Vital Type B1 zugzwangs

[guyhaw]

A type B1-x zug is defined to be a position where the side to move. wins - but would win more quickly (in terms of the DTx metric) if it could 'pass' the move across to the side not to move. c.f. http://centaur.reading.ac.uk/23047/. The DTx zug-depth is the DTx-difference in depth between the position with wtm and with btm.

A Vital type B1 zug is one in which the win from the first position can be forced by the defender to go through the second position (with the other side to move). If this is the case, the position is a B1 zug regardless of the metric DTx.

If a position is not a B1-x zug for some metric DTx, it is not a 'Vital type B1 zug'.

Some 143 positions appear in the mainlines of studies (with both sides to move) in Study Database HHdbIV which are B1-C, B1-M and B1-Z zugs. So the question is 'Which of these are Vital Type B1 zugs?'. There are certainly some required triangulations of zug-depth 3, and there are certainly positions with some zug-depth less than 3 which are not Vital type B1 zugs.

A possible clue that something is a Vital type B1 Zug is that the zug-depth is the same under DTC, DTM and DTZ. Here are some positions that may be Vital type B1 zugs ... comments welcome:

Vital B1-zug with zug-depth 3 ?: HHDBIV#223, Lasker, 5k2/8/5P1p/4K2P/8/8/8/8 w
Vital B1-zug with zug-depth 4 ?: HHDBIV#35,067, Cheron (1955), 8/2k1p3/8/2KP4/8/8/3P4/8 w
Vital B1-zug with zug-depth 5 ?: HHDBIV#279, Troitzky, 6k1/8/4N1K1/8/p7/N7/8/8 w
Vital B1-zug with zug-depth 6 ?: HHDBIV#17774, Dedrle (1937), 8/8/8/3Q4/5r2/4k3/5p2/5K2 w
Vital B1-zug with zug-depth 7 ?: HHDBIV#5,704, Troitzky, 8/8/1k6/3KN3/3p4/3N4/8/8 w
Vital B1-zug with zug-depth 9 ??: HHDBIV#63,156, Nunn (1995), 8/8/1K6/P7/kn6/4N3/8/8 w
Vital B1-zug with zug-depth 11 ?: HHDBIV#63159, Nunn (1995), 3k4/1Kn5/8/P1N5/8/8/8/8 w

g

[Arpad Rusz]

Some Vital Type B1 zugzwangs from Polgar Starchess:


1.K25 K34 2.K19 K27 3.K20 K34 4.K21 P7 5.27Q#


1.K31 (1.K20? K32 2.K21 K25 3.K16 K20 4.K9 K14! zz = ) 1.-K27 2.K24! K34 3.K19! K33 4.K25 K34 5.K20 K27 6.P33! K33 7.K21 K32 8.K16 K26 9.K9 K21 10.K10 K20 11.K16 +-


1.K25!! K29 2.K31 K28 3.K24 K29 4.N19 K28 5.K23(30) P5 6.N35#


1.K2 Q34 2.Q19 Q28 3.K3 Q29 4.Q17...

[byakuugan]

I've never seen that kind of star-shaped board before. It's funny because I just now got done making a video on hexagonal chess http://www.youtube.com/watch?v=8knIqGEDQsM when I saw those star-shaped boards.