This reports the work of Karrer and Wirth in identifying percentage results and, respectively, the Depth to Mate (DTM) and Depth to Conversion (DTC) data in all 2-5-man chess endgames

Haworth, Guy McCrossan

English

Central Archive at the University of Reading

3-5-Man Chess Data 13-5-MAN CHESS DATA  G.McC. Haworth1 UK   ABSTRACT  This reports the work of Karrer and Wirth in identifying percentage results and, respectively, the Depth to Mate (DTM) and Depth to Conversion (DTC) data in all 2-5-man chess endgames.   1. INTRODUCTION   Karrer (2000) mined Nalimov’s endgame tables (EGTs) to produce a complete list of DTM maximals and sta-tistics, wtm and btm. Wirth (2000) then computed the 4-1 EGTs to complete his 2-5-man DTC suite and to produce the analogous data for the DTC metric which was compared with Thompson’s ‘CD’ data (2000).  Wirth (2000) also provided the results percentages, wtm and btm. As he also provided the number of positions won in a specific number of plies, quick wins based on shallow tactical devices may be discounted as required from these percentages. As Wirth eliminates from his EGTs duplicates of positions with two Kings on a long diagonal, his statistics are marginally more accurate than Nalimov’s. Both, for reasons of comparability, dis-count only those unreachable positions where the side-not-to-move is in check. Most obvious among residual unreachables, White is credited with 77 unreachable KNNK wins in 1 move.    Tamplin (2001) provides an excellent query interface to these DTM and DTC EGTs, the latter via Lincke (2001) where even the 4-man tables are to the DTC metric.  Here are some sidelights on Table 1’s statistics. • Independent maxDTM computations by Rasmussen (2000) agreed completely with Karrer’s data. • Thompson’s 5-man EGTs maximise the DTC of the next position rather than postponing the next conver-sion to mate or a subgame: the weaker side is allowed to capture voluntarily as a human player might do. This produced different maxDTC data for KRKNP, KRRKN and KBNKP.  Thompson (2001) now maxi-mises the current DTC by maximising the number of men on the board first. Note that under DTC, the stronger side may unnaturally force-sacrifice surplus force, e.g., as in KQQQK. • Wirth used the existing ETH(Zürich) software RETROENGINE which assumes that captures are made by the winner. Where this need not be so as in wKc3Rb4c2/bKa1, Wirth’s depths in plies are 1 ply too great: the wtm maxDTCs for KQRKR and KRRKQ are therefore suspect. Similarly, Thompson (2001), e.g., with Ra4+ and Kd4/5/6 alongside Ra2+ for wKc5Rb4c2/bKa1Na7a8, can rate moves equi-optimal which differ in depth by one ply.  It is unlikely that any player has incurred a 50-move draw on these grounds yet.    2. REFERENCES  Karrer, P. (2000). Private communication. Lincke, T. (2000). http://wwwjn.inf.ethz.ch/games/chess/statistics/chs_statistics.html. DTC win and draw sta-tistics for 3-man to 6-man endgames. Rasmussen, L (2000). Private communication. Tamplin, J. (2001). http://chess.jaet.org/endings/. Chess endgame site: EGTs, maximals and mzugs. Thompson, K. (2000). Private communication. Thompson, K. (2001). http://cm.bell-labs.com/cm/cs/who/ken/chesseg.html. 6-man EGTs, maximal positions, maximal mutual zugzwangs and endgame statistics. Wirth, C.W. (2000). Private communications.                                                           1 33, Alexandra Rd., Reading, Berkshire, UK  RG1 5PG. email: guy.haworth@icl.com   Computer Olympiad Workshop 6 August 2001 2    = =Force GBR # w-b wtm btm wtm btm wtm btm wtm btm wtm btm wtm btm wtm btm wtm btm wtm btm wtm btm wtm btm1 KK 0000.00 2 1-1 100.00 100.00 0.00 0.00 0.00 0.00 0 0 0 0 — — — — 0 0 0 0 — — — —2 KB K 0010.00 3 2-1 100.00 100.00 0.00 0.00 0.00 0.00 0 0 0 0 — — — — 0 0 0 0 — — — —3 KNK 0001.00 3 2-1 100.00 100.00 0.00 0.00 0.00 0.00 0 0 0 0 — — — — 0 0 0 0 — — — —4 KP K 0000.10 3 2-1 23.49 41.91 76.51 58.09 0.00 0.00 3 2 0 0 19 19 — — 3 2 0 0 28 28 — —5 KQK 1000.00 3 2-1 0.00 10.32 100.00 89.68 0.00 0.00 1 8 0 0 10 10 — — 1 8 0 0 10 10 — —6 KRK 0100.00 3 2-1 0.00 9.97 100.00 90.03 0.00 0.00 121 390 0 0 16 16 — — 121 390 0 0 16 16 — —7 KB KB 0040.00 4 2-2 100 - ε 100 - ε ε 0.00 0.00 ε 52 14 14 52 1 0 0 1 52 14 14 52 1 0 0 18 KB KN 0013.00 4 2-2 100 - ε 100 - ε ε 0.00 0.00 ε 2 1 1 5 1 0 0 1 2 1 1 5 1 0 0 19 KB KP 0010.01 4 2-2 94.76 76.43 ε ε 5.24 23.57 104 28 6 14 1 0 5 6 104 28 20 8 1 0 19 2910 KNKN 0004.00 4 2-2 100 - ε 100 - ε ε 0.00 0.00 ε 5 1 1 5 1 0 0 1 5 1 1 5 1 0 0 111 KNKP 0001.01 4 2-2 87.06 67.44 ε ε 12.93 32.56 29 7 3 3 7 6 12 13 29 7 4 13 7 6 28 2912 KP KP 0000.11 4 2-2 33.81 33.81 44.50 21.69 21.69 44.50 1 1 1 1 14 14 14 14 12 1 1 12 33 33 33 3313 KQKB 1030.00 4 2-2 0.31 23.12 99.69 76.88 0.00 0.00 798 3804 0 0 12 12 — — 2 6 0 0 17 17 — —14 KQKN 1003.00 4 2-2 0.65 19.52 99.35 80.48 0.00 0.00 4 17 0 0 19 19 — — 3 12 0 0 21 21 — —15 KQKP 1000.01 4 2-2 0.63 12.08 99.37 80.17 ε 7.75 1 1 20 20 27 27 1 2 3 13 2 8 28 28 10 2916 KQKQ 4000.00 4 2-2 57.80 57.80 41.74 0.45 0.45 41.74 5 3 3 5 10 9 9 10 2 2 2 2 13 12 12 1317 KQKR 1300.00 4 2-2 0.80 5.83 99.01 65.51 0.19 28.66 2 11 55 291 31 31 2 3 10 59 4 23 35 35 18 1918 KRKB 0130.00 4 2-2 64.88 96.77 35.12 3.23 0.00 0.00 29 1 0 0 18 18 — — 29 1 0 0 29 29 — —19 KRKN 0103.00 4 2-2 51.67 89.11 48.33 10.89 ε ε 2 2 1 4 27 27 0 1 1 1 1 4 40 40 0 120 KRKP 0100.01 4 2-2 8.40 17.50 91.43 66.10 0.17 16.40 28 42 3 3 16 16 10 11 82 2 1 1 26 32 42 4321 KRKR 0400.00 4 2-2 70.21 70.21 29.12 0.67 0.67 29.12 58 108 108 58 4 3 3 4 136 18 18 136 19 19 19 1922 KB B K 0020.00 4 3-1 50.76 58.82 49.24 41.18 0.00 0.00 15 45 0 0 19 19 — — 15 45 0 0 19 19 — —23 KB NK 0011.00 4 3-1 0.49 18.10 99.51 81.90 0.00 0.00 138 370 0 0 33 33 — — 138 370 0 0 33 33 — —24 KB P K 0010.10 4 3-1 4.05 16.78 95.95 83.22 0.00 0.00 2 8 0 0 21 21 — — 1 2 0 0 31 31 — —25 KNNK 0002.00 4 3-1 99.99 100 - ε 0.01 ε 0.00 0.00 77 15 0 0 1 0 — — 77 15 0 0 1 0 — —26 KNP K 0001.10 4 3-1 3.70 18.50 96.30 81.50 0.00 0.00 24 32 0 0 22 22 — — 26 22 0 0 27 28 — —27 KP P K 0000.20 4 3-1 1.61 7.91 98.39 92.09 0.00 0.00 62 21 0 0 16 16 — — 9 10 0 0 32 32 — —28 KQB K 1010.00 4 3-1 0.00 9.38 100.00 90.62 0.00 0.00 311 2054 0 0 7 7 — — 4 8 0 0 8 10 — —29 KQNK 1001.00 4 3-1 0.00 9.64 100.00 90.36 0.00 0.00 172 1012 0 0 8 8 — — 1 8 0 0 9 10 — —30 KQP K 1000.10 4 3-1 0.00 2.85 100.00 97.15 0.00 0.00 750 1862 0 0 7 7 — — 4 22 0 0 10 28 — —31 KQQK 2000.00 4 3-1 0.00 2.07 100.00 97.93 0.00 0.00 20 62 0 0 4 4 — — 118 8 0 0 4 10 — —32 KQRK 1100.00 4 3-1 0.00 1.04 100.00 98.96 0.00 0.00 8 42 0 0 5 5 — — 6 896 0 0 6 16 — —33 KRB K 0110.00 4 3-1 0.00 8.80 100.00 91.20 0.00 0.00 3 15 0 0 12 12 — — 28 906 0 0 16 16 — —34 KRNK 0101.00 4 3-1 0.00 9.18 100.00 90.82 0.00 0.00 1427 4568 0 0 12 12 — — 22 865 0 0 16 16 — —35 KRP K 0100.10 4 3-1 0.00 2.46 100.00 97.54 0.00 0.00 1066 4664 0 0 8 8 — — 45 22 0 0 16 28 — —36 KRRK 0200.00 4 3-1 0.00 0.29 100.00 99.71 0.00 0.00 15 76 0 0 6 6 — — 1444 896 0 0 7 16 — —depths, moves1-0 0-11-0 0-1 1-0 0-11-0 0-1 1-0 0-1maxDTC maxDTM% of unbroken positions counts counts depths, movesTable 1a. 2-4-man chess endgame statistics. 3-5-Man Chess Data 3   = =Force # w-b wtm btm wtm btm wtm btm wtm btm wtm btm wtm btm wtm btm wtm btm wtm btm wtm btm wtm btm37 KB B KB 0050.00 5 3-2 84.36 98.63 15.64 1.37 0.00 0.01 503 6 141 464 6 6 1 2 111 12 141 464 22 22 1 238 KB B KN 0023.00 5 3-2 51.77 66.12 48.23 33.88 ε ε 32 43 44 222 66 66 0 1 32 43 44 222 78 78 0 139 KB B KP 0020.01 5 3-2 50.23 54.13 48.01 34.46 1.76 11.41 34 69 5 11 21 21 8 9 1 15 54 82 74 73 82 8340 KB B KQ 3020.00 5 3-2 20.15 2.87 15.29 0.64 64.56 96.49 242 58 74 15 4 3 71 71 39 70 74 15 21 20 81 8141 KB B KR 0320.00 5 3-2 83.43 97.22 16.51 1.51 0.06 1.28 26 7 2 6 7 6 8 9 36 6 1 6 23 22 30 3142 KB NKB 0041.00 5 3-2 74.46 98.75 25.54 1.25 ε ε 21 18 133 445 13 12 1 2 9 1 133 445 39 39 1 243 KB NKN 0014.00 5 3-2 67.88 96.15 32.12 3.85 ε ε 2 1 104 533 77 76 0 1 2 1 104 533 107 106 0 144 KB NKP 0011.01 5 3-2 5.45 22.98 91.38 62.35 3.16 14.67 1 2 523 535 27 27 8 9 9 9 33 33 104 104 54 5545 KB NKQ 3011.00 5 3-2 6.44 1.71 24.98 0.70 68.58 97.59 67 1 22 4 5 5 42 42 4 4 22 4 36 35 53 5346 KB NKR 0311.00 5 3-2 73.81 94.68 26.01 1.58 0.18 3.74 115 23 4 2 6 5 12 13 72 42 3 17 36 35 39 4147 KB P KB 0040.10 5 3-2 58.70 86.90 41.30 13.09 ε 0.01 14 14 508 1524 40 39 2 3 14 14 508 1524 51 50 2 348 KB P KN 0013.10 5 3-2 43.38 73.03 56.62 26.97 ε ε 16 6 23 86 42 42 3 4 1 1 1 3 100 96 7 849 KB P KP 0010.11 5 3-2 9.21 23.93 87.20 58.98 3.59 17.09 92 52 34 30 53 53 6 7 92 52 2 3 67 67 50 5150 KB P KQ 3010.10 5 3-2 11.49 2.82 21.32 0.36 67.19 96.82 30 30 3 2 4 3 42 42 25 4 3 2 35 34 50 5051 KB P KR 0310.10 5 3-2 67.26 73.15 30.95 3.46 1.80 23.39 76 53 5 6 13 12 20 21 3 3 5 6 45 44 38 3952 KNNKB 0032.00 5 3-2 99.98 100 - ε 0.02 ε ε ε 251 82 51 109 4 3 0 1 251 82 51 109 4 3 0 153 KNNKN 0005.00 5 3-2 99.92 99.99 0.08 0.01 ε ε 20 10 56 293 7 6 0 1 20 10 56 293 7 6 0 154 KNNKP 0002.01 5 3-2 66.40 73.61 31.31 13.56 2.30 12.84 2 4 1 1 114 114 12 13 2 4 11 9 115 114 73 7455 KNNKQ 3002.00 5 3-2 42.78 6.02 0.01 ε 57.22 93.98 2387 465 10 2 1 0 63 63 2387 465 10 2 1 0 72 7256 KNNKR 0302.00 5 3-2 99.61 93.76 0.01 ε 0.38 6.24 2 1 6 11 3 2 10 11 2 1 4 18 3 2 40 4157 KNP KB 0031.10 5 3-2 61.16 88.09 38.84 11.91 ε ε 11 3 5 18 31 30 8 9 11 3 5 18 43 42 8 958 KNP KN 0004.10 5 3-2 50.81 77.22 49.19 22.78 ε ε 9 2 27 132 48 48 3 4 5 12 27 61 97 97 3 759 KNP KP 0001.11 5 3-2 13.24 27.49 79.66 50.15 7.11 22.35 2 6 6 9 33 33 13 14 10 10 3 3 57 57 57 5860 KNP KQ 3001.10 5 3-2 11.90 2.27 17.86 0.49 70.24 97.24 2 2 1 1 5 4 43 43 1 6 1 2 41 33 62 5561 KNP KR 0301.10 5 3-2 69.34 68.52 26.68 2.19 3.98 29.29 8 36 7 1 18 18 42 43 3 1 7 1 44 43 66 6762 KP P KB 0030.20 5 3-2 45.63 75.36 54.37 24.63 ε 0.01 31 34 14 34 18 17 3 4 1 1 14 34 43 43 3 463 KP P KN 0003.20 5 3-2 35.30 62.39 64.69 37.59 ε 0.02 3 5 21 12 30 29 13 14 2 1 12 31 50 50 16 1764 KP P KP 0000.21 5 3-2 9.96 18.89 78.55 52.44 11.48 28.67 2 11 66 58 28 28 11 12 6 7 3 3 127 127 42 4365 KP P KQ 3000.20 5 3-2 12.62 1.53 16.02 0.07 71.37 98.40 14 15 19 8 6 5 30 30 7 2 12 6 124 100 41 4166 KP P KR 0300.20 5 3-2 20.05 18.19 35.41 6.59 44.53 75.22 1 1 2 3 25 24 25 25 1 1 1 3 54 53 41 4067 KQB KB 1040.00 5 3-2 0.26 19.78 99.74 80.22 ε ε 597 2743 187 645 8 8 1 2 4 11 187 645 17 17 1 268 KQB KN 1013.00 5 3-2 0.55 16.73 99.45 83.27 ε ε 91 454 30 153 7 7 0 1 1 14 30 153 21 21 0 169 KQB KP 1010.01 5 3-2 0.01 14.12 99.99 84.90 ε 0.98 2 8 791 789 12 12 1 2 1 34 14 1 32 33 17 2470 KQB KQ 4010.00 5 3-2 44.04 62.29 55.65 7.19 0.31 30.53 31 1 1 1 30 30 16 17 33 1 1 1 33 33 23 2471 KQB KR 1310.00 5 3-2 0.62 27.51 99.34 71.81 0.03 0.69 1 6 8848 52298 19 19 1 2 1 6 2 11 40 40 25 300-11-0 0-1 1-0 0-10-1 1-0maxDTC maxDTM1-0 0-1 1-0depths, moves counts depths, moves% of unbroken positions counts  Table 1b. 5-man chess endgame statistics:  3-2, Part I.  Computer Olympiad Workshop 6 August 2001 4  = =Force # w-b wtm btm wtm btm wtm btm wtm btm wtm btm wtm btm wtm btm wtm btm wtm btm wtm btm wtm btm72 KQNKB 1031.00 5 3-2 0.24 20.89 99.76 79.11 ε ε 203 569 28 64 9 9 0 1 98 259 28 64 17 17 0 173 KQNKN 1004.00 5 3-2 0.61 17.82 99.39 82.18 ε ε 10 54 31 166 9 9 0 1 1 15 31 166 21 21 0 174 KQNKP 1001.01 5 3-2 0.10 14.97 99.90 83.12 ε 1.91 7 8 928 911 17 17 1 2 2 7 1 31 30 41 22 2975 KQNKQ 4001.00 5 3-2 49.57 62.25 50.09 4.29 0.34 33.46 7 1 1 4 35 35 13 14 7 1 2 6 41 41 23 2476 KQNKR 1301.00 5 3-2 0.71 27.20 99.24 69.83 0.04 2.97 2 12 15 86 22 22 2 3 1 5 9 17 38 38 38 4177 KQP KB 1030.10 5 3-2 0.12 16.75 99.88 83.25 ε ε 1271 4925 374 1290 9 9 1 2 16 68 374 1290 28 29 1 278 KQP KN 1003.10 5 3-2 0.33 12.48 99.67 87.52 ε ε 1 6 3 9 10 10 1 2 4 24 1 3 30 30 7 879 KQP KP 1000.11 5 3-2 ε 7.41 100 - ε 89.15 0.00 3.43 17436 59666 16 16 6 6 2 3 1 6 4 3 105 122 14 3480 KQP KQ 4000.10 5 3-2 31.21 51.20 68.39 13.61 0.40 35.19 5 4 2 13 114 103 15 16 5 13 24 268 124 123 28 2981 KQP KR 1300.10 5 3-2 0.29 6.14 99.59 74.15 0.13 19.72 4 20 5177 26128 20 20 2 3 7 11 6 32 37 43 27 3382 KQQKB 2030.00 5 3-2 0.00 0.05 100.00 99.95 0.00 0.00 1031 4239 0 0 4 4 — — 3 11 0 0 15 17 — —83 KQQKN 2003.00 5 3-2 ε 0.09 100 - ε 99.91 0.00 0.00 10 50 0 0 5 5 — — 2 15 0 0 19 21 — —84 KQQKP 2000.01 5 3-2 ε 0.65 100 - ε 99.34 ε 0.01 35764 49022 140 140 3 3 1 2 1 3 140 4 22 30 2 1385 KQQKQ 5000.00 5 3-2 0.82 32.76 99.10 66.65 0.09 0.59 2 21 25 115 25 25 6 7 4 44 1 35 30 30 12 1386 KQQKR 2300.00 5 3-2 0.01 0.20 99.97 99.68 0.02 0.12 2 12 2383 16681 14 14 1 2 2 100 1017 27 35 35 2 1987 KQRKB 1130.00 5 3-2 0.03 11.63 99.97 88.37 0.00 0.00 1005 3433 0 0 5 5 — — 18 197 0 0 29 29 — —88 KQRKN 1103.00 5 3-2 0.11 7.75 99.89 92.25 ε ε 285 1399 36 149 5 5 0 1 6 35 36 149 40 40 0 189 KQRKP 1100.01 5 3-2 ε 1.36 100 - ε 98.34 ε 0.30 153744 225124 683 683 3 3 1 2 1 3 2 6 40 67 35 4390 KQRKQ 4100.00 5 3-2 2.76 21.23 97.01 54.34 0.24 24.43 3 31 1 2 60 60 8 9 3 31 11 79 67 67 37 3891 KQRKR 1400.00 5 3-2 0.12 17.66 99.85 82.09 0.03 0.25 4 22 8040 56088 16 16 1 2 5 82 2810 139 34 35 2 2092 KRB KB 0140.00 5 3-2 1.82 31.12 98.18 68.88 ε ε 25 35 251 836 25 25 1 2 14 9 251 836 30 30 1 293 KRB KN 0113.00 5 3-2 1.07 24.04 98.93 75.96 ε ε 10 39 105 476 21 21 0 1 6 30 105 476 40 40 0 194 KRB KP 0110.01 5 3-2 0.94 17.06 99.06 80.50 ε 2.44 2 12 4 12 11 11 4 5 1 4 1 6 28 36 65 7095 KRB KQ 3110.00 5 3-2 47.94 25.58 38.70 3.21 13.36 71.20 1 3 5 4 7 6 41 42 79 31 3 4 21 20 70 7096 KRB KR 0410.00 5 3-2 58.74 94.08 41.21 5.07 0.05 0.85 28 19 3 11 59 58 3 4 28 19 3 11 65 64 26 3097 KRNKB 0131.00 5 3-2 2.28 32.37 97.72 67.63 ε ε 3 6 41 89 25 25 0 1 1 1 41 89 31 31 0 198 KRNKN 0104.00 5 3-2 1.02 24.64 98.98 75.36 ε ε 5 18 101 468 24 24 0 1 1 3 101 468 37 40 0 199 KRNKP 0101.01 5 3-2 1.53 17.10 98.45 78.39 0.01 4.51 69 85 2 2 15 15 10 11 2 2 2 7 29 29 63 68100 KRNKQ 3101.00 5 3-2 41.12 19.71 35.44 2.10 23.43 78.19 24 5 7 3 9 8 46 46 72 15 3 1 20 19 69 69101 KRNKR 0401.00 5 3-2 63.29 93.60 36.63 3.24 0.07 3.16 1 1 1 3 33 32 4 5 1 1 1 17 37 36 39 41102 KRP KB 0130.10 5 3-2 3.60 32.61 96.40 67.39 ε ε 11 26 502 1672 62 62 1 2 3 13 502 1672 73 73 1 2103 KRP KN 0103.10 5 3-2 2.51 24.70 97.49 75.30 ε ε 2 7 4 12 46 46 1 2 6 24 2 6 54 54 7 8104 KRP KP 0100.11 5 3-2 0.33 6.51 99.44 83.26 0.24 10.23 7 8 17 22 10 10 10 11 3 3 5 6 56 68 100 103105 KRP KQ 3100.10 5 3-2 11.84 7.12 37.70 1.83 50.46 91.04 5 5 5 1 9 8 78 79 45 1 3 1 68 59 103 104106 KRP KR 0400.10 5 3-2 33.02 54.39 66.57 25.54 0.41 20.07 33 4 23 80 60 60 6 7 33 4 2 32 74 74 28 33107 KRRKB 0230.00 5 3-2 0.73 22.40 99.27 77.60 0.00 0.00 1 2 0 0 10 10 — — 39 232 0 0 29 29 — —108 KRRKN 0203.00 5 3-2 0.28 14.97 99.72 85.03 ε ε 1 6 45 184 8 8 0 1 6 32 45 184 40 40 0 1109 KRRKP 0200.01 5 3-2 ε 5.71 99.99 93.28 ε 1.01 16 48 988 988 9 9 1 2 1 1 1 1 33 40 40 50110 KRRKQ 3200.00 5 3-2 36.78 36.96 58.13 11.01 5.09 52.03 14 4 2 3 16 15 20 20 14 6 3 5 29 28 49 49111 KRRKR 0500.00 5 3-2 0.71 33.41 99.25 66.17 0.04 0.42 3 15 6150 42805 25 25 1 2 2 10 1980 139 31 31 2 201-0 0-10-11-0 0-1 1-0counts depths, moves1-0 0-1 1-0 0-1% of unbroken positions counts depths, movesmaxDTC maxDTMTable 1c. 5-man chess endgame statistics:  3-2, Part II. 3-5-Man Chess Data 5    = =Force # w-b wtm btm wtm btm wtm btm wtm btm wtm btm wtm btm wtm btm wtm btm wtm btm wtm btm wtm btm112 KB B B K 0090.00/30 5 4-1 26.05 31.60 73.95 68.40 0.00 0.00 48 140 0 0 11 11 — — 2 45 0 0 16 19 — —113 KB B NK 0021.00 5 4-1 0.02 4.06 99.98 95.94 0.00 0.00 663 1754 0 0 14 14 — — 4 832 0 0 33 33 — —114 KB B P K 0020.10 5 4-1 1.67 6.83 98.33 93.17 0.00 0.00 4 3 0 0 16 16 — — 1 4 0 0 30 31 — —115 KB NNK 0012.00 5 4-1 0.02 8.41 99.98 91.59 0.00 0.00 21 50 0 0 14 14 — — 1 3 0 0 34 34 — —116 KB NP K 0011.10 5 4-1 ε 0.83 100 - ε 99.17 0.00 0.00 1 5 0 0 11 11 — — 1 2831 0 0 33 33 — —117 KB P P K 0010.20 5 4-1 0.20 1.27 99.80 98.73 0.00 0.00 56 46 0 0 16 16 — — 3 63 0 0 25 32 — —118 KNNNK 0009.00/30 5 4-1 1.27 25.01 98.73 74.99 0.00 0.00 43 163 0 0 21 21 — — 43 163 0 0 21 21 — —119 KNNP K 0002.10 5 4-1 1.62 12.01 98.38 87.99 0.00 0.00 20 32 0 0 16 16 — — 90 198 0 0 28 28 — —120 KNP P K 0001.20 5 4-1 0.02 1.03 99.98 98.97 0.00 0.00 44 105 0 0 12 12 — — 1 66 0 0 32 32 — —121 KP P P K 0000.30 5 4-1 0.06 0.63 99.94 99.37 0.00 0.00 6 6 0 0 12 12 — — 7 6 0 0 33 33 — —122 KQB B K 1020.00 5 4-1 0.00 5.03 100.00 94.97 0.00 0.00 10850 61334 0 0 6 6 — — 36905 105 0 0 6 19 — —123 KQB NK 1011.00 5 4-1 ε 1.11 100 - ε 98.89 0.00 0.00 16504 69137 0 0 5 5 — — 1082 849 0 0 7 33 — —124 KQB P K 1010.10 5 4-1 0.00 1.22 100.00 98.78 0.00 0.00 16724 75101 0 0 6 6 — — 1 4 0 0 9 31 — —125 KQNNK 1002.00 5 4-1 0.00 9.07 100.00 90.93 0.00 0.00 12262 58699 0 0 7 7 — — 59 8 0 0 8 9 — —126 KQNP K 1001.10 5 4-1 0.00 1.03 100.00 98.97 0.00 0.00 1678 8471 0 0 6 6 — — 67 197 0 0 9 27 — —127 KQP P K 1000.20 5 4-1 ε 0.67 100 - ε 99.33 0.00 0.00 9493 28496 0 0 6 6 — — 14918 63 0 0 9 32 — —128 KQQB K 2010.00 5 4-1 0.00 2.67 100.00 97.33 0.00 0.00 825 3167 0 0 4 4 — — 3793 28 0 0 4 8 — —129 KQQNK 2001.00 5 4-1 0.00 2.39 100.00 97.61 0.00 0.00 2282 7648 0 0 4 4 — — 7873 8 0 0 4 9 — —130 KQQP K 2000.10 5 4-1 0.00 2.06 100.00 97.94 0.00 0.00 25977 77812 0 0 4 4 — — 1E+05 32 0 0 4 10 — —131 KQQQK 9000.00/30 5 4-1 0.00 3.96 100.00 96.04 0.00 0.00 9854 42894 0 0 3 3 — — 18820 892 0 0 3 4 — —132 KQQRK 2100.00 5 4-1 0.00 3.06 100.00 96.94 0.00 0.00 2 12 0 0 4 4 — — 31 45 0 0 4 6 — —133 KQRB K 1110.00 5 4-1 0.00 1.68 100.00 98.32 0.00 0.00 13 72 0 0 5 5 — — 4174 168 0 0 5 16 — —134 KQRNK 1101.00 5 4-1 0.00 1.42 100.00 98.58 0.00 0.00 678 2930 0 0 5 5 — — 69499 123 0 0 5 16 — —135 KQRP K 1100.10 5 4-1 ε 1.08 100 - ε 98.92 0.00 0.00 5217 20520 0 0 5 5 — — 21 270 0 0 7 16 — —136 KQRRK 1200.00 5 4-1 0.00 1.97 100.00 98.03 0.00 0.00 2913 13057 0 0 4 4 — — 7373 10811 0 0 4 7 — —137 KRB B K 0120.00 5 4-1 ε 4.30 100 - ε 95.70 0.00 0.00 4 12 0 0 11 11 — — 190 105 0 0 12 19 — —138 KRB NK 0111.00 5 4-1 ε 0.47 100 - ε 99.53 0.00 0.00 2578 8114 0 0 8 8 — — 9 849 0 0 29 33 — —139 KRB P K 0110.10 5 4-1 ε 0.63 100 - ε 99.37 0.00 0.00 2006 6175 0 0 8 8 — — 1 4 0 0 16 31 — —140 KRNNK 0102.00 5 4-1 ε 8.52 100 - ε 91.48 0.00 0.00 6 30 0 0 11 11 — — 1 104 0 0 15 16 — —141 KRNP K 0101.10 5 4-1 ε 0.54 100 - ε 99.46 0.00 0.00 4494 11986 0 0 8 8 — — 9 197 0 0 17 27 — —142 KRP P K 0100.20 5 4-1 ε 0.25 100 - ε 99.75 0.00 0.00 93 284 0 0 8 8 — — 32 63 0 0 15 32 — —143 KRRB K 0210.00 5 4-1 ε 0.78 100 - ε 99.22 0.00 0.00 1254 4742 0 0 6 6 — — 2 168 0 0 10 16 — —144 KRRNK 0201.00 5 4-1 0.00 0.63 100.00 99.37 0.00 0.00 3273 11652 0 0 6 6 — — 3 123 0 0 10 16 — —145 KRRP K 0200.10 5 4-1 ε 0.34 100 - ε 99.66 0.00 0.00 8908 30941 0 0 6 6 — — 3 270 0 0 14 16 — —146 KRRRK 0900.00/30 5 4-1 0.00 0.90 100.00 99.10 0.00 0.00 10 49 0 0 5 5 — — 95 10811 0 0 5 7 — —1-0 0-11-0 0-1 1-0 0-11-0 0-1 1-0 0-1depths, moves counts depths, moves% of unbroken positions countsmaxDTC maxDTM  Table 1d. 5-man chess endgame statistics:  4-1. 

http://wwwjn.inf.ethz.ch/ gam es/chess/statistics/chs_statistics.htm l . DTC wi n and draw st at i s t i c s for 3-m a n t o 6-m a n endgam e s. R a sm ussen, L

3-5-Man chess data

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