On Tue, 2012-08-21 at 20:25 -0400, Ryan McKinnon wrote: > Cube analysis > 2-ply cubeless equity +0.243 (Money: +0.246) > 0.573 0.222 0.024 - 0.427 0.140 0.006 > Cubeful equities: > 1. No double +0.349 > 2. Double, pass +1.000 ( +0.651) > 3. Double, take +0.219 ( -0.130) > Proper cube action: No double, take (16.6%) > > (see image here: > http://img689.imageshack.us/img689/2342/doubleaction.png) > > And the corresponding section in the sgf file, when a double was > mistakenly offered: > > ;B[double]DA[E ver 3 2C 1 0.000000 1 0.572881 0.222155 0.024300 > 0.139598 0.006174 0.243145 0.527005 0.572881 0.222155 0.024300 > 0.139598 0.006174 0.243145 0.516940]BM[2]
I think I understood it now. Finally. ;) Click the MWC button under the cube analysis and things should become obvious. You will see match winning probabilities of 51.6940 % (0.516940) for double and take, and 52.7005 % (0.527005) for no double. When you display equities instead of match winning changes, these values get converted by the function mwc2eq(). An example: In a match with a centered cube at 7-away/6-away the leader doubles. The analysis data looks like this: ;B[double] DA[E ver 3 3C 1 0.000000 1 0.697536 0.295444 0.006992 0.073738 0.003115 0.661274 0.615284 0.697536 0.295444 0.006992 0.073738 0.003115 0.661274 0.631003] The interesting values for the cube analysis are the rightmost ones. The match winning chances are presented as this: 1. Double, pass 62.67 % 2. Double, take 63.10 % 0.43 % 3. No double 61.53 % -1.14 % The values for double, take and no double come directly from the analysis data saved in the SGF file. The value for double, pass comes from the match equity table. I used Rockwell-Kazaross here. We are currently at 7-away/6-away. If the trailer drops we are at 7-away/5-away, and we lookup 62.6658 (ca. 62.67) from the MET. When you display equities instead of MWC, the probabilities have to be transformed. For that, you first lookup the match winning probabilities for either opponent winning the game at the current cube value. If black wins we are at 7-away/5-away, if black loses we are at 6-away/6-away. Therefore, black's match winning chance after winning the game will be p_win = 0.626658 We know that value already from the lookup above and this is no coincidence. If black loses we are at 6-away/6-away, and the trivial value for the match winning probability is p_lose = 0.500000 This is now transformed to an equity: eq = (2 * mwc - (p_win + p_lose)) / (p_win - p_lose) Let's feed the values from above into the formula. For double, take (0.631003 or 63.1003 %) we get an equity of +1.06860995752340949643. For double, drop (0.615284) we get an equity of +0.82039823777416349539, and for double, pass (0.626658) we get - surprise, surprise - an equity of exactly 1.0, which is no wonder but only a proof of correctness. Correct me if I'm wrong, but I think that the corresponding code in GNUBG - which is more complicated - is rather a creative way of applying rounding errors to already computed values. Guido -- Империя ООД | Imperia OOD ул. „Княз-Борис-I“ № 86, София 1000 | ul. "Knyaz-Boris-I" № 86, Sofia http://www.imperia.bg/ _______________________________________________ Bug-gnubg mailing list Bug-gnubg@gnu.org https://lists.gnu.org/mailman/listinfo/bug-gnubg