symetrical endgames

[notnale]

Are there any positions you know of where the side to go first loses in KQRkqr or similar endgames ?

[kronsteen]

http://chess.jaet.org/cgi-bin/mzugs
Lots of info about mzugs here.
"Side to move loses" is full-point mutual zugzwang. Such hot positions are very few. There are none in kqrkqr.

Regards,
k

[guyhaw]

I have lists of all known 3- to 6-man zugs on my machine, but haven't finished reviewing and summarising them for general release yet.
The work was done (with me turning the handle) with Eiko Bleicher's Java program running on his copy of the Nalimov DTM EGTs.

Try these for KQRKQR - '0 n' means 'lost in n' - of course if you start with the second position you get a draw-win-draw zug:

8/8/1Q6/6q1/3R4/8/5r2/3K2k1 w 0 67 1 =
8/4r3/8/8/Q2R4/3K3k/8/4q3 w 0 62 1 =
8/1r6/3Q4/3R4/3K4/8/4q3/1k6 w 0 60 1 =
8/6q1/1Q3R2/8/8/8/6r1/K6k w 0 59 1 =
8/8/8/8/1Q2R3/5q2/5rk1/K7 w 0 59 1 =
6q1/8/8/5Q2/8/2K4R/8/r5k1 w 0 56 1 =
2r5/8/8/5k2/8/3q4/1QR5/1K6 w 0 55 1 =
8/1k6/1r6/Q1R5/5q2/3K4/8/8 w 0 55 1 =
r7/8/8/5k2/8/3q4/2R5/1KQ5 w 0 54 1 =
3r4/6qk/8/1Q2R3/8/8/1K6/8 w 0 54 1 =
5k2/1q3r2/2R5/8/8/8/2K3Q1/8 w 0 53 1 =
8/8/1Q6/4qr1k/8/8/2RK4/8 w 0 52 1 =
3Q4/4r3/3R4/6q1/3K4/8/8/5k2 w 0 52 1 =
8/8/8/5rqk/1Q6/3K4/3R4/8 w 0 51 1 =
8/8/1r4k1/8/8/Q2KR3/5q2/8 w 0 51 1 =
8/6r1/Q7/8/5q1k/8/3R4/2K5 w 0 50 1 =
8/8/8/5Q2/3K4/6q1/R7/4r1k1 w 0 50 1 =
8/1r6/8/5Q2/8/8/q7/k1K1R3 w 0 49 1 =
8/5k2/4q3/3R4/5r2/8/2K3Q1/8 w 0 49 1 =
8/8/8/8/8/3Q4/qr6/k1K1R3 w 0 48 1 =
6q1/8/8/Q7/1R6/8/5rk1/3K4 w 0 47 1 =
2k5/8/8/1q6/8/1r6/2KR4/2Q5 w 0 47 1 =
8/5rk1/8/8/8/6q1/1R6/KQ6 w 0 46 1 =
8/2q3k1/6r1/8/8/8/QR6/K7 w 0 46 1 =
8/8/3Q4/6rk/3R4/8/q7/2K5 w 0 46 1 =
8/1q6/8/8/3Q4/1k1K3R/2r5/8 w 0 46 1 =
8/8/2r4k/8/3K4/1QR5/8/q7 w 0 46 1 =
r5k1/2Q5/8/8/2R5/8/6q1/1K6 w 0 45 1 =
4k3/8/4q3/8/2R5/1r6/8/2K2Q2 w 0 45 1 =
7k/8/5q2/8/3R4/7r/3K4/6Q1 w 0 45 1 =
8/8/k6r/8/8/2RK2Q1/1q6/8 w 0 45 1 =
4q3/3R4/k5r1/5Q2/8/3K4/8/8 w 0 45 1 =
2r3k1/8/5R2/6q1/3Q4/3K4/8/8 w 0 45 1 =
8/8/3R4/7r/3K4/6Q1/4q3/7k w 0 45 1 =
8/7q/8/8/R7/2Q5/6r1/K6k w 0 44 1 =
8/8/8/8/r7/1RK1Q3/8/k2q4 w 0 44 1 =
8/8/8/2Q5/q7/2K5/2R5/k2r4 w 0 44 1 =
8/7q/4Q3/8/4R3/3K4/2r5/2k5 w 0 44 1 =
8/8/q7/8/1QR5/3K4/5r2/5k2 w 0 44 1 =
8/3k1q2/5r2/8/8/2QK2R1/8/8 w 0 44 1 =
4r1k1/2Q5/8/8/6q1/8/8/2KR4 w 0 43 1 =
7k/8/4R3/3r3q/8/8/8/2K3Q1 w 0 43 1 =
8/6q1/8/8/3R4/k6r/5Q2/3K4 w 0 43 1 =
1k6/8/2R5/8/1r6/Q7/2K5/4q3 w 0 43 1 =
8/3q3k/5Q2/8/8/1RK5/7r/8 w 0 43 1 =
8/8/8/r7/3K1RQ1/8/8/1k5q w 0 43 1 =
7q/3Q4/8/8/3R4/8/6r1/K5k1 w 0 42 1 =
8/8/2Q5/8/5q2/5r2/2K4k/2R5 w 0 42 1 =
8/8/8/kr6/6Q1/8/3KR3/q7 w 0 42 1 =
8/4q2k/1R6/7r/8/8/3K1Q2/8 w 0 42 1 =
8/2k5/2q5/4r3/1Q6/3K4/3R4/8 w 0 42 1 =
5k2/5q2/8/8/5r2/3KR3/4Q3/8 w 0 42 1 =
8/8/6q1/8/3QR3/8/5r2/1K4k1 w 0 41 1 =
5k2/8/8/8/5q2/4r3/3R4/2KQ4 w 0 41 1 =
8/8/8/8/8/4Q3/1qr5/1k1KR3 w 0 41 1 =
k7/8/4q3/1Q6/8/6R1/r7/3K4 w 0 41 1 =
8/8/6Q1/8/2R5/5q2/1K6/4rk2 w 0 41 1 =
3k4/r7/8/3q4/8/2R5/2K5/2Q5 w 0 41 1 =
7q/8/8/2Q5/8/8/2RK4/6rk w 0 41 1 =
q2k4/6r1/8/2R5/8/4Q3/3K4/8 w 0 41 1 =
5Q2/8/8/1r6/8/2K2R2/6q1/6k1 w 0 41 1 =
3R4/8/8/8/5q2/3K4/4Q3/1kr5 w 0 41 1 =
8/8/8/8/5r2/1Q1KR3/8/2q2k2 w 0 41 1 =
8/5R2/8/8/2Q5/3K2kq/8/r7 w 0 41 1 =
2r5/5Q2/8/8/8/3K2kq/3R4/8 w 0 41 1 =
6q1/8/5Q2/8/3K4/5R2/8/1r4k1 w 0 41 1 =
8/3Q4/8/6r1/3K4/7R/3kq3/8 w 0 41 1 =
8/6q1/8/8/2Q5/5rk1/8/1R1K4 w 0 40 1 =
1R6/8/3q4/2r2k2/1Q6/8/1K6/8 w 0 40 1 =
8/8/2k1r3/6Q1/8/1q6/3K2R1/8 w 0 40 1 =
3k4/6r1/8/q7/8/2R1Q3/3K4/8 w 0 40 1 =
8/8/4q2k/5R2/8/2KQ4/7r/8 w 0 40 1 =
2q2r2/8/8/8/3K3k/1Q1R4/8/8 w 0 40 1 =
7q/8/2Q2R2/8/8/8/6r1/K6k w 0 39 1 =
8/8/8/1kr5/1q6/5R2/8/Q2K4 w 0 39 1 =
8/8/8/8/2R5/2KQ4/1r3q2/2k5 w 0 39 1 =
8/8/6k1/3q4/5Q2/2K5/6r1/2R5 w 0 39 1 =
8/8/8/1R6/2rq2k1/1Q6/8/1K6 w 0 38 1 =
4k3/8/8/1R6/5q2/3Q4/6r1/1K6 w 0 38 1 =
8/4rk2/5q2/8/3R4/8/3K4/6Q1 w 0 38 1 =
1q6/8/2Q5/8/8/2K5/2R5/1k3r2 w 0 38 1 =
8/8/2q5/8/3Q4/1k1KR3/2r5/8 w 0 38 1 =
8/8/7k/8/3K4/r3R3/3Q4/6q1 w 0 38 1 =
8/8/2R5/5q2/2Q5/8/4r3/K4k2 w 0 37 1 =
8/8/R7/8/1r6/1k4q1/8/1K3Q2 w 0 37 1 =
8/8/8/q4r2/8/8/2R1Q3/k1K5 w 0 37 1 =
8/8/8/1q6/4R3/kr6/2Q5/2K5 w 0 37 1 =
8/4q3/8/8/6R1/kr6/5Q2/2K5 w 0 37 1 =
8/7q/8/4R3/5k2/7r/1K2Q3/8 w 0 37 1 =
8/6k1/6r1/8/3q4/5R1Q/2K5/8 w 0 37 1 =
8/8/5q2/3R4/8/8/3K1kr1/3Q4 w 0 37 1 =
8/8/8/4q3/8/3Q4/2RK1k2/4r3 w 0 37 1 =
8/4r3/8/8/8/2K3Q1/2R5/k2q4 w 0 37 1 =
8/2Q5/8/6r1/q7/1RK5/8/k7 w 0 37 1 =
6Q1/8/q7/8/2R5/3K4/k7/2r5 w 0 37 1 =
1q6/8/8/3Q4/3R4/3K4/1k6/6r1 w 0 37 1 =
8/8/4q3/8/3Q4/2RK1k2/4r3/8 w 0 37 1 =
8/8/4q3/7Q/k7/3K4/3R4/5r2 w 0 37 1 =
8/8/8/k3q3/8/1QRK4/8/r7 w 0 37 1 =
8/6k1/8/8/3K4/2R3r1/2Q5/q7 w 0 37 1 =
8/2r3k1/8/8/3K4/1QR5/8/q7 w 0 37 1 =
8/8/5q2/1Q2R3/8/8/3r4/K5k1 w 0 36 1 =
8/8/2q3k1/Q7/6r1/8/8/1K2R3 w 0 36 1 =
8/4k3/8/3q4/1R6/4r3/8/1K3Q2 w 0 36 1 =
8/8/1Q6/3q1r1k/8/1RK5/8/8 w 0 36 1 =
8/5q2/3R4/8/8/3K1kr1/3Q4/8 w 0 36 1 =
3k4/6r1/8/2q5/8/3K4/4Q3/3R4 w 0 36 1 =
8/8/3R4/6q1/Q7/8/4r2k/1K6 w 0 35 1 =
8/3Q4/q7/8/8/8/6r1/k2KR3 w 0 35 1 =
8/8/8/1q6/3R4/1k3r2/8/3KQ3 w 0 35 1 =
1q6/8/8/6rk/3Q4/8/8/R2K4 w 0 35 1 =
8/8/8/k2rq3/7R/8/2K5/5Q2 w 0 35 1 =
8/8/4k3/4q3/r7/3R4/2K5/3Q4 w 0 35 1 =
8/8/4r1k1/8/7Q/8/2K2R2/6q1 w 0 35 1 =
3R4/2q5/8/6Q1/k3r3/8/3K4/8 w 0 35 1 =
8/8/1r2q3/2k5/3R1Q2/8/3K4/8 w 0 35 1 =
r7/8/8/3q2k1/1Q6/2K5/2R5/8 w 0 35 1 =
8/7k/8/4q3/7r/3K4/2QR4/8 w 0 35 1 =
2k5/8/2q5/5r2/1Q6/3K4/3R4/8 w 0 35 1 =
5q2/3R4/8/8/3K1kr1/3Q4/8/8 w 0 35 1 =
8/2q5/Q2R4/8/3K1k1r/8/8/8 w 0 35 1 =
8/7q/5R2/1Q6/3K2k1/8/2r5/8 w 0 35 1 =
8/6k1/8/8/3K4/1r2R3/4Q3/6q1 w 0 35 1 =
8/q5k1/8/1QR5/3K4/8/2r5/8 w 0 35 1 =
k5r1/8/2R5/8/q7/8/1Q6/1K6 w 0 34 1 =
8/8/8/4q3/2R5/r3k3/8/1QK5 w 0 34 1 =
8/8/q7/8/3Q4/8/1r6/k2KR3 w 0 34 1 =
8/8/6Q1/8/q7/2r5/2R5/k2K4 w 0 34 1 =
1r2k3/8/8/8/8/R7/7q/Q2K4 w 0 34 1 =
8/8/8/8/3k4/2r3q1/3KQ3/3R4 w 0 34 1 =
2k5/8/8/8/1Q1R4/8/3K4/2r2q2 w 0 34 1 =
8/8/8/4Q3/1q6/3K4/4R3/1kr5 w 0 34 1 =
8/8/3R4/8/7q/3K4/1r3k2/3Q4 w 0 34 1 =
8/8/1r6/8/8/QR1K4/5q1k/8 w 0 34 1 =
8/8/8/8/8/3K1kr1/Q3R3/5q2 w 0 34 1 =
8/5k2/2q5/5r2/1Q6/3K4/3R4/8 w 0 34 1 =
4k3/8/4q3/1r6/5Q2/3K4/3R4/8 w 0 34 1 =
4R3/2r5/8/5q2/Q2K1k2/8/8/8 w 0 34 1 =
8/1r6/8/Q7/8/5q1k/4R3/K7 w 0 33 1 =
8/8/8/8/R6r/8/6q1/Q2K2k1 w 0 33 1 =
8/8/8/5q2/3R4/1r3k2/8/2QK4 w 0 33 1 =
1R6/q7/8/8/k5r1/8/2K4Q/8 w 0 33 1 =
8/2r5/R7/2k5/3q4/8/2K1Q3/8 w 0 33 1 =
8/3r4/8/6k1/4Q3/6q1/2K5/2R5 w 0 33 1 =
1q6/8/8/8/3R4/4r3/3K1k2/2Q5 w 0 33 1 =
8/8/8/4q1k1/8/8/2QK1R2/6r1 w 0 33 1 =
8/8/k1r5/4Q3/2q5/8/1R1K4/8 w 0 33 1 =
8/8/7q/8/1Q2R3/3K1k2/r7/8 w 0 33 1 =
8/3k4/6q1/8/r3RQ2/3K4/8/8 w 0 33 1 =
8/8/1q6/2R5/8/k2r4/5Q2/2K5 w 0 32 1 =
8/8/7q/8/1k5r/8/3R1Q2/2K5 w 0 32 1 =
8/8/3R4/8/6Q1/4q3/7r/3K3k w 0 32 1 =
8/5Q2/8/7r/5R2/4k2q/8/3K4 w 0 32 1 =
8/8/8/8/2q5/7k/2rR4/1Q1K4 w 0 32 1 =
8/8/8/1q6/8/2Q5/k1KR4/1r6 w 0 32 1 =
8/8/q7/2k5/4r3/1Q6/1RK5/8 w 0 32 1 =
8/3r3q/Q7/5k2/8/8/2K3R1/8 w 0 32 1 =
8/8/8/5qk1/6r1/2R5/3K3Q/8 w 0 32 1 =
8/8/1k6/2q5/3R4/1r6/3K4/Q7 w 0 32 1 =
8/6q1/1Q6/8/8/R7/5r2/2K3k1 w 0 31 1 =
3q4/8/r7/8/3k4/5Q2/8/3K1R2 w 0 31 1 =
8/k7/8/8/8/2q1r3/8/1R1K2Q1 w 0 31 1 =
8/8/r6k/7q/8/8/2K2RQ1/8 w 0 31 1 =
8/8/1q6/8/8/3Q4/1k1K3R/2r5 w 0 31 1 =
8/8/8/1Q6/2r1q2k/8/1R1K4/8 w 0 31 1 =
8/8/k5r1/8/2q5/8/1R1K3Q/8 w 0 31 1 =
8/8/1r4k1/Q7/8/4q3/8/K2R4 w 0 30 1 =
1q6/8/2QR4/1r6/1k6/8/8/1K6 w 0 30 1 =
8/8/Q7/8/6q1/4r3/4R3/3K2k1 w 0 30 1 =
8/R4r2/8/1k2q3/8/8/8/3K2Q1 w 0 30 1 =
8/8/8/2q5/8/3Q4/1k1KR3/2r5 w 0 30 1 =
8/8/1k2r3/1q6/8/Q7/3K4/6R1 w 0 30 1 =
8/1q6/8/2Q5/8/2K5/2R5/1k3r2 w 0 30 1 =
8/8/8/8/8/rk1K4/2R3Q1/1q6 w 0 30 1 =
8/8/8/8/q7/1R3r1k/1QK5/8 w 0 29 1 =
8/8/8/7q/8/1Q2R3/3K1k2/r7 w 0 29 1 =
8/8/8/8/8/3K3R/1q3kr1/7Q w 0 29 1 =
8/7r/8/4k3/4q3/5R2/8/K2Q4 w 0 28 1 =
6r1/8/2R5/3qk3/Q7/8/8/K7 w 0 28 1 =
8/8/8/4r3/1Q6/8/5q2/RK4k1 w 0 28 1 =
8/8/3r3q/Q7/5k2/8/8/2K3R1 w 0 28 1 =
8/8/8/8/7Q/2q1r3/8/1R1K2k1 w 0 28 1 =
8/3r4/3k4/8/8/1q6/2R5/2QK4 w 0 28 1 =
8/8/2r5/2k5/R7/1Q6/2K5/5q2 w 0 28 1 =
8/8/7k/8/4q3/7r/3K4/2QR4 w 0 28 1 =
8/r7/8/6q1/2Q5/4k3/8/2K2R2 w 0 27 1 =
8/8/8/3k4/q3r3/2QK4/3R4/8 w 0 27 1 =
1r6/3Q4/8/4q1k1/8/3K3R/8/8 w 0 27 1 =
8/8/8/8/3K2R1/5k1r/4q3/6Q1 w 0 27 1 =
8/8/5r2/8/3K1k2/Q3R3/8/6q1 w 0 27 1 =
2r5/8/8/3Q4/8/2k1q3/3R4/2K5 w 0 26 1 =
8/7q/8/8/4R3/1kr5/6Q1/3K4 w 0 26 1 =
8/8/3Q4/1r6/2k5/3R4/1q6/3K4 w 0 26 1 =
8/8/3q4/8/2Q5/1RK1k3/3r4/8 w 0 26 1 =
7Q/8/2q5/k2r4/8/8/8/1K5R w 0 25 1 =
8/8/5Q2/8/3rq3/1R6/8/2K1k3 w 0 25 1 =
8/8/2rq4/1k6/2RQ4/8/8/3K4 w 0 25 1 =
8/8/1Q6/2r2k2/1R6/4q3/1K6/8 w 0 25 1 =
8/6Q1/8/8/4r2q/5k2/2K3R1/8 w 0 25 1 =
8/8/8/3q1k2/8/8/1QK1R3/5r2 w 0 25 1 =
1q2r3/3k4/1Q2R3/8/8/8/8/1K6 w 0 24 1 =
8/8/r2q4/1k6/R2Q4/8/8/3K4 w 0 24 1 =
8/2r5/4Q3/8/8/8/4R3/1K1k1q2 w 0 23 1 =
1rq5/k7/1RQ5/8/8/8/8/2K5 w 0 23 1 =
3r4/8/8/4Q3/8/3k1q2/4R3/3K4 w 0 23 1 =
3q4/8/6r1/8/3k4/1Q6/8/1R1K4 w 0 23 1 =
8/1r6/3Q4/8/4q1k1/8/3K3R/8 w 0 23 1 =
2q5/8/3Q4/8/3K4/3R4/2k3r1/8 w 0 23 1 =
8/8/3Q4/6r1/4k3/3R4/5q2/2K5 w 0 22 1 =
8/8/8/8/3q1k2/2R5/5r2/2K1Q3 w 0 22 1 =
8/2q5/1R6/r7/2k5/8/2K5/6Q1 w 0 22 1 =
8/8/RQ6/1qr5/2k5/8/2K5/8 w 0 22 1 =
8/1R6/8/3Q4/5q2/4k3/4r3/2K5 w 0 21 1 =
8/8/8/2q5/Q7/5R2/1K1kr3/8 w 0 21 1 =
8/8/8/3q4/8/2Q5/1RK1k3/3r4 w 0 21 1 =
8/Q7/8/5q2/4R3/1r3k2/8/K7 w 0 20 1 =
8/8/8/1q2r3/3k4/2R3Q1/8/K7 w 0 20 1 =
8/2Q5/8/4r3/3k4/2R5/4q3/K7 w 0 20 1 =
8/Q7/8/1q6/1k2r3/8/8/2K3R1 w 0 20 1 =
8/8/1r6/8/8/2RK1Q2/1k5q/8 w 0 20 1 =
8/8/5R2/4k1q1/8/3K1Q2/8/2r5 w 0 20 1 =
8/2Q5/8/8/3K4/2R5/3k1r2/q7 w 0 20 1 =
8/8/1r6/8/8/2q1k3/QR6/K7 w 0 19 1 =
8/8/2Q5/5r2/3k4/2R5/4q3/1K6 w 0 19 1 =
4R3/8/2r5/8/8/8/1K1k3q/5Q2 w 0 19 1 =
8/8/3Q4/8/2q2r2/4k3/1K1R4/8 w 0 19 1 =
8/8/4q3/2Q2R2/4k3/2K5/r7/8 w 0 18 1 =
8/8/8/8/1r2q3/2R5/Q7/K2k4 w 0 17 1 =
7Q/8/8/6q1/1r6/8/2R5/K2k4 w 0 17 1 =
R6Q/8/8/3q4/8/8/3r4/K2k4 w 0 17 1 =
8/8/8/3q4/8/r3k3/2Q5/1RK5 w 0 17 1 =
8/8/4Q3/8/r7/8/4R3/1K1k1q2 w 0 16 1 =
8/8/8/3r4/2k5/1R3Q2/3q4/1K6 w 0 16 1 =
6R1/7q/8/Q7/8/8/4r2k/K7 w 0 15 1 =
8/8/4q1k1/Q7/8/8/6r1/K4R2 w 0 15 1 =
8/8/4q1k1/Q7/3R4/1r6/8/K7 w 0 15 1 =
8/8/4r3/8/8/5q1k/3QR3/3K4 w 0 14 1 =
8/8/8/8/4q3/2Q5/3rk3/K5R1 w 0 13 1 =
8/8/3r4/8/8/4q1k1/2QR4/2K5 w 0 13 1 =
8/2q5/8/1Q6/6R1/2k5/5r2/2K5 w 0 12 1 =
8/8/8/4r1k1/8/2R5/5q2/3K3Q w 0 11 1 =
8/8/8/8/2k5/1r3q2/2KQ4/2R5 w 0 10 1 =
8/8/8/2q5/8/1Q6/RK1k4/2r5 w 0 9 1 =

g

[guyhaw]

... to kronsteen's remark that 'stm loses is a full-point mzug'.

Not in fact: more commonly, the position is drawn if a null-move is played.

It is true that there are no full-point (i.e. loss-win-loss) zugs in KQRKQR: as was long suspected, there are none in 6-man P-less chess (althought this is 'only just' the case in one sense).

g