Replies to 24/21, 13/9

Best Nearly Best Pretty Good Not So Good Here are White's best replies after Red opens 24/21, 13/9. 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:       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   6/4*(2)   + .549, .162, .007   − .451, .121, .005 +.142   RBC   6/4*, 6/5(2)   + .544, .162, .007   − .456, .136, .007 +.115   (.027) (.010) (.011) (.039)
	PLAY W      G     BG     EQUITY VOTES CL DMP GG GS   24/23, 6/4*   + .470, .124, .005   − .530, .163, .009 −.102   RBC   6/4*/3   + .453, .118, .005   − .547, .170, .010 −.152   (.050) (.036) (.047) (.050)
	PLAY W      G     BG     EQUITY VOTES CL DMP GG GS   13/11(2), 6/4*(2)   + .596, .196, .010   − .404, .108, .005 +.285   RBC   24/22, 13/11, 6/4*(2)   + .586, .184, .009   − .414, .110, .004 +.251   (.034) (.020) (.044) (.024)   24/22(2), 6/4*(2)   + .580, .175, .008   − .420, .094, .003 +.245   (.039) (.032) (.074) (.003)   24/20, 6/4*(2)   + .580, .177, .010   − .420, .105, .004 +.237   (.048) (.033) (.070) (.027)
	PLAY W      G     BG     EQUITY VOTES CL DMP GG GS   8/5, 6/5   + .501, .136, .005   − .499, .140, .006 −.003   RBC
	PLAY W      G     BG     EQUITY VOTES CL DMP GG GS   24/21, 6/4*   + .480, .126, .006   − .520, .158, .008 −.076   (.024)   13/10, 6/4*   + .479, .139, .006   − .521, .169, .012 −.079   RBC (.003) (.002) (.022)   6/4*/1*   + .466, .129, .005   − .534, .159, .008 −.102   (.026) (.028) (.045) (.030)
	PLAY W      G     BG     EQUITY VOTES CL DMP GG GS   24/21(2), 13/10(2)   + .552, .128, .004   − .448, .087, .003 +.147   RBC
	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)
	PLAY W      G     BG     EQUITY VOTES CL DMP GG GS   8/4*, 6/4   + .545, .175, .008   − .455, .126, .006 +.142   RBC
	PLAY W      G     BG     EQUITY VOTES CL DMP GG GS   24/21, 8/4*   + .468, .128, .006   − .532, .165, .009 −.105   R (.019)   13/10, 8/4*   + .466, .139, .006   − .534, .175, .013 −.110   B (.005) (.004) (.023)   8/4*/1*   + .457, .132, .005   − .543, .166, .008 −.124   C (.019) (.022) (.033) (.024)
	PLAY W      G     BG     EQUITY VOTES CL DMP GG GS   24/16*, 8/4*(2)   + .621, .233, .015   − .379, .095, .004 +.391   RBC
	PLAY W      G     BG     EQUITY VOTES CL DMP GG GS   24/23, 13/8   + .453, .111, .004   − .547, .157, .006 −.142   RBC   24/23, 6/1*   + .447, .116, .004   − .553, .164, .008 −.160   (.017) (.013) (.003) (.028)   24/18   + .448, .098, .004   − .552, .165, .006 −.174   (.032) (.011) (.037) (.027)   13/8, 6/5   + .439, .107, .004   − .561, .168, .010 −.188   (.045) (.028) (.035) (.049)
	PLAY W      G     BG     EQUITY VOTES CL DMP GG GS   13/8, 6/4*   + .476, .132, .006   − .524, .156, .008 −.075   RBC
	PLAY W      G     BG     EQUITY VOTES CL DMP GG GS   24/16*   + .539, .132, .006   − .461, .127, .004 +.085   RBC
	PLAY W      G     BG     EQUITY VOTES CL DMP GG GS   13/4*   + .471, .137, .006   − .529, .158, .009 −.081   RBC   24/20, 13/8   + .461, .117, .005   − .539, .156, .006 −.118   (.037) (.020) (.062) (.016)   24/20, 6/1*   + .460, .118, .004   − .540, .157, .007 −.122   (.041) (.022) (.060) (.021)
	PLAY W      G     BG     EQUITY VOTES CL DMP GG GS   8/3(2), 6/1*(2)   + .518, .199, .007   − .482, .131, .006 +.104   RBC   13/8(2), 6/1*(2)   + .512, .159, .005   − .488, .129, .004 +.056   (.049) (.012) (.091) (.007)
	PLAY W      G     BG     EQUITY VOTES CL DMP GG GS   13/7, 8/7   + .473, .122, .005   − .527, .150, .006 −.084   RBC
	PLAY W      G     BG     EQUITY VOTES CL DMP GG GS   24/16*   + .539, .132, .006   − .461, .127, .004 +.085   RBC
	PLAY W      G     BG     EQUITY VOTES CL DMP GG GS   13/4*   + .471, .137, .006   − .529, .158, .009 −.081   RBC
	PLAY W      G     BG     EQUITY VOTES CL DMP GG GS   24/14   + .457, .099, .004   − .543, .157, .006 −.147   RBC (.035)   8/2, 6/2   + .447, .127, .005   − .553, .165, .007 −.148   (.001) (.020) (.036)   24/18, 8/4*   + .448, .116, .005   − .552, .183, .010 −.175   (.029) (.017) (.019) (.069)   13/7, 8/4*   + .443, .126, .005   − .557, .186, .014 −.183   (.037) (.028) (.009) (.085)   24/20, 13/7   + .437, .114, .004   − .563, .169, .009 −.185   (.039) (.039) (.045) (.063)   13/3   + .433, .117, .005   − .567, .170, .009 −.191   (.044) (.047) (.047) (.072)
	PLAY W      G     BG     EQUITY VOTES CL DMP GG GS   24/13   + .477, .089, .003   − .523, .143, .004 −.101   RBC (.003)   24/18, 13/8   + .463, .105, .004   − .537, .155, .006 −.125   (.024) (.029) (.051)
	PLAY W      G     BG     EQUITY VOTES CL DMP GG GS   24/18(2), 13/7(2)   + .603, .117, .004   − .397, .071, .002 +.254   RBC
Summary Rolls in order from luckiest to unluckiest, and calculation of average equity. (+.399) 24/16*, 8/4*(2) +.391 × 1  =   +.391 (+.293) 13/11(2), 6/4*(2) +.285 × 1  =   +.285 (+.262) 24/18(2), 13/7(2) +.254 × 1  =   +.254 (+.155) 24/21(2), 13/10(2) +.147 × 1  =   +.147 (+.150) 8/4*, 6/4 +.142 × 2  =   +.284 (+.150) 6/4*(2) +.142 × 1  =   +.142 (+.113) 8/3(2), 6/1*(2) +.104 × 1  =   +.104 (+.093) 24/16* +.085 × 2  =   +.169 (+.093) 24/16* +.085 × 2  =   +.169 (+.005) 8/5, 6/5 −.003 × 2  =   −.007 (−.067) 13/8, 6/4* −.075 × 2  =   −.151 (−.068) 24/21, 6/4* −.076 × 2  =   −.152 (−.073) 13/4* −.081 × 2  =   −.163 (−.073) 13/4* −.081 × 2  =   −.163 (−.075) 13/7, 8/7 −.084 × 2  =   −.167 (−.093) 24/13 −.101 × 2  =   −.202 (−.094) 24/23, 6/4* −.102 × 2  =   −.205 (−.097) 24/21, 8/4* −.105 × 2  =   −.210 (−.115) 24/23, 8/4* −.123 × 2  =   −.246 (−.134) 24/23, 13/8 −.142 × 2  =   −.285 (−.138) 24/14 −.147 × 2  =   −.293   ———   White's Average Equity −.299  ÷  36  =  −.008

 

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