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| Carpenter's Square Endgame Evaluation http://www.lifein19x19.com/viewtopic.php?f=15&t=16994 |
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| Author: | RobertJasiek [ Mon Oct 21, 2019 10:52 pm ] |
| Post subject: | Carpenter's Square Endgame Evaluation |
I evaluate the following carpenter's square as a local endgame on the marked locale. I apply the modern endgame theory explained in [14]. For Black's start, I presume this sequence: Furthermore, I assume this sequence and the studied variations to be dominating. Further study should verify this. If a different ko variation should be dominating, the values might have to be corrected slightly. White starts on the 2-2, of course. The most important conclusions are as follows: Initial position: Count = 4 2/3 Move value = 11 2/3 Type = gote Length of sequence worth playing successively = 1 In practice, it can often be correct to play the first five moves successively because their gains are at least 10 2/3 and therefore similar to the initial move value. The gains of the 6th and especially 7th moves are much smaller though: 5 2/3 and 1 2/3. Moves with move value 9 2/3 (as in the created ko): Moves 8 to 11. In particular, it would be a mistake to derive the wrong initial values from the sente follower after move 10 as the count 2 2/3 and move value 9 2/3, as done in the book Yose Size List. Black's alternating sequence Code: after move count move gain move value type length of successive sequence(s) 0 4 2/3 1 11 2/3 11 2/3 gote 1 1 16 1/3 2 10 2/3 5 2/3 gote 5 2 5 2/3 3 10 2/3 10 2/3 gote 3 3 16 1/3 4 11 11/12 5 2/3 gote 3 4 4 5/12 5 11 11/12 7 11/12 gote 1 5 16 1/3 6 5 2/3 5 2/3 gote 1 6 10 2/3 7 1 2/3 1 2/3 sente Black's 5 White's 4 7 12 1/3 8 9 2/3 9 2/3 sente 4 8 2 2/3 9 9 2/3 9 2/3 gote 3 9 12 1/3 10 9 2/3 9 2/3 sente 2 10 2 2/3 11 9 2/3 9 2/3 ko Black's 2 White's 1 11 12 1/3 9 2/3 ko Black's 1 White's 2 Copy and save the following SGF file, best viewed with GoWrite: (;SZ[19]CA[UTF-8]GM[1]FF[4]ST[2]AP[GOWrite:3.0.10]AB[mb][oe][ob][pe][qe][re][oc][od][rg]PM[2]FG[259:]C[Each just stated value is a count. The locale is marked. M is the move value of the currently studied hypothesis and position. Gb1, Gb2,... are the gains of move 1, 2,... of Black's alternating sequence of the currently studied hypothesis and position. Gw1, Gw2,... are the gains of move 1, 2,... of White's alternating sequence of the currently studied hypothesis and position. So far, we assume, but do not verify, that Black's alternating sequence and its variations shown are dominating. Refuted Hypotheses Black's 7/9/11-move sequence gote move value M = (12 1/3 - (-7)) / 2 = (19 1/3) / 2 = 9 2/3 M > Gb6 9 2/3 > 1 2/3 Refuted Hypotheses Black's 8/10-move sequence sente move value M = 2 2/3 - (-7) = 9 2/3 M > Gb6 9 2/3 > 1 2/3 Refuted Hypothesis Black's 6-move sequence sente move value M = 10 2/3 - (-7) = 17 2/3 M > Gb6 17 2/3 > 1 2/3 Refuted Hypotheses Black's 3/5-move sequence gote move value M = (16 1/3 - (-7)) / 2 = (23 1/3) / 2 = 11 2/3 M > Gb2 11 2/3 > 10 2/3 Refuted Hypothesis Black's 4-move sequence sente move value M = 4 5/12 - (-7) = 11 5/12 M > Gb2 11 5/12 > 10 2/3 Refuted Hypothesis Black's 2-move sequence sente move value M = 5 2/3 - (-7) = 12 2/3 M > Gb2 12 2/3 > 10 2/3 Confirmed Hypothesis gote count = (16 1/3 + (-7)) / 2 = (9 1/3) / 2 = 4 2/3 gote move value M = (16 1/3 - (-7)) / 2 = (23 1/3) / 2 = 11 2/3 Gb1 = 11 2/3 Gw1 = 11 2/3 M <= Gb1 11 2/3 <= 11 2/3 M <= Gw1 11 2/3 <= 11 2/3 ]PW[ ]SQ[rd][sd][se][na][oa][pa][qa][ra][sa][pb][qb][rb][sb][pc][qc][rc][sc][pd][qd]AW[rd][pc][pb][pd][qd]PB[ ]GN[ ] ( ;B[rb] ;FG[259:]C[16 1/3 position after move 1 refuted hypotheses White's 6/8/10-move sequence sente move value M = 9 2/3 M > Gw6 9 2/3 > 1 2/3 refuted hypotheses White's 7/9-move sequence gote move value M = (22 - 2 2/3) / 2 = 9 2/3 M > Gw6 9 2/3 > 1 2/3 confirmed hypothesis White's 5-move sequence gote count = (22 + 10 2/3) / 2 = (32 2/3) / 2 = 16 1/3 gote move value M = (22 - 10 2/3) / 2 = (11 1/3) / 2 = 5 2/3 Gb1 = 5 2/3 Gw1 = 10 2/3 M <= Gb1 5 2/3 <= 5 2/3 M <= Gw1, Gw2, Gw3, Gw4, Gw5 5 2/3 <= 10 2/3, 10 2/3, 11 11/12, 11 11/12, 5 2/3]PM[2] ( ;W[sb] ;FG[259:]C[5 2/3 position after move 2 refuted hypotheses Black's 5/7/9-move sequence and White's 1/3-move sequence gote move value M = (12 1/3 - (-5)) / 2 = (17 1/3) / 2 = 8 2/3 M > Gb5 8 2/3 > 1 2/3 refuted hypotheses Black's 5/7/9-move sequence and White's 2-move sequence sente move value M = 12 1/3 - 0 = 12 1/3 M > Gb5 12 1/3 > 1 2/3 refuted hypotheses Black's 6/8-move sequence and White's 1/3-move sequence sente move value M = 2 2/3 - (-5) = 7 2/3 M > Gb5 7 2/3 > 1 2/3 refuted hypotheses Black's 4-move sequence and White's 1/3-move sequence sente move value M = 10 2/3 - (-5) = 15 2/3 M > Gb4 15 2/3 > 5 2/3 refuted hypothesis Black's 1/3-move sequence and White's 3-move sequence gote move value M = (16 1/3 - (-5)) / 2 = (21 1/3) / 2 = 10 2/3 M > Gw3 10 2/3 > 5 refuted hypothesis Black's 3-move sequence and White's 2-move sequence sente move value M = 16 1/3 - 0 = 16 1/3 M > Gw2 16 1/3 > 5 confirmed hypothesis Black's 3-move sequence and White's 1-move sequence gote count = (16 1/3 + (-5)) / 2 = (11 1/3) / 2 = 5 2/3 gote move value M = (16 1/3 - (-5)) / 2 = (21 1/3) / 2 = 10 2/3 Gb1 = 10 2/3 Gw1 = 10 2/3 M <= Gb1, Gb2, Gb3 10 2/3 <= 10 2/3, 11 11/12, 11 11/12 M <= Gw1 10 2/3 <= 10 2/3]PM[2] ( ;B[qb] ;FG[259:]C[16 1/3 position after move 3 refuted hypotheses White's 4/6/8-move sequence sente move value M = 22 - 12 1/3 = 9 2/3 M > Gw4 9 2/3 > 1 2/3 refuted hypotheses White's 5/7-move sequence gote move value M = (22 - 2 2/3) / 2 = (19 1/3) / 2 = 9 2/3 M > Gw4 9 2/3 > 1 2/3 confirmed hypothesis White's 3-move sequence gote count = (22 + 10 2/3) / 2 = (32 2/3) / 2 = 16 1/3 gote move value M = (22 - 10 2/3) / 2 = (11 1/3) / 2 = 5 2/3 Gb1 = 5 2/3 Gw1 = 16 1/3 - 4 5/12 = 11 11/12 M <= Gb1 5 2/3 <= 5 2/3 M <= Gw1, Gw2, Gw3 5 2/3 <= 11 11/12, 11 11/12, 5 2/3]PM[2] ( ;C[ ]W[pa] ;FG[259:]C[4 5/12 position after move 4 refuted hypotheses Black's 3/5/7-move sequence and White's 4/2-move sequence sente move value M = 12 1/3 - 0 = 12 1/3 M > Gb2 12 1/3 > 1 2/3 refuted hypotheses Black's 3/5/7-move sequence and White's 3-move sequence gote move value M = (12 1/3 - (-5)) / 2 = (17 1/3) / 2 = 8 2/3 M > Gb2 8 2/3 > 1 2/3 refuted hypotheses Black's 3/5/7-move sequence and White's 1-move sequence gote move value M = (12 1/3 - (-3 1/2)) / 2 = (15 5/6) / 2 = 7 11/12 M > Gb2 7 11/12 > 1 2/3 refuted hypotheses Black's 6/4-move sequence and White's 3-move sequence sente move value M = 2 2/3 - (-5) = 7 2/3 M > Gb2 7 2/3 > 1 2/3 refuted hypotheses Black's 6/4-move sequence and White's 1-move sequence sente move value M = 2 2/3 - (-3 1/2) = 6 1/6 M > Gb2 6 1/6 > 1 2/3 refuted hypothesis Black's 2-move sequence and White's 3-move sequence sente move value M = 10 1/2 - (-5) = 15 1/2 M > Gb2 15 1/2 > 1 2/3 refuted hypothesis Black's 2-move sequence and White's 1-move sequence gote move value M = 10 1/2 - (-3 1/2) = 14 M > Gb2 14 > 1 2/3 refuted hypotheses Black's 1-move sequence and White's 4/2-move sequence sente move value M = 12 1/3 - 0 = 12 1/3 M > Gw2 12 1/3 > 3 1/2 refuted hypothesis Black's 1-move sequence and White's 3-move sequence gote move value M = (12 1/3 - (-5)) / 2 = (17 1/3) / 2 = 8 2/3 M > Gw2 8 2/3 > 3 1/2 confirmed hypothesis Black's 1-move sequence and White's 1-move sequence gote count = (12 1/3 + (-3 1/2)) / 2 = (8 5/6) / 2 = 4 5/12 gote move value M = (12 1/3 - (-3 1/2)) / 2 = (15 5/6) / 2 = 7 11/12 Gb1 = 7 11/12 Gw1 = 7 11/12 M <= Gb1 7 11/12 <= 7 11/12 M <= Gw1 7 11/12 <= 7 11/12 ]PM[2] ( ;B[sd] ;FG[259:]C[16 1/3 position after move 5 Hypothesis 1 White's long sente with White's 6-move sequence sente count = 12 1/3 sente move value M = 22 - 12 1/3 = 9 2/3 Gb1 = 9 2/3 Gw1 = 1 2/3 refuting Hypothesis 1\: M > Gw1 9 2/3 > 1 2/3 Hypothesis 2 White's long gote with White's 5-move sequence gote count = (22 + 2 2/3) / 2 = (24 2/3) / 2 = 12 1/3 gote move value M = (22 - 2 2/3) / 2 = (19 1/3) / 2 = 9 2/3 Gb1 = 9 2/3 Gw1 = 1 2/3 refuting Hypothesis 2\: M > Gw1 9 2/3 > 1 2/3 Hypothesis 3 White's long sente with White's 4-move sequence sente count = 12 1/3 sente move value M = 22 - 12 1/3 = 9 2/3 Gb1 = 9 2/3 Gw1 = 1 2/3 refuting Hypothesis 3\: M > Gw1 9 2/3 > 1 2/3 Hypothesis 4 White's long gote with White's 3-move sequence gote count = (22 + 2 2/3) / 2 = (24 2/3) / 2 = 12 1/3 gote move value M = (22 - 2 2/3) / 2 = (19 1/3) / 2 = 9 2/3 Gb1 = 9 2/3 Gw1 = 1 2/3 refuting Hypothesis 4\: M > Gw1 9 2/3 > 1 2/3 Hypothesis 5 White's local sente with White's 2-move sequence sente count = 12 1/3 sente move value M = 22 - 12 1/3 = 9 2/3 Gb1 = 9 2/3 Gw1 = 1 2/3 refuting Hypothesis 5\: M > Gw1 9 2/3 > 1 2/3 Hypothesis 6 White's local gote with White's 1-move sequence gote count = (22 + 10 2/3) / 2 = (32 2/3) / 2 = 16 1/3 gote move value M = (22 - 10 2/3) / 2 = (11 1/3) / 2 = 5 2/3 Gb1 = 5 2/3 Gw1 = 5 2/3 confirming Hypothesis 6\: M <= Gb1 5 2/3 <= 5 2/3 M <= Gw1 5 2/3 <= 5 2/3]PM[2] ( ;W[sc] ;FG[259:]C[position after move 6 Hypothesis 1 White's long sente with Black's 5-move sequence and White's 4-move sequence sente count = 10 2/3 sente move value M = 12 1/3 - 10 2/3 = 1 2/3 Gb1 = 1 2/3 Gw1 = 9 2/3 confirming Hypothesis 1\: M <= Gb1, Gb2, Gb3, Gb4, Gb5 1 2/3 <= 1 2/3, 9 2/3, 9 2/3, 9 2/3, 9 2/3 M <= Gw1, Gw2, Gw3, Gw4 9 2/3 <= 9 2/3, 9 2/3, 9 2/3, 9 2/3]PM[2] ( ;B[se] ;FG[259:]C[position after move 7 Hypothesis 1 White's long sente sente count = 12 1/3 sente move value M = 22 - 12 1/3 = 9 2/3 Gb1 = 9 2/3 Gw1 = 9 2/3 confirming Hypothesis 1\: M <= Gb1 9 2/3 <= 9 2/3 M <= Gw1, Gw2, Gw3, Gw4 9 2/3 <= 9 2/3, 9 2/3, 9 2/3, 9 2/3]PM[2] ( ;W[rc] ;FG[259:]C[position after move 8 Hypothesis 1 Black's long gote gote count = (12 1/3 + (-7)) / 2 = (5 1/3) / 2 = 2 2/3 gote move value M = (12 1/3 - (-7)) / 2 = (19 1/3) / 2 = 9 2/3 Gb1 = 9 2/3 Gw1 = 9 2/3 confirming Hypothesis 1\: M <= Gb1, Gb2, Gb3 9 2/3 <= 9 2/3, 9 2/3, 9 2/3 M <= Gw1 9 2/3 <= 9 2/3]PM[2] ( ;B[qa] ;FG[259:]C[position after move 9 Hypothesis 1 White's local sente sente count = 12 1/3 sente move value M = 22 - 12 1/3 = 9 2/3 Gb1 = 9 2/3 Gw1 = 9 2/3 confirming Hypothesis 1\: M <= Gb1 9 2/3 <= 9 2/3 M <= Gw1, Gw2 9 2/3 <= 9 2/3, 9 2/3]PM[2] ( ;W[ra] ;FG[259:]C[position after move 10 ordinary ko move value (22 - (-7)) / 3 = 29/3 = 9 2/3 count -7 + 1 * 9 2/3 = 2 2/3]PM[2] ( ;B[sa] ;FG[259:]PM[2]MN[1]C[position after move 11 ordinary ko move value (22 - (-7)) / 3 = 29/3 = 9 2/3 count 22 - 1 * 9 2/3 = 12 1/3] ( ;W[ra];B[tt];C[-7]W[qc] ) ( ;FG[259:]PM[2];B[ra]C[22] ) ) ( ;FG[259:]MN[1]PM[2] ( ;B[sa];W[tt];B[ra]C[22] ) ( ;FG[259:]PM[2];C[-7]W[qc] ) ) ) ( ;FG[259:]MN[1]PM[2] ( ;B[ra]C[22] ) ( ;FG[259:]PM[2];C[2 2/3]W[ra] ;B[sa]C[12 1/3 Gw2 = 9 2/3] ) ) ) ( ;FG[259:]MN[1]PM[2] ( ;B[qa]C[12 1/3] ;C[2 2/3 Gb2 = 9 2/3]W[ra] ;B[sa]C[12 1/3 Gb3 = 9 2/3] ) ( ;FG[259:]PM[2];C[-7]W[ra] ) ) ) ( ;FG[259:]MN[1]PM[2] ( ;B[rc]C[22] ) ( ;FG[259:]PM[2];C[2 2/3]W[rc] ;B[qa]C[12 1/3 Gw2 = 9 2/3] ;C[2 2/3 Gw3 = 9 2/3]W[ra] ;B[sa]C[12 1/3 Gw4 = 9 2/3] ) ) ) ( ;FG[259:]MN[1]PM[2] ( ;B[se]C[12 1/3] ;C[2 2/3 Gb2 = 9 2/3]W[rc] ;B[qa]C[12 1/3 Gb3 = 9 2/3] ;C[2 2/3 Gb4 = 9 2/3]W[ra] ;B[sa]C[12 1/3 Gb5 = 9 2/3] ) ( ;FG[259:]PM[2] ;C[Hypothesis 1 Black's long gote gote count = (10 2/3 + (-8 2/3)) / 2 = 2/2 = 1 gote move value M = (10 2/3 - (-8 2/3)) / 2 = (19 1/3) / 2 = 9 2/3 Gb2 = 11 1/3 Gw2 = 9 2/3 confirming Hypothesis 1\: M <= Gb2, Gb3, Gb4 9 2/3 <= 9 2/3, 9 2/3, 9 2/3 M <= Gw2 9 2/3 <= 9 2/3]W[ra] ( ;B[qa]C[10 2/3 Gw2 = 9 2/3] ;C[best because W avoids approach ko 2 2/3 + (-1 2/3) = 1 Gw3 = 9 2/3]W[rc] ;B[sa]C[10 2/3 Gw4 = 9 2/3 After dissolution of the ko, the count of the remaining endgame with W's privilege on the right side, with a locale temporarily expanded by one intersection, is\: -2/3 Shrinking the expanded locale means modifying the count by -1. Accounted for the initial locale, the the remaining endgame has the adjusted count -1 2/3. In the initial locale, the count is 12 1/3. In the initial locale, the total count including the remaining local endgame is 12 1/3 + (-1 2/3) = 10 2/3.] ) ( ;FG[259:]MN[2]PM[2] ;C[simply speaking, this is the best move -7 + (-1 2/3) = -8 2/3]W[rc] ) ) ) ) ( ;FG[259:]MN[1]PM[2] ( ;B[sc]C[22] ) ( ;FG[259:]C[2 2/3 Gw3 = 9 2/3]PM[2] ;C[10 2/3]W[sc] ;B[se]C[12 1/3 Gw2 = 1 2/3] ;C[2 2/3 Gw3 = 9 2/3]W[rc] ;B[qa]C[12 1/3 Gw4 = 9 2/3] ;C[2 2/3 Gw5 = 9 2/3]W[ra] ;B[sa]C[12 1/3 Gw6 = 9 2/3] ) ) ) ( ;FG[259:]MN[1]PM[2] ( ;B[sd]C[12 1/3] ;C[10 2/3 Gb2 = 1 2/3]W[sc] ;B[se]C[12 1/3 Gb3 = 1 2/3] ;C[2 2/3 Gb4 = 9 2/3]W[rc] ;B[qa]C[12 1/3 Gb5 = 9 2/3] ;C[2 2/3 Gb6 = 9 2/3]W[ra] ;B[sa]C[12 1/3 Gb7 = 9 2/3] ) ( ;FG[259:]PM[2] ;C[-3 1/2 best choice because possible seki is better than the kos In locale, white follower's count -8. In expanded locale, white follower's count -7. In locale with accounting remaining endgame of expanded locale to the locale, white follower's count -7. Hypothesis 1 Black's long gote gote count = -3 1/2 gote move value M = 3 1/2 Gb2 = 3 1/2 Gb3 = 12 Gb4 = 5 Gw2 = 3 1/2 confirming Hypothesis 1\: M <= Gb2, Gb3, Gb4 3 1/2 <= 3 1/2, 12, 5 M <= Gw2 3 1/2 <= 3 1/2]W[rc] ;B[ra]C[best sente count 0 Gw2 = 3 1/2] ;C[sente seki is best with expanded locale\: gote count -5 Gw3 = 12]W[qa] ;B[sd]C[0 Gw4 = 5] ) ) ) ( ;FG[259:]MN[1]PM[2] ( ;B[pa]C[22] ) ( ;FG[259:]PM[2];C[4 5/12]W[pa] ;B[sd]C[16 1/3 Gw2 = 11 11/12] ;C[10 2/3 Gw3 = 5 2/3]W[sc] ;B[se]C[12 1/3 Gw4 = 1 2/3] ;C[2 2/3 Gw5 = 9 2/3]W[rc] ;B[qa]C[12 1/3 Gw6 = 9 2/3] ;C[2 2/3 Gw7 = 9 2/3]W[ra] ;B[sa]C[12 1/3 Gw8 = 9 2/3] ) ) ) ( ;FG[259:]MN[1]PM[2] ;B[qb]C[16 1/3] ;C[4 5/12 Gb2 = 11 11/12]W[pa] ;B[sd]C[16 1/3 Gb3 = 11 11/12] ;C[10 2/3 Gb4 = 5 2/3]W[sc] ;B[se]C[12 1/3 Gb5 = 1 2/3] ;C[2 2/3 Gb6 = 9 2/3]W[rc] ;B[qa]C[12 1/3 Gb7 = 9 2/3] ;C[2 2/3 Gb8 = 9 2/3]W[ra] ;B[sa]C[12 1/3 Gb9 = 9 2/3] ) ( ;FG[259:]MN[1]PM[2] ;C[-5 because Black next sente result -5 White next result -6]W[rc] ;B[sd]C[0 because Black next sente result 0 Gw2 = 5] ;C[-5 Gw3 = 5]W[ra] ) ) ( ;FG[259:]MN[1]PM[2] ;B[sd]C[22] ) ( ;FG[259:]MN[1]PM[2] ;C[5 2/3]W[sb] ;B[qb]C[16 1/3 Gw2 = 10 2/3] ;C[4 5/12 Gw3 = 11 11/12]W[pa] ;B[sd]C[16 1/3 Gw4 = 11 11/12] ;C[10 2/3 Gw5 = 5 2/3]W[sc] ;B[se]C[12 1/3 Gw6 = 1 2/3] ;C[2 2/3 Gw7 = 9 2/3]W[rc] ;B[qa]C[12 1/3 Gw8 = 9 2/3] ;C[2 2/3 Gw9 = 9 2/3]W[ra] ;B[sa]C[12 1/3 Gw10 = 9 2/3] ) ) ( ;FG[259:]PM[2];C[-7]W[rb] ) ) |
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| Author: | Bill Spight [ Mon Oct 21, 2019 11:57 pm ] |
| Post subject: | Re: Carpenter's Square Endgame Evaluation |
Many thanks, Robert!  You may need some SGF tags in that post.  I did a fairly thorough analysis of the Carpenter's Square in the early 2000s. If I didn't trust you I might try to dig it up now. (Java problems on my machine make that difficult at the moment.) Sometime this year I may have something to add to the discussion. Adelante! |
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| Author: | RobertJasiek [ Tue Oct 22, 2019 12:16 am ] |
| Post subject: | Re: Carpenter's Square Endgame Evaluation |
SGF tags do not help because my file is more complicated on its SGF-level than supported here. Your later additions are welcome, also because it is so easy to make accidental mistakes, such as overlooking another but relevant variation. |
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| Author: | Bill Spight [ Tue Oct 22, 2019 3:55 am ] |
| Post subject: | Re: Carpenter's Square Endgame Evaluation |
Here is an SGF with some Carpenter's Square variations. For evaluation you need to add more, OC. |
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| Author: | Gomoto [ Tue Oct 22, 2019 5:26 am ] |
| Post subject: | Re: Carpenter's Square Endgame Evaluation |
Gomoto, how do you evaluate the Carpenter"s Square? I try to avoid it, I lost once a tournament game because misevaluating it. I have only found one pro game with carpenter square in my database of recent games (It is a game of Yeonwoo by the way! Perhaps something for her channel.): |
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