Study 79

Árpád Rusz
2nd UAPA Ty
2015
Special Prize
- after J. Bryant -

White wins

1.Kc5+! 1.Kd5+? Nf6+ 2.Ke6 hxg6 3.Bxf6+ Kh7 4.Bd4 gxh5 5.gxh5 Kg8 6.Kd7! catching the N 6...Kf7! 7.Kxc8 Ke6 8.Bg7 Kf5 9.Bxh6 Kg4!= 1...Nf6 2.gxh7 Kh8!! Triangulation 2...Kxh7 3.Bxf6 Kg8 4.Bd4 Ne7 5.Be3 Kg7 6.Kd6 Ng6 (6...Ng8 7.Ke6+–) 7.hxg6 Kxg6 8.Ke5 h5 9.g5+– 3.Bxf6+ 3.Kb4? Kxh7 (3...Nd6? 4.Bxf6+ Kxh7 5.Bd4+–) 4.Bxf6 Kg8=; 3.Kc6? Ne7+ 4.Kd6 Ned5=; 3.Be5?! Kg7 waste of time] 3...Kxh7 White needs to reach to same position but with BTM. The cycle to achieve this is 36 moves long!! That is a record. Surprisingly, this manoeuvre is almost free of duals (except time wasting duals, the only time when there is an alternative way for a few moves is at move 6 but that also leads to the main line some moves later).

Cyclic zugzwang - WTM

4.Bd4 Ne7 5.Kd6 Ng6!

Position A

5...Nc8+ 6.Kd7+– catching the N; 5...Ng8 6.Ke6+– zugzwang 6.Be5 [minor dual 6.Be3 Nh4 7.Ke5 Nf3+ 8.Ke4 Ne1 9.Bd2 Nc2 10.Kd3 Na3 11.Bf4 Nb5 12.Kc4 Na3+ 13.Kb4 Nc2+ 14.Kc3 Ne1 15.Kd2 etc. as in the main line; 6.hxg6+? Kxg6 7.Be3 h5=] 6...Nh4 7.Kd5 Nf3 8.Bf4 Ne1 9.Kc4 Kg7 10.Kd4! Kh7 11.Kc3 Ng2 12.Bd2 Nh4 13.Kd3 Nf3 14.Bf4 Ne1+ 15.Kd2 Nf3+ 16.Ke3 Ne1

Position B

17.Bg3 Nc2+ 18.Kd3 Nb4+ 19.Kc4 Nc6 20.Kc5 Na5 21.Bf4 Kg7 22.Kb6 Nc4+ 23.Kb5 Na3+ 24.Kb4 Nc2+ 25.Kc3 Ne1 26.Kd2 Nf3+ 27.Ke3 Ne1

Position B'

28.Be5+ Kg8 29.Bc3 Nc2+ 30.Kd3 Na3 31.Be5 Kf7 32.Bf4 Kg7 33.Kc3 Kh7 34.Be5 Nb1+ 35.Kc2 Na3+ 36.Kb3 Nb5 37.Kb4 Na7 38.Kc5 Nc8 39.Bf6

Cyclic zugzwang - BTM

39...Kg8 40.Bd4! Ne7 41.Be3 Kh7 41...Kg7 42.Kd6 Ng8 43.Ke6+– 42.Kd6 Ng6! 42...Nc8+ 43.Kd7+–

Position A'

43.hxg6+ Kxg6 44.Ke5 h5 45.g5 +- This analysis uses the term "Cyclic Zugzwang" which is the generalization of the common 3–move (or 5 ply) long triangulation to pass the move to the weaker side. If the stronger side is to move in a "cyclic zugzwang" position, it wins more slowly than with the other side to move, and in order to win, the stronger side can be forced to visit the same position but with the other side to move. The key position for this study was discovered by John Bryant (see https://www.youtube.com/watch?v=2h_b0puS8Vk). I conjectured that this position is a genuine cyclic zugzwang (not only the shortest path but all paths to win must go through the BTM position) and that later was proved to be true by some specially modified Freezer and FinalGen softwares.

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