Replies to 24/21, 24/20

Best Nearly Best Pretty Good Not So Good Here are White's best replies after Red opens 24/21, 24/20. 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). 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   6/5*/4*(2)   + .593, .194, .008   − .407, .099, .004 +.285   R   6/5*(2), 6/4*   + .587, .189, .007   − .413, .107, .005 +.258   (.027) (.013) (.024) (.028)
	PLAY W      G     BG     EQUITY VOTES CL DMP GG GS   6/5*, 6/4*   + .499, .139, .005   − .501, .150, .010 −.018   R
	PLAY W      G     BG     EQUITY VOTES CL DMP GG GS   13/11(2), 6/4*(2)   + .577, .165, .007   − .423, .102, .004 +.219   R
	PLAY W      G     BG     EQUITY VOTES CL DMP GG GS   8/5*, 6/5   + .554, .157, .006   − .446, .106, .004 +.161   R
	PLAY W      G     BG     EQUITY VOTES CL DMP GG GS   8/5*, 6/4*   + .494, .143, .005   − .506, .153, .010 −.026   R (.004)   24/21, 6/4*   + .475, .110, .004   − .525, .132, .006 −.074   (.048) (.037) (.104)
	PLAY W      G     BG     EQUITY VOTES CL DMP GG GS   8/5*(2), 6/3(2)   + .581, .205, .008   − .419, .098, .004 +.274   R
	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)
	PLAY W      G     BG     EQUITY VOTES CL DMP GG GS   8/4*, 6/4   + .526, .143, .005   − .474, .115, .005 +.081   R
	PLAY W      G     BG     EQUITY VOTES CL DMP GG GS   24/20, 8/5*   + .473, .115, .004   − .527, .135, .006 −.077   R (.034) (.013)   24/21, 8/4*   + .466, .109, .004   − .534, .135, .007 −.097   (.020) (.013) (.059) (.026)   24/21, 24/20   + .462, .090, .003   − .538, .118, .004 −.105   (.027) (.021) (.105)   24/20, 6/3   + .460, .103, .004   − .540, .129, .005 −.107   (.030) (.025) (.084) (.025)   8/5*, 8/4*   + .467, .137, .005   − .533, .172, .014 −.109   (.031) (.010) (.098)   13/10, 8/4*   + .458, .126, .005   − .542, .156, .010 −.121   (.044) (.030) (.043) (.085)
	PLAY W      G     BG     EQUITY VOTES CL DMP GG GS   13/5*, 8/4*(2)   + .586, .244, .009   − .414, .107, .005 +.314   R (.005) (.033)   13/5*(2)   + .589, .192, .007   − .411, .093, .003 +.279   (.034) (.101)
	PLAY W      G     BG     EQUITY VOTES CL DMP GG GS   13/8, 6/5*   + .475, .118, .004   − .525, .142, .007 −.076   R   24/23, 13/8   + .454, .103, .003   − .546, .125, .005 −.116   (.040) (.043) (.073) (.010)   24/18   + .460, .088, .003   − .540, .128, .005 −.122   (.045) (.031) (.089) (.005)
	PLAY W      G     BG     EQUITY VOTES CL DMP GG GS   13/8, 6/4*   + .473, .112, .004   − .527, .135, .006 −.079   R   24/22, 13/8   + .458, .102, .003   − .542, .130, .005 −.112   (.033) (.030) (.049) (.019)
	PLAY W      G     BG     EQUITY VOTES CL DMP GG GS   8/3, 6/3   + .466, .118, .004   − .534, .126, .006 −.077   R (.013) (.018) (.014)   13/5*   + .473, .121, .004   − .527, .140, .007 −.077   (.000) (.029)   24/21, 13/8   + .469, .102, .003   − .531, .122, .004 −.084   (.006) (.007) (.046)   13/8, 6/3   + .456, .109, .004   − .544, .132, .006 −.113   (.035) (.033) (.056) (.047)
	PLAY W      G     BG     EQUITY VOTES CL DMP GG GS   24/20, 13/8   + .474, .099, .003   − .526, .119, .004 −.073   R (.024)   13/4*   + .471, .115, .004   − .529, .135, .006 −.081   (.008) (.006) (.038)
	PLAY W      G     BG     EQUITY VOTES CL DMP GG GS   13/3(2)   + .514, .139, .004   − .486, .109, .004 +.057   R
	PLAY W      G     BG     EQUITY VOTES CL DMP GG GS   13/7, 8/7   + .471, .108, .003   − .529, .117, .004 −.069   R (.006) (.030)   13/7, 6/5*   + .471, .123, .004   − .529, .147, .009 −.087   (.017) (.005) (.059)   24/18, 6/5*   + .473, .104, .004   − .526, .150, .007 −.102   (.033) (.033) (.059)
	PLAY W      G     BG     EQUITY VOTES CL DMP GG GS   13/5*   + .473, .121, .004   − .527, .140, .007 −.077   R   13/7, 6/4*   + .466, .117, .004   − .534, .146, .008 −.101   (.023) (.013) (.020) (.024)   24/18, 6/4*   + .465, .096, .003   − .535, .148, .007 −.124   (.047) (.015) (.063) (.030)
	PLAY W      G     BG     EQUITY VOTES CL DMP GG GS   13/4*   + .471, .115, .004   − .529, .135, .006 −.081   R   24/18, 6/3   + .467, .098, .004   − .533, .138, .006 −.108   (.027) (.008) (.041) (.015)   13/7, 8/5*   + .459, .124, .004   − .541, .152, .010 −.115   (.035) (.024) (.004) (.059)   24/21, 13/7   + .453, .111, .004   − .547, .131, .006 −.117   (.037) (.037) (.044) (.029)   24/18, 8/5*   + .463, .105, .004   − .537, .153, .007 −.125   (.044) (.016) (.034) (.052)
	PLAY W      G     BG     EQUITY VOTES CL DMP GG GS   8/2, 6/2   + .459, .118, .004   − .541, .132, .006 −.099   R (.001) (.001)   13/3   + .459, .113, .004   − .541, .132, .005 −.103   (.004) (.009)   24/20, 13/7   + .453, .108, .004   − .547, .129, .006 −.118   (.019) (.013) (.032) (.006)   13/7, 8/4*   + .455, .117, .004   − .545, .150, .009 −.128   (.029) (.009) (.008) (.044)   24/18, 8/4*   + .458, .098, .003   − .542, .151, .007 −.141   (.042) (.003) (.041) (.041)   24/18, 6/2   + .453, .099, .004   − .547, .147, .006 −.143   (.043) (.012) (.047) (.040)   24/20, 24/18   + .453, .083, .003   − .547, .133, .005 −.146   (.047) (.013) (.082) (.014)
	PLAY W      G     BG     EQUITY VOTES CL DMP GG GS   24/18, 13/8   + .485, .098, .003   − .515, .123, .004 −.055   (.013)   24/13   + .477, .082, .003   − .523, .109, .003 −.073   R (.018) (.016) (.048)
	PLAY W      G     BG     EQUITY VOTES CL DMP GG GS   24/18(2), 13/7(2)   + .610, .105, .003   − .390, .054, .001 +.274   R
Summary Rolls in order from luckiest to unluckiest, and calculation of average equity. (+.307) 13/5*, 8/4*(2) +.314 × 1  =   +.314 (+.279) 6/5*/4*(2) +.285 × 1  =   +.285 (+.267) 8/5*(2), 6/3(2) +.274 × 1  =   +.274 (+.267) 24/18(2), 13/7(2) +.274 × 1  =   +.274 (+.213) 13/11(2), 6/4*(2) +.219 × 1  =   +.219 (+.154) 8/5*, 6/5 +.161 × 2  =   +.321 (+.074) 8/4*, 6/4 +.081 × 2  =   +.162 (+.050) 13/3(2) +.057 × 1  =   +.057 (−.025) 6/5*, 6/4* −.018 × 2  =   −.036 (−.032) 8/5*, 6/4* −.026 × 2  =   −.052 (−.032) 8/4*, 6/5* −.026 × 2  =   −.052 (−.062) 24/18, 13/8 −.055 × 2  =   −.111 (−.076) 13/7, 8/7 −.069 × 2  =   −.138 (−.079) 24/20, 13/8 −.073 × 2  =   −.145 (−.083) 13/8, 6/5* −.076 × 2  =   −.153 (−.084) 8/3, 6/3 −.077 × 2  =   −.155 (−.084) 13/5* −.077 × 2  =   −.155 (−.084) 24/20, 8/5* −.077 × 2  =   −.155 (−.086) 13/8, 6/4* −.079 × 2  =   −.159 (−.087) 13/4* −.081 × 2  =   −.161 (−.106) 8/2, 6/2 −.099 × 2  =   −.199   ———   White's Average Equity +.236  ÷  36  =  +.007

 

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