Replies to 24/20, 13/8

Best Nearly Best Pretty Good Not So Good Here are White's best replies after Red opens 24/20, 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:       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)   + .582, .169, .007   − .418, .100, .004 +.235   (.010)   8/7(2), 6/5*(2)   + .577, .179, .007   − .423, .111, .005 +.224   RBC (.011) (.009) (.031)   24/23, 6/5*(3)   + .572, .169, .006   − .428, .108, .004 +.207   (.028) (.019) (.030) (.034)   24/23(2), 6/5*(2)   + .566, .169, .006   − .434, .109, .005 +.193   (.041) (.031) (.042) (.049)   8/5*, 6/5   + .563, .178, .007   − .437, .114, .005 +.193   (.042) (.036) (.028) (.064)   24/23, 8/7, 6/5*(2)   + .565, .173, .007   − .435, .117, .005 +.186   (.049) (.034) (.037) (.067)
	PLAY W      G     BG     EQUITY VOTES CL DMP GG GS   13/11, 6/5*   + .486, .134, .005   − .514, .160, .011 −.060   RBC   24/22, 6/5*   + .472, .120, .004   − .528, .151, .007 −.090   (.030) (.028) (.056) (.009)
	PLAY W      G     BG     EQUITY VOTES CL DMP GG GS   13/11(2), 6/4(2)   + .534, .139, .005   − .466, .118, .005 +.088   RBC (.008)   24/22(2), 6/4(2)   + .512, .115, .003   − .488, .093, .003 +.047   (.041) (.043) (.090)
	PLAY W      G     BG     EQUITY VOTES CL DMP GG GS   8/5*, 6/5   + .563, .178, .007   − .437, .114, .005 +.193   RBC
	PLAY W      G     BG     EQUITY VOTES CL DMP GG GS   13/11, 8/5*   + .472, .136, .005   − .528, .163, .011 −.088   RBC   24/22, 8/5*   + .459, .122, .004   − .541, .154, .007 −.118   (.030) (.026) (.054) (.010)
	PLAY W      G     BG     EQUITY VOTES CL DMP GG GS   8/5*(2), 6/3(2)   + .604, .232, .009   − .396, .102, .005 +.342   RBC
	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)
	PLAY W      G     BG     EQUITY VOTES CL DMP GG GS   8/4, 6/4   + .482, .124, .004   − .518, .137, .006 −.052   RBC
	PLAY W      G     BG     EQUITY VOTES CL DMP GG GS   13/9, 8/5*   + .466, .136, .005   − .534, .167, .012 −.106   BC (.030)   24/20, 8/5*   + .462, .119, .004   − .538, .148, .007 −.108   R (.001) (.007) (.041)   8/5*/1*   + .454, .127, .004   − .546, .159, .008 −.127   (.021) (.023) (.040) (.037)   24/21, 24/20   + .450, .093, .003   − .550, .138, .005 −.147   (.041) (.032) (.118) (.005)   24/21, 13/9   + .448, .118, .004   − .552, .159, .008 −.149   (.043) (.037) (.072) (.051)
	PLAY W      G     BG     EQUITY VOTES CL DMP GG GS   13/5*(2)   + .601, .210, .008   − .399, .099, .004 +.318   RBC
	PLAY W      G     BG     EQUITY VOTES CL DMP GG GS   13/8, 6/5*   + .479, .129, .004   − .521, .149, .008 −.065   RBC
	PLAY W      G     BG     EQUITY VOTES CL DMP GG GS   24/22, 13/8   + .455, .101, .003   − .545, .144, .005 −.135   RBC   13/8, 6/4   + .443, .103, .003   − .557, .152, .008 −.168   (.034) (.025) (.021) (.040)   24/22, 6/1*   + .440, .101, .003   − .560, .150, .006 −.172   (.037) (.030) (.029) (.041)   13/6   + .434, .103, .003   − .566, .154, .006 −.184   (.049) (.041) (.036) (.060)
	PLAY W      G     BG     EQUITY VOTES CL DMP GG GS   13/5*   + .474, .132, .005   − .526, .148, .008 −.071   RBC (.007)   8/3, 6/3   + .468, .122, .004   − .532, .143, .006 −.088   (.017) (.013) (.032) (.012)   24/21, 13/8   + .466, .103, .004   − .534, .135, .005 −.102   (.031) (.017) (.074)
	PLAY W      G     BG     EQUITY VOTES CL DMP GG GS   24/20, 13/8   + .462, .101, .004   − .538, .137, .005 −.114   RBC (.013)   13/9, 13/8   + .444, .125, .004   − .556, .153, .008 −.144   (.030) (.035) (.068)   24/20, 6/1*   + .450, .098, .003   − .550, .141, .006 −.145   (.032) (.023) (.042) (.030)   24/15   + .452, .091, .003   − .548, .149, .005 −.156   (.042) (.020) (.053) (.043)
	PLAY W      G     BG     EQUITY VOTES CL DMP GG GS   8/3(2), 6/1*(2)   + .509, .184, .005   − .491, .132, .005 +.070   RBC (.000) (.012)   13/8(2), 6/1*(2)   + .509, .149, .004   − .491, .126, .004 +.041   (.028) (.070)   13/3(2)   + .505, .145, .005   − .495, .126, .005 +.030   (.040) (.008) (.085) (.007)
	PLAY W      G     BG     EQUITY VOTES CL DMP GG GS   13/7, 8/7   + .476, .115, .004   − .524, .134, .005 −.069   RBC   13/7, 6/5*   + .465, .124, .004   − .535, .163, .011 −.116   (.047) (.023) (.004) (.081)
	PLAY W      G     BG     EQUITY VOTES CL DMP GG GS   13/5*   + .474, .132, .005   − .526, .148, .008 −.071   RBC
	PLAY W      G     BG     EQUITY VOTES CL DMP GG GS   13/7, 8/5*   + .449, .124, .004   − .551, .170, .012 −.156   (.006) (.049)   24/15   + .452, .091, .003   − .548, .149, .005 −.156   C (.000) (.059)   24/18, 8/5*   + .450, .108, .004   − .550, .168, .008 −.165   RB (.009) (.005) (.030) (.043)   13/4   + .441, .107, .003   − .559, .151, .008 −.166   (.011) (.022) (.050) (.026)   24/21, 13/7   + .439, .108, .004   − .561, .156, .007 −.174   (.019) (.026) (.052) (.041)   24/21, 24/18   + .443, .090, .003   − .557, .160, .005 −.185   (.029) (.017) (.079) (.039)   24/18, 13/10   + .434, .092, .003   − .566, .157, .007 −.202   (.046) (.036) (.095) (.053)
	PLAY W      G     BG     EQUITY VOTES CL DMP GG GS   8/2, 6/2   + .451, .119, .004   − .549, .148, .006 −.130   BC   24/14   + .450, .092, .003   − .550, .152, .005 −.163   R (.033) (.003) (.057) (.011)
	PLAY W      G     BG     EQUITY VOTES CL DMP GG GS   24/13   + .476, .084, .003   − .524, .131, .004 −.095   RBC   24/18, 13/8   + .464, .094, .003   − .536, .144, .004 −.122   (.027) (.024) (.004) (.050)
	PLAY W      G     BG     EQUITY VOTES CL DMP GG GS   24/18(2), 13/7(2)   + .602, .112, .004   − .398, .065, .002 +.253   RBC
Summary Rolls in order from luckiest to unluckiest, and calculation of average equity. (+.367) 8/5*(2), 6/3(2) +.342 × 1  =   +.342 (+.342) 13/5*(2) +.318 × 1  =   +.318 (+.278) 24/18(2), 13/7(2) +.253 × 1  =   +.253 (+.259) 24/22, 6/5*(2) +.235 × 1  =   +.235 (+.217) 8/5*, 6/5 +.193 × 2  =   +.385 (+.112) 13/11(2), 6/4(2) +.088 × 1  =   +.088 (+.094) 8/3(2), 6/1*(2) +.070 × 1  =   +.070 (−.028) 8/4, 6/4 −.052 × 2  =   −.105 (−.036) 13/11, 6/5* −.060 × 2  =   −.120 (−.041) 13/8, 6/5* −.065 × 2  =   −.131 (−.044) 13/7, 8/7 −.069 × 2  =   −.138 (−.046) 13/5* −.071 × 2  =   −.142 (−.046) 13/5* −.071 × 2  =   −.142 (−.050) 13/9, 6/5* −.074 × 2  =   −.148 (−.064) 13/11, 8/5* −.088 × 2  =   −.177 (−.071) 24/13 −.095 × 2  =   −.190 (−.082) 13/9, 8/5* −.106 × 2  =   −.212 (−.089) 24/20, 13/8 −.114 × 2  =   −.227 (−.105) 8/2, 6/2 −.130 × 2  =   −.260 (−.110) 24/22, 13/8 −.135 × 2  =   −.269 (−.131) 13/7, 8/5* −.156 × 2  =   −.311   ———   White's Average Equity −.881  ÷  36  =  −.024

 

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