List of All Known Mutual Zugzwangs

Each endgame names White's pieces in Q-R-B-N-P order folllowed by Black's pieces in the same order. White is chosen to have at least as many pieces as black. If the number of pieces on each side are equal, the Q-R-B-N-P order determines White (eg, KQRKQB rather than KQBKQR).

For positions in symmetric-force endings, White is arbitrarily chosen as the side with the first piece (in the order above) on the first square (a1-h1, a2-h2, etc).

Where there is more than one bishop, a "bishop signature" is added of the form "_abcd". This indicates `a' white and `c' black Bishops of one square-color, and `b' white and `d' black Bishops of the other square-color, where a>=b and c>=d if a=b.

The maxDTC/maxDTM columns are the maximum DTC/DTM (depth to conversion/mate) of any mzug for that ending with the losing side to play. The values are only available for the endings which have been analyzed by the respective data sources. Where depths are not provided from the source, they are looked up in Eugene Nalimov's DTM EGTs and Christopher Wirth's DTC EGTs.

Sources:

  • PK - Peter Karrer (using Eugene Nalimov's EGTs as well as his own KQQKQP DTM EGT)
  • LR - Lars Rasumussen
  • LS - Lewis Stiller
  • JT - John Tamplin (using Eugene Nalimov's EGTs as well as his own DTC EGTs)
  • KT - Ken Thompson
  • CW - Christopher Wirth

No data sources contradict each other, so we believe this list to be complete for the endings listed and without error. Any endgame not listed with less than 6 pieces is known to have no mutual zugzwangs, as are KBBKBB, KBBBKB, KBBBKN, and KQQKRB (for which only btm/1-0 is known). If you are aware of any mutual zugzwang that is not listed on this site or you find any error in this data, please email me at jat@jaet.org.

This data was collected by Guy Haworth and collated by John Tamplin.

The highlighted column is the current sort order -- click on other column headers to sort by that column. All full-point mzugs can be found here.

An Excel spreadsheet is available containing only 3-5 man endings.

? = unknown, * = assumed -- see footnote at bottom of table
Ending # mzugs btm, 1-0 wtm, 0-1 Full-point
mzugs
Sources
Count maxDTC maxDTM Count maxDTC maxDTM
KPK 80 80 18 27 0 -- -- 0 PK,CW
KBKP 1 0 -- -- 1 1 12 0 PK,CW
KNKP 29 22 6 6 7 9 24 0 PK,CW
KPKP 121 106 10 27 Symmetric 15 PK,CW
KRKB 5 5 14 25 0 -- -- 0 PK,KT,CW
KRKN 18 18 10 24 0 -- -- 0 PK,KT,CW
KRKP 12 12 6 20 0 -- -- 0 PK,CW
KBPK 6 6 14 20 0 -- -- 0 PK,CW
KNPK 75 75 14 19 0 -- -- 0 PK,CW
KPPK 43 43 11 26 0 -- -- 0 PK,CW
KBBKN_1100 1 1 2 2 0 -- -- 0 PK,LR,CW
KBBKP_1100 1 1 2 2 0 -- -- 0 PK,CW
KBBKQ_1100 1 0 -- -- 1 5 17 0 PK,LR,CW
KBBKR_1100 3 3 1 19 0 -- -- 0 PK,LR,CW
KBNKB_1001 16 16 2 33 0 -- -- 0 PK,LR,KT,CW
KBNKB_1010 29 29 10 36 0 -- -- 0 PK,LR,KT,CW
KBNKN 922 922 67 97 0 -- -- 0 PK,LR,KT,CW
KBNKP 62 61 13 37 1 1 45 0 PK,CW
KBNKQ 1 0 -- -- 1 33 44 0 PK,LR,CW
KBNKR 8 6 5 32 2 8 28 0 PK,LR,CW
KBPKB_1001 33 33 3 19 0 -- -- 0 PK,LR,CW
KBPKB_1010 127 127 33 44 0 -- -- 0 PK,LR,CW
KBPKN 2125 2112 37 50 13 2 2 0 PK,LR,CW
KBPKP 406 403 20 31 2 2 16 1 PK,CW
KBPKQ 16 0 -- -- 16 20 28 0 PK,LR,CW
KBPKR 306 4 3 32 302 15 33 0 PK,LR,CW
KNNKN 362 362 4 4 0 -- -- 0 PK,LR,KT,CW
KNNKP 3143 3124 105 105 19 3 53 0 PK,CW
KNNKQ 229 0 -- -- 229 53 62 0 PK,LR,CW
KNNKR 25 0 -- -- 25 5 35 0 PK,LR,CW
KNPKB 642 640 28 40 2 2 2 0 PK,LR,CW
KNPKN 4191 4128 40 56 63 2 2 0 PK,LR,CW
KNPKP 2303 2281 21 33 14 5 24 8 PK,CW
KNPKQ 52 0 -- -- 52 29 45 0 PK,LR,CW
KNPKR 1181 23 4 28 1158 34 58 0 PK,LR,CW
KPPKB 212 211 14 28 1 2 2 0 PK,CW
KPPKN 1077 920 22 36 157 12 12 0 PK,CW
KPPKP 4237 4179 24 86 52 7 23 6 PK,CW
KPPKQ 2 0 -- -- 2 8 13 0 PK,CW
KPPKR 119 18 11 39 99 21 36 2 PK,CW
KQBKQ 25 25 9 14 0 -- -- 0 PK,LR,KT,CW
KQNKQ 38 38 24 30 0 -- -- 0 PK,LR,KT,CW
KQPKQ 640 640 91 102 0 -- -- 0 PK,LR,CW
KQPKR 1 1 2 11 0 -- -- 0 PK,LR,CW
KQRKQ 1 1 11 18 0 -- -- 0 PK,LR,CW
KRBKP 1 1 1 8 0 -- -- 0 PK,CW
KRBKQ 372 0 -- -- 372 38 67 0 PK,LR,CW
KRBKR 17 17 49 55 0 -- -- 0 PK,LR,KT,CW
KRNKN 3 3 19 24 0 -- -- 0 PK,LR,KT,CW
KRNKQ 455 0 -- -- 455 42 63 0 PK,LR,CW
KRNKR 10 10 22 23 0 -- -- 0 PK,LR,KT,CW
KRPKB 225 225 58 67 0 -- -- 0 PK,LR,CW
KRPKN 413 413 37 47 0 -- -- 0 PK,LR,CW
KRPKP 3 0 -- -- 2 1 15 1 PK,CW
KRPKQ 243 2 2 12 241 63 91 0 PK,LR,CW
KRPKR 209 209 43 54 0 -- -- 0 PK,LR,CW
KRRKB 1 1 8 16 0 -- -- 0 PK,LR,CW
KRRKQ 10 10 7 20 0 -- -- 0 PK,LR,KT,CW
KBPPK 6 6 6 16 0 -- -- 0 PK,CW
KNPPK 93 93 5 16 0 -- -- 0 PK,CW
KPPPK 11 11 7 17 0 -- -- 0 PK,CW
KBBKBN_1110 16 16 ? 84 0 -- -- 0 JT
KBBKNN_1100 817 817 25 93 ? ? ? 0 KT
KBNKBN_1001 12 12 ? 48 Symmetric 0 JT
KBNKBN_1010 4 4 ? 82 Symmetric 0 JT
KBNKNN 402 402 8 99 ? ? ? 0 KT
KNNKNN 32 32 1 2 Symmetric 0 KT
KQBKQB_1001 13 13 7 ? Symmetric 0 KT
KQBKQB_1010 8 8 4 ? Symmetric 0 KT
KQBKQN 110 76 10 ? 34 15 ? 0 * KT
KQBKRB_1001 7 7 12 ? ? ? ? 0 * KT
KQBKRB_1010 9 9 10 ? ? ? ? 0 * KT
KQBKRN 15 15 15 ? ? ? ? 0 * KT
KQBKRR 158 158 70 92 ? ? ? 0 KT
KQNKQN 149 149 11 ? Symmetric 0 KT
KQNKRB 88 88 18 ? ? ? ? 0 * KT
KQNKRN 123 123 20 ? ? ? ? 0 * KT
KQNKRR 905 905 137 158 ? ? ? 0 KT
KQQKQB 2 2 ? 19 0 -- -- 0 JT
KQQKQN 3 3 ? 21 0 -- -- 0 JT
KQQKQP 4 4 ? 22 0 -- -- 0 PK
KQQKQQ 8 8 14 20 Symmetric 0 LS,KT
KQQKQR 15 15 15 38 ? ? ? 0 KT
KQQKRB 0 0 -- -- ? ? ? 0 KT
KQRKQB 1365 1359 56 ? 6 4 ? 0 * KT
KQRKQN 1725 1722 48 ? 3 3 ? 0 * KT
KQRKQR 236 236 40 ? Symmetric 0 KT
KQRKRB 1 1 1 ? ? ? ? 0 * KT
KQRKRR 5 5 11 ? ? ? ? 0 * KT
KRBKBB_1002 120 120 73 77 ? ? ? 0 KT
KRBKBB_1011 90 90 68 85 ? ? ? 0 KT
KRBKBB_1020 166 166 36 44 ? ? ? 0 KT
KRBKBN_1001 23 23 79 ? ? ? ? 0 * KT
KRBKBN_1010 1433 1433 50 ? ? ? ? 0 * KT
KRBKNN 203 203 213 228 ? ? ? 0 KT
KRBKRB_1001 4 4 5 ? Symmetric 0 KT
KRBKRB_1010 7 7 7 ? Symmetric 0 KT
KRBKRN 103 96 13 ? 7 5 ? 0 * KT
KRNKBB_0011 253 253 42 59 ? ? ? 0 KT
KRNKBB_0020 548 548 133 145 ? ? ? 0 KT
KRNKBN 7933 7933 180 ? ? ? ? 0 * KT
KRNKNN 8997 8997 226 245 ? ? ? 0 KT
KRNKRN 69 69 11 ? Symmetric 0 KT
KRRKBB_0011 13 13 18 26 ? ? ? 0 LS,KT
KRRKBB_0020 2 2 21 27 ? ? ? 0 KT
KRRKBN 57 57 17 35 ? ? ? 0 KT
KRRKNN 41 41 22 34 ? ? ? 0 KT
KRRKRB 501 499 41 54 2 ? 27 0 KT,JT
KRRKRN 697 697 50 64 0 -- -- 0 KT,JT
KRRKRR 4 4 6 28 Symmetric 0 KT,JT
KBBBKB 0 0 -- -- 0 -- -- 0 KT
KBBBKN 0 0 -- -- 0 -- -- 0 KT
KBBBKQ_2100 392 ? ? ? 392 35 ? 0 * KT
KBBBKQ_3000 71 ? ? ? 71 38 ? 0 * KT
KBBBKR_2100 8 8 61 ? ? ? ? 0 * KT
KBBNKB_1110 1 1 18 ? ? ? ? 0 KT
KBBNKB_2001 9 9 6 ? ? ? ? 0 KT
KBBNKB_2010 13 13 24 ? ? ? ? 0 KT
KBBNKN_2000 29 29 26 ? ? ? ? 0 KT
KBBNKQ_1100 1322 17 4 ? 1305 46 ? 0 * KT
KBBNKQ_2000 1985 0 -- -- 1985 59 ? 0 KT
KBBNKR_1100 80 80 54 ? ? ? ? 0 * KT
KBBNKR_2000 257 257 54 ? ? ? ? 0 * KT
KBNNKB_1001 15 15 25 ? ? ? ? 0 KT
KBNNKB_1010 109 109 27 ? ? ? ? 0 KT
KBNNKN 91 91 22 ? ? ? ? 0 KT
KBNNKQ 3779 ? ? ? 3779 37 ? 0 * KT
KBNNKR 628 628 37 ? ? ? ? 0 * KT
KNNNKB 1009 1009 66 ? ? ? ? 0 KT
KNNNKN 2115 2115 78 ? ? ? ? 0 KT
KNNNKQ 2886 ? ? ? 2886 25 ? 0 * KT
KNNNKR 82 82 5 ? ? ? ? 0 * KT
KQNNKQ 1082 1082 57 ? ? ? ? 0 * KT
KRBBKQ_1100 192 192 36 ? ? ? ? 0 * KT
KRBBKQ_2000 30 30 7 ? ? ? ? 0 * KT
KRBBKR_1100 5 5 15 ? ? ? ? 0 * KT
KRBBKR_2000 5 5 18 ? ? ? ? 0 * KT
KRBNKQ 983 983 92 ? ? ? ? 0 * KT
KRNNKQ 198 198 14 ? ? ? ? 0 * KT
KRRBKQ 191 191 56 ? ? ? ? 0 * KT
KRRNKQ 739 739 86 ? ? ? ? 0 * KT
KRRRKQ 1 1 17 ? 0 -- -- 0 KT,JT
* Ken Thompson's encoding used for his data does not differentiate between black losses and draws, so it is not possible to detect full-point mzugs using only his data. For those endings where KT's data is the only available source and black has sufficient mating material, we have assumed that there are no full-point mzugs. Hopefully, we will soon be able to verify this from additional data sources.