Replies to 24/20, 13/10

Best Nearly Best Pretty Good Not So Good Here are White's best replies after Red opens 24/20, 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:       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   24/22, 6/5*(2)   + .597, .173, .008   − .403, .097, .004 +.274   B   24/23, 6/5*(3)   + .587, .173, .008   − .413, .104, .004 +.248   (.026) (.020) (.019) (.033)   8/7(2), 6/5*(2)   + .581, .179, .009   − .419, .111, .005 +.233   R (.041) (.032) (.021) (.059)
	PLAY W      G     BG     EQUITY VOTES CL DMP GG GS   13/11, 6/5*   + .485, .134, .006   − .515, .161, .011 −.062   RB   24/22, 6/5*   + .476, .123, .005   − .524, .152, .008 −.080   (.018) (.018) (.040)
	PLAY W      G     BG     EQUITY VOTES CL DMP GG GS   13/11(2), 6/4(2)   + .524, .135, .005   − .476, .125, .005 +.059   RB (.069)   24/20(2)   + .508, .092, .003   − .492, .074, .002 +.035   (.024) (.032) (.118)   24/22(2), 6/4(2)   + .501, .111, .004   − .499, .098, .003 +.015   (.044) (.047) (.095) (.063)
	PLAY W      G     BG     EQUITY VOTES CL DMP GG GS   8/5*, 6/5   + .570, .180, .009   − .430, .114, .005 +.210   RB
	PLAY W      G     BG     EQUITY VOTES CL DMP GG GS   13/11, 8/5*   + .470, .136, .006   − .530, .164, .011 −.092   RB (.003)   24/22, 8/5*   + .463, .123, .005   − .537, .155, .008 −.108   (.016) (.015) (.040)
	PLAY W      G     BG     EQUITY VOTES CL DMP GG GS   8/5*(2), 6/3(2)   + .610, .232, .012   − .390, .101, .005 +.359   RB
	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)
	PLAY W      G     BG     EQUITY VOTES CL DMP GG GS   8/4, 6/4   + .473, .116, .004   − .527, .139, .006 −.078   RB
	PLAY W      G     BG     EQUITY VOTES CL DMP GG GS   24/20, 8/5*   + .470, .124, .005   − .530, .155, .008 −.092   RB (.017)   13/9, 8/5*   + .466, .137, .006   − .534, .170, .012 −.107   (.015) (.008) (.039)   8/5*/1*   + .459, .131, .005   − .541, .161, .008 −.115   (.023) (.022) (.025) (.035)
	PLAY W      G     BG     EQUITY VOTES CL DMP GG GS   13/5*(2)   + .602, .216, .011   − .398, .100, .004 +.328   RB
	PLAY W      G     BG     EQUITY VOTES CL DMP GG GS   13/8, 6/5*   + .479, .130, .005   − .521, .150, .008 −.064   RB
	PLAY W      G     BG     EQUITY VOTES CL DMP GG GS   24/22, 13/8   + .454, .104, .004   − .546, .149, .005 −.139   RB   24/22, 6/1*   + .441, .102, .003   − .559, .150, .007 −.170   (.031) (.025) (.029) (.028)   13/8, 6/4   + .439, .098, .003   − .561, .155, .007 −.182   (.043) (.029) (.040) (.041)
	PLAY W      G     BG     EQUITY VOTES CL DMP GG GS   13/5*   + .474, .135, .006   − .526, .150, .008 −.070   RB   8/3, 6/3   + .459, .123, .005   − .541, .153, .007 −.114   (.045) (.029) (.054) (.036)
	PLAY W      G     BG     EQUITY VOTES CL DMP GG GS   24/15*   + .530, .127, .006   − .470, .131, .004 +.058   RB
	PLAY W      G     BG     EQUITY VOTES CL DMP GG GS   8/3(2), 6/1*(2)   + .515, .193, .007   − .485, .131, .005 +.093   RB   13/8(2), 6/1*(2)   + .508, .156, .005   − .492, .128, .004 +.045   (.048) (.013) (.086) (.008)
	PLAY W      G     BG     EQUITY VOTES CL DMP GG GS   13/7, 8/7   + .465, .112, .004   − .535, .144, .005 −.103   RB (.010) (.019)   24/18, 6/5*   + .470, .116, .005   − .530, .169, .008 −.115   (.012) (.039)   13/7, 6/5*   + .462, .123, .005   − .538, .167, .011 −.127   (.024) (.017) (.003) (.053)
	PLAY W      G     BG     EQUITY VOTES CL DMP GG GS   13/5*   + .474, .135, .006   − .526, .150, .008 −.070   RB
	PLAY W      G     BG     EQUITY VOTES CL DMP GG GS   24/15*   + .530, .127, .006   − .470, .131, .004 +.058   RB
	PLAY W      G     BG     EQUITY VOTES CL DMP GG GS   8/2, 6/2   + .443, .121, .004   − .557, .159, .007 −.157   B (.014) (.012)   24/14   + .449, .094, .004   − .551, .160, .006 −.169   R (.013) (.039)   24/18, 13/9   + .442, .114, .005   − .558, .178, .009 −.183   (.026) (.014) (.013) (.050)
	PLAY W      G     BG     EQUITY VOTES CL DMP GG GS   24/13   + .474, .088, .003   − .526, .141, .004 −.106   RB   24/18, 13/8   + .465, .096, .004   − .535, .144, .005 −.120   (.014) (.019) (.003) (.025)
	PLAY W      G     BG     EQUITY VOTES CL DMP GG GS   24/18(2), 13/7(2)   + .604, .115, .004   − .396, .069, .002 +.256   RB
Summary Rolls in order from luckiest to unluckiest, and calculation of average equity. (+.363) 8/5*(2), 6/3(2) +.359 × 1  =   +.359 (+.333) 13/5*(2) +.328 × 1  =   +.328 (+.279) 24/22, 6/5*(2) +.274 × 1  =   +.274 (+.261) 24/18(2), 13/7(2) +.256 × 1  =   +.256 (+.215) 8/5*, 6/5 +.210 × 2  =   +.420 (+.097) 8/3(2), 6/1*(2) +.093 × 1  =   +.093 (+.063) 13/11(2), 6/4(2) +.059 × 1  =   +.059 (+.063) 24/15* +.058 × 2  =   +.116 (+.063) 24/15* +.058 × 2  =   +.116 (−.057) 24/20, 6/5* −.061 × 2  =   −.122 (−.057) 13/11, 6/5* −.062 × 2  =   −.124 (−.060) 13/8, 6/5* −.064 × 2  =   −.129 (−.065) 13/5* −.070 × 2  =   −.139 (−.065) 13/5* −.070 × 2  =   −.139 (−.074) 8/4, 6/4 −.078 × 2  =   −.156 (−.088) 24/20, 8/5* −.092 × 2  =   −.185 (−.088) 13/11, 8/5* −.092 × 2  =   −.185 (−.098) 13/7, 8/7 −.103 × 2  =   −.206 (−.101) 24/13 −.106 × 2  =   −.211 (−.134) 24/22, 13/8 −.139 × 2  =   −.278 (−.152) 8/2, 6/2 −.157 × 2  =   −.313   ———   White's Average Equity −.167  ÷  36  =  −.005

 

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