 × 2  =   −.241 (−.121) 24/23, 13/8 −.122 × 2  =   −.243   ———   White's Average Equity −.038  ÷  36  =  −.001

 

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