Long post: Frequency of the different TB-endgames in games
Posted: 19 Dec 2005, 19:36I decided to open a new thread because of the long post, so that people interested in TB-sharing but not in this, can easily skip it, and the other thread stay more readable.
For Dann Corbit's "crapbase" of Oct. 2005 (at least this is the date on my disk), I get the statistics further down. It might be preferable, to use a commercial database (which I don't have). I showed the method in the other thread.
The code to calculate this, was more or less a one time shot, and not debugged/confirmed for correctness at all. Perhaps somebody with a chess database can check one datapoint or the other. AFAIK, the known databases cannot give a whole list.
Of course, each material constellation was only counted once, for any game.
Regards,
Dieter
For Dann Corbit's "crapbase" of Oct. 2005 (at least this is the date on my disk), I get the statistics further down. It might be preferable, to use a commercial database (which I don't have). I showed the method in the other thread.
The code to calculate this, was more or less a one time shot, and not debugged/confirmed for correctness at all. Perhaps somebody with a chess database can check one datapoint or the other. AFAIK, the known databases cannot give a whole list.
Of course, each material constellation was only counted once, for any game.
Regards,
Dieter
- Code: Select all
TB: no of games (relative occurence in 3505657 games)
KRPKR: 46033 (1.31311%)
KRPKRP: 42006 (1.19823%)
KRPPKR: 37666 (1.07443%)
KPPKP: 33519 (0.95614%)
KPK: 26949 (0.76873%)
KPPKPP: 24837 (0.70848%)
KPKP: 19657 (0.56072%)
KQK: 19018 (0.54249%)
KRK: 17259 (0.49232%)
KRKP: 15806 (0.45087%)
KRKR: 14746 (0.42063%)
KPPPKP: 13953 (0.39801%)
KPPK: 13359 (0.38107%)
KRPKPP: 12889 (0.36766%)
KRPKP: 12454 (0.35525%)
KBPKP: 12178 (0.34738%)
KBPKPP: 11870 (0.33860%)
KK: 11790 (0.33631%)
KQPK: 11486 (0.32764%)
KQPKP: 10120 (0.28868%)
KBPKNP: 10085 (0.28768%)
KQKP: 10020 (0.28582%)
KPPKR: 9899 (0.28237%)
KRPPKP: 9820 (0.28012%)
KNPKPP: 9502 (0.27105%)
KRPK: 9498 (0.27093%)
KNPKP: 9009 (0.25698%)
KQPPKP: 8665 (0.24717%)
KRPKBP: 8658 (0.24697%)
KBPK: 8434 (0.24058%)
KBPPKP: 8205 (0.23405%)
KQPKPP: 8018 (0.22872%)
KBKP: 6440 (0.18370%)
KBPKBP: 6253 (0.17837%)
KQPKQ: 6230 (0.17771%)
KQPPK: 5962 (0.17007%)
KNKP: 5946 (0.16961%)
KNPPKP: 5892 (0.16807%)
KRPKNP: 5792 (0.16522%)
KNPK: 5602 (0.15980%)
KRBKRP: 5569 (0.15886%)
KBPPKB: 5551 (0.15834%)
KQPKQP: 5459 (0.15572%)
KBPKB: 5305 (0.15133%)
KRBPKR: 5273 (0.15041%)
KPPKQ: 5254 (0.14987%)
KRPPK: 5207 (0.14853%)
KNPKB: 4813 (0.13729%)
KNPKNP: 4791 (0.13666%)
KQBK: 4775 (0.13621%)
KQRKR: 4685 (0.13364%)
KBK: 4656 (0.13281%)
KQQK: 4631 (0.13210%)
KRNKRP: 4628 (0.13202%)
KQKR: 4614 (0.13162%)
KPPKN: 4564 (0.13019%)
KRPKB: 4549 (0.12976%)
KNPKN: 4524 (0.12905%)
KRBKR: 4489 (0.12805%)
KQRK: 4420 (0.12608%)
KNPPKN: 4337 (0.12371%)
KNPPKB: 4274 (0.12192%)
KBPKR: 4266 (0.12169%)
KPPKB: 4217 (0.12029%)
KNK: 4179 (0.11921%)
KQPKRP: 4159 (0.11864%)
KRNPKR: 4053 (0.11561%)
KPPPK: 3937 (0.11230%)
KPPPKR: 3894 (0.11108%)
KRKB: 3860 (0.11011%)
KQPPKQ: 3810 (0.10868%)
KBPPKN: 3778 (0.10777%)
KRNKR: 3772 (0.10760%)
KBPKN: 3744 (0.10680%)
KBPPKR: 3620 (0.10326%)
KRKN: 3554 (0.10138%)
KQRPK: 3550 (0.10126%)
KNPKR: 3324 (0.09482%)
KRPKN: 3323 (0.09479%)
KBPPK: 3269 (0.09325%)
KQKQ: 3142 (0.08963%)
KQRKRP: 3102 (0.08849%)
KQPKR: 3099 (0.08840%)
KQRPKR: 3088 (0.08809%)
KRPKQ: 3086 (0.08803%)
KQNK: 2997 (0.08549%)
KRPPKB: 2778 (0.07924%)
KQBPK: 2766 (0.07890%)
KQQPK: 2734 (0.07799%)
KQBPKP: 2660 (0.07588%)
KNPPKR: 2652 (0.07565%)
KQRPKP: 2581 (0.07362%)
KNPPK: 2311 (0.06592%)
KPPPKN: 2101 (0.05993%)
KRPPKN: 2050 (0.05848%)
KPPPKB: 1975 (0.05634%)
KRPPKQ: 1965 (0.05605%)
KBKN: 1948 (0.05557%)
KQKN: 1909 (0.05445%)
KRBK: 1874 (0.05346%)
KRBPKP: 1849 (0.05274%)
KQQPKP: 1836 (0.05237%)
KQRKP: 1780 (0.05078%)
KQPKBP: 1765 (0.05035%)
KPPPKQ: 1762 (0.05026%)
KRBPK: 1751 (0.04995%)
KQNPK: 1700 (0.04849%)
KQPPKR: 1696 (0.04838%)
KQBKP: 1599 (0.04561%)
KQPKNP: 1582 (0.04513%)
KQKB: 1546 (0.04410%)
KRRKRP: 1436 (0.04096%)
KQNPKP: 1411 (0.04025%)
KRRPKR: 1355 (0.03865%)
KRBKRN: 1341 (0.03825%)
KNPKQ: 1276 (0.03640%)
KBPKQ: 1266 (0.03611%)
KRPKBN: 1258 (0.03588%)
KNKN: 1252 (0.03571%)
KQQKP: 1237 (0.03529%)
KRNK: 1220 (0.03480%)
KQPKN: 1174 (0.03349%)
KRBKP: 1173 (0.03346%)
KBNK: 1165 (0.03323%)
KRNPKP: 1116 (0.03183%)
KQPKB: 1115 (0.03181%)
KQRKPP: 1101 (0.03141%)
KBNPKR: 1062 (0.03029%)
KBKB: 1031 (0.02941%)
KRNPK: 1017 (0.02901%)
KQNKP: 963 (0.02747%)
KRRKR: 940 (0.02681%)
KRBKPP: 910 (0.02596%)
KRBKBP: 905 (0.02582%)
KBNKP: 894 (0.02550%)
KBNPKP: 839 (0.02393%)
KRNKP: 819 (0.02336%)
KQBKPP: 809 (0.02308%)
KRBPKB: 782 (0.02231%)
KQRBK: 781 (0.02228%)
KBPPKQ: 764 (0.02179%)
KNPPKQ: 735 (0.02097%)
KBNKR: 723 (0.02062%)
KQBKQP: 722 (0.02060%)
KRBKRB: 712 (0.02031%)
KQPPKB: 702 (0.02002%)
KRNKPP: 700 (0.01997%)
KBNPKB: 693 (0.01977%)
KQNKQP: 682 (0.01945%)
KQBPKB: 677 (0.01931%)
KRBPKQ: 662 (0.01888%)
KQPPKN: 653 (0.01863%)
KQPKRR: 650 (0.01854%)
KRBKNP: 633 (0.01806%)
KBNPK: 622 (0.01774%)
KBNKPP: 608 (0.01734%)
KRBKB: 604 (0.01723%)
KRNKBP: 593 (0.01692%)
KQNKQ: 590 (0.01683%)
KQNKPP: 584 (0.01666%)
KQPKRB: 576 (0.01643%)
KBNKBP: 572 (0.01632%)
KQQBK: 564 (0.01609%)
KQRKB: 550 (0.01569%)
KRNKRN: 549 (0.01566%)
KQQKPP: 548 (0.01563%)
KRNKNP: 539 (0.01538%)
KRNPKQ: 526 (0.01500%)
KQBKQ: 514 (0.01466%)
KQBPKQ: 512 (0.01460%)
KQBPKR: 510 (0.01455%)
KQRNK: 506 (0.01443%)
KRBPKN: 500 (0.01426%)
KQRKQP: 500 (0.01426%)
KQQKQ: 495 (0.01412%)
KRRPKP: 489 (0.01395%)
KQBKRP: 489 (0.01395%)
KQNPKB: 489 (0.01395%)
KRRPK: 468 (0.01335%)
KRRK: 463 (0.01321%)
KBNKNP: 451 (0.01286%)
KQPKRN: 451 (0.01286%)
KQNPKQ: 448 (0.01278%)
KRBKN: 445 (0.01269%)
KRNPKB: 444 (0.01267%)
KQRPKB: 438 (0.01249%)
KQBPKN: 436 (0.01244%)
KRBKQ: 430 (0.01227%)
KQRBKR: 424 (0.01209%)
KBNKB: 419 (0.01195%)
KBBPKP: 409 (0.01167%)
KNNKP: 406 (0.01158%)
KBBK: 406 (0.01158%)
KBNPKN: 403 (0.01150%)
KQBKR: 400 (0.01141%)
KQRKQ: 397 (0.01132%)
KRRPKQ: 393 (0.01121%)
KRNKB: 385 (0.01098%)
KQBKB: 379 (0.01081%)
KBBPKB: 379 (0.01081%)
KQNPKR: 371 (0.01058%)
KBNKN: 368 (0.01050%)
KQRPKQ: 367 (0.01047%)
KQQNK: 365 (0.01041%)
KQRKBP: 362 (0.01033%)
KRNKN: 360 (0.01027%)
KQBKBP: 360 (0.01027%)
KRRKRB: 359 (0.01024%)
KRNPKN: 359 (0.01024%)
KRPKBB: 358 (0.01021%)
KBBPKR: 357 (0.01018%)
KQRNKR: 357 (0.01018%)
KQRBKP: 353 (0.01007%)
KRNKQ: 349 (0.00996%)
KRRKQ: 345 (0.00984%)
KBBKBP: 344 (0.00981%)
KQBNK: 339 (0.00967%)
KQRKN: 336 (0.00958%)
KBBKP: 319 (0.00910%)
KQNKR: 308 (0.00879%)
KQNPKN: 308 (0.00879%)
KQNKRP: 304 (0.00867%)
KQQKQP: 302 (0.00861%)
KBBPK: 296 (0.00844%)
KQQPKQ: 293 (0.00836%)
KRRKRR: 293 (0.00836%)
KQNKB: 292 (0.00833%)
KRPKNN: 292 (0.00833%)
KRRKP: 290 (0.00827%)
KRRKPP: 290 (0.00827%)
KQNKBP: 287 (0.00819%)
KQBKNP: 285 (0.00813%)
KQBKN: 281 (0.00802%)
KQRPKN: 273 (0.00779%)
KRRKRN: 256 (0.00730%)
KQRKRB: 256 (0.00730%)
KQQKR: 254 (0.00725%)
KQQRK: 246 (0.00702%)
KBBKPP: 244 (0.00696%)
KQNKN: 242 (0.00690%)
KNNKPP: 242 (0.00690%)
KQRKRN: 242 (0.00690%)
KQRKNP: 237 (0.00676%)
KBBKB: 237 (0.00676%)
KQNKNP: 236 (0.00673%)
KBBKR: 229 (0.00653%)
KNNPKP: 220 (0.00628%)
KQQBKP: 218 (0.00622%)
KNNK: 214 (0.00610%)
KBNKQ: 195 (0.00556%)
KQQKN: 194 (0.00553%)
KQRNKP: 190 (0.00542%)
KBBKNP: 187 (0.00533%)
KNNKNP: 186 (0.00531%)
KQQPKR: 185 (0.00528%)
KQQKRP: 184 (0.00525%)
KQBBK: 180 (0.00513%)
KNNPKR: 180 (0.00513%)
KNNKR: 177 (0.00505%)
KBBKN: 170 (0.00485%)
KRBKBN: 166 (0.00474%)
KQPKBN: 166 (0.00474%)
KRBNKR: 163 (0.00465%)
KQRKQR: 155 (0.00442%)
KBNPKQ: 154 (0.00439%)
KBBPKN: 154 (0.00439%)
KRRKBP: 151 (0.00431%)
KNNPKN: 149 (0.00425%)
KBBKBN: 146 (0.00416%)
KQBKQN: 141 (0.00402%)
KNNPK: 139 (0.00397%)
KQQKB: 137 (0.00391%)
KNNPKB: 137 (0.00391%)
KRRKNP: 135 (0.00385%)
KQBNKP: 133 (0.00379%)
KQQPKN: 131 (0.00374%)
KQRRK: 118 (0.00337%)
KRRPKB: 116 (0.00331%)
KQQNKP: 114 (0.00325%)
KQQPKB: 113 (0.00322%)
KBPKNN: 111 (0.00317%)
KRRPKN: 109 (0.00311%)
KQBNKR: 103 (0.00294%)
KNNKN: 103 (0.00294%)
KQRRKR: 101 (0.00288%)
KQQRKP: 95 (0.00271%)
KRNKBN: 94 (0.00268%)
KQQRKR: 93 (0.00265%)
KRBNKQ: 91 (0.00260%)
KQRBKB: 85 (0.00242%)
KQBKRB: 84 (0.00240%)
KRBNKP: 83 (0.00237%)
KQQKBP: 82 (0.00234%)
KRBNK: 82 (0.00234%)
KQBNKB: 81 (0.00231%)
KRRKN: 78 (0.00222%)
KQQKNP: 77 (0.00220%)
KQRKQB: 77 (0.00220%)
KNNKQ: 76 (0.00217%)
KRRKB: 71 (0.00203%)
KQBBKP: 69 (0.00197%)
KQRKQN: 68 (0.00194%)
KBBPKQ: 66 (0.00188%)
KRBKBB: 65 (0.00185%)
KQNNK: 64 (0.00183%)
KBNKBN: 63 (0.00180%)
KQNKRB: 63 (0.00180%)
KQRRKP: 61 (0.00174%)
KBBKQ: 61 (0.00174%)
KQPKNN: 57 (0.00163%)
KQRKBN: 57 (0.00163%)
KQPKBB: 56 (0.00160%)
KRRBKR: 56 (0.00160%)
KNNKB: 55 (0.00157%)
KQRNKQ: 55 (0.00157%)
KQQBKB: 55 (0.00157%)
KQNKQN: 54 (0.00154%)
KRNNKR: 53 (0.00151%)
KQBKQB: 52 (0.00148%)
KQQKRB: 51 (0.00145%)
KQBBKR: 48 (0.00137%)
KQRKRR: 48 (0.00137%)
KRRBKP: 45 (0.00128%)
KQRBKN: 44 (0.00126%)
KRRNK: 44 (0.00126%)
KQQKRR: 43 (0.00123%)
KQNKRN: 43 (0.00123%)
KQBKRN: 43 (0.00123%)
KQRNKB: 42 (0.00120%)
KRNKBB: 41 (0.00117%)
KNNPKQ: 41 (0.00117%)
KQQQK: 40 (0.00114%)
KQRBKQ: 40 (0.00114%)
KRRBK: 40 (0.00114%)
KRRNKR: 40 (0.00114%)
KQQBKN: 39 (0.00111%)
KQQKQB: 38 (0.00108%)
KBNKNN: 37 (0.00106%)
KQNKBN: 35 (0.00100%)
KRRBKQ: 34 (0.00097%)
KQBBKB: 34 (0.00097%)
KRRNKQ: 34 (0.00097%)
KRBBKR: 33 (0.00094%)
KQBNKN: 33 (0.00094%)
KQQNKB: 33 (0.00094%)
KQQKQN: 31 (0.00088%)
KRBKNN: 30 (0.00086%)
KQQBKQ: 30 (0.00086%)
KQQKRN: 30 (0.00086%)
KQQNKN: 29 (0.00083%)
KBBNKR: 29 (0.00083%)
KRRNKP: 28 (0.00080%)
KQBNKQ: 28 (0.00080%)
KRRKBN: 27 (0.00077%)
KQRKBB: 27 (0.00077%)
KRNKNN: 26 (0.00074%)
KQQKQR: 26 (0.00074%)
KQQBKR: 25 (0.00071%)
KQQNKQ: 25 (0.00071%)
KQRNKN: 24 (0.00068%)
KBBNK: 24 (0.00068%)
KRBBKP: 23 (0.00066%)
KQNNKP: 23 (0.00066%)
KRBBK: 22 (0.00063%)
KQBKRR: 22 (0.00063%)
KQNKRR: 22 (0.00063%)
KRNNKQ: 21 (0.00060%)
KQQRKB: 21 (0.00060%)
KQRRKQ: 21 (0.00060%)
KBBKNN: 20 (0.00057%)
KRBNKB: 20 (0.00057%)
KQQKQQ: 20 (0.00057%)
KQBBKN: 19 (0.00054%)
KRBNKN: 19 (0.00054%)
KQQNKR: 19 (0.00054%)
KBNNKR: 18 (0.00051%)
KRBBKQ: 18 (0.00051%)
KRNNK: 18 (0.00051%)
KQBKBN: 17 (0.00048%)
KBBKBB: 16 (0.00046%)
KRNNKP: 16 (0.00046%)
KQNKNN: 15 (0.00043%)
KBBNKB: 14 (0.00040%)
KQBKBB: 14 (0.00040%)
KQNNKR: 13 (0.00037%)
KQNNKN: 13 (0.00037%)
KQRKNN: 13 (0.00037%)
KBBNKP: 12 (0.00034%)
KQQRKN: 12 (0.00034%)
KBNNK: 12 (0.00034%)
KQNKBB: 11 (0.00031%)
KNNKNN: 11 (0.00031%)
KQQQKP: 11 (0.00031%)
KBNNKB: 11 (0.00031%)
KQQKBN: 11 (0.00031%)
KRRKNN: 10 (0.00029%)
KQRRKB: 9 (0.00026%)
KQBBKQ: 8 (0.00023%)
KQNNKQ: 8 (0.00023%)
KRBBKN: 8 (0.00023%)
KRRKBB: 8 (0.00023%)
KRBBKB: 7 (0.00020%)
KQNNKB: 7 (0.00020%)
KBBNKQ: 7 (0.00020%)
KRRBKB: 7 (0.00020%)
KBNNKP: 7 (0.00020%)
KRRRKR: 6 (0.00017%)
KRRNKN: 6 (0.00017%)
KRRRK: 6 (0.00017%)
KBBNKN: 6 (0.00017%)
KQRRKN: 6 (0.00017%)
KRNNKN: 6 (0.00017%)
KQBKNN: 6 (0.00017%)
KQQRKQ: 6 (0.00017%)
KBNNKQ: 6 (0.00017%)
KRRBKN: 5 (0.00014%)
KBNNKN: 5 (0.00014%)
KQQKNN: 4 (0.00011%)
KRNNKB: 4 (0.00011%)
KQQKBB: 4 (0.00011%)
KRRNKB: 2 (0.00006%)
KQQQKQ: 2 (0.00006%)
KQQQKB: 2 (0.00006%)
KNNNK: 2 (0.00006%)
KNNNKQ: 1 (0.00003%)
KRRRKB: 1 (0.00003%)
KRRRKN: 1 (0.00003%)
KRRRKP: 1 (0.00003%)
KQQQKN: 1 (0.00003%)
KBBBKB: 1 (0.00003%)
KNNNKN: 1 (0.00003%)
KBBBK: 1 (0.00003%)
KNNNKR: 0 (0.00000%)
KNNNKB: 0 (0.00000%)
KBBBKN: 0 (0.00000%)
KNNNKP: 0 (0.00000%)
KBBBKQ: 0 (0.00000%)
KBBBKP: 0 (0.00000%)
KRRRKQ: 0 (0.00000%)
KQQQKR: 0 (0.00000%)
KBBBKR: 0 (0.00000%)
Summary for 3505657 games
1-1 : 11790 (0.33631%)
2 pieces: 11790 (0.33631%)
2-1 : 61496 (1.75419%)
3 pieces: 61496 (1.75419%)
2-2 : 83583 (2.38423%)
3-1 : 51948 (1.48183%)
4 pieces: 135531 (3.86607%)
3-2 : 206714 (5.89658%)
4-1 : 27939 (0.79697%)
5 pieces: 234653 (6.69355%)
3-3 : 179984 (5.13410%)
4-2 : 157138 (4.48241%)
5-1 : 14997 (0.42779%)
6 pieces: 352119 (10.04431%)
4-3 : 396530 (11.31115%)
5-2 : 78719 (2.24548%)
6-1 : 7458 (0.21274%)
7 pieces: 482707 (13.76937%)
4-4 : 313900 (8.95410%)
5-3 : 270089 (7.70438%)
6-2 : 34324 (0.97910%)
7-1 : 3420 (0.09756%)
8 pieces: 621733 (17.73513%)
5-4 : 623123 (17.77479%)
6-3 : 125705 (3.58578%)
7-2 : 14237 (0.40612%)
8-1 : 1311 (0.03740%)
9 pieces: 764376 (21.80407%)
5-5 : 474357 (13.53119%)
6-4 : 390033 (11.12582%)
7-3 : 49278 (1.40567%)
8-2 : 5440 (0.15518%)
9-1 : 487 (0.01389%)
10 pieces: 919595 (26.23174%)
6-5 : 888129 (25.33417%)
7-4 : 167535 (4.77899%)
8-3 : 17887 (0.51023%)
9-2 : 1892 (0.05397%)
10-1 : 169 (0.00482%)
11 pieces: 1075612 (30.68218%)
6-6 : 672258 (19.17638%)
7-5 : 513980 (14.66145%)
8-4 : 58771 (1.67646%)
9-3 : 5944 (0.16955%)
10-2 : 630 (0.01797%)
11-1 : 60 (0.00171%)
12 pieces: 1251643 (35.70352%)
7-6 : 1202785 (34.30983%)
8-5 : 202273 (5.76990%)
9-4 : 18573 (0.52980%)
10-3 : 1854 (0.05289%)
11-2 : 229 (0.00653%)
12-1 : 23 (0.00066%)
13 pieces: 1425737 (40.66961%)
7-7 : 920610 (26.26070%)
8-6 : 635132 (18.11735%)
9-5 : 62797 (1.79130%)
10-4 : 5473 (0.15612%)
11-3 : 657 (0.01874%)
12-2 : 79 (0.00225%)
13-1 : 13 (0.00037%)
14 pieces: 1624761 (46.34683%)
8-7 : 1569417 (44.76813%)
9-6 : 222369 (6.34315%)
10-5 : 17113 (0.48815%)
11-4 : 1749 (0.04989%)
12-3 : 218 (0.00622%)
13-2 : 27 (0.00077%)
14-1 : 4 (0.00011%)
15 pieces: 1810897 (51.65642%)
8-8 : 1222514 (34.87261%)
9-7 : 731917 (20.87817%)
10-6 : 58963 (1.68194%)
11-5 : 4672 (0.13327%)
12-4 : 534 (0.01523%)
13-3 : 75 (0.00214%)
14-2 : 12 (0.00034%)
16 pieces: 2018687 (57.58370%)
9-8 : 1961996 (55.96657%)
10-7 : 221157 (6.30857%)
11-6 : 14000 (0.39935%)
12-5 : 1320 (0.03765%)
13-4 : 169 (0.00482%)
14-3 : 20 (0.00057%)
15-2 : 4 (0.00011%)
16-1 : 2 (0.00006%)
17 pieces: 2198668 (62.71772%)
9-9 : 1556895 (44.41093%)
10-8 : 781467 (22.29160%)
11-7 : 49411 (1.40946%)
12-6 : 3557 (0.10146%)
13-5 : 364 (0.01038%)
14-4 : 50 (0.00143%)
15-3 : 5 (0.00014%)
16-2 : 3 (0.00009%)
18 pieces: 2391752 (68.22550%)
10-9 : 2337471 (66.67712%)
11-8 : 196294 (5.59935%)
12-7 : 10289 (0.29350%)
13-6 : 880 (0.02510%)
14-5 : 90 (0.00257%)
15-4 : 11 (0.00031%)
16-3 : 3 (0.00009%)
19 pieces: 2545038 (72.59803%)
10-10: 1903328 (54.29305%)
11-9 : 767563 (21.89498%)
12-8 : 36645 (1.04531%)
13-7 : 2305 (0.06575%)
14-6 : 219 (0.00625%)
15-5 : 29 (0.00083%)
16-4 : 4 (0.00011%)
20 pieces: 2710093 (77.30628%)
11-10: 2667458 (76.09010%)
12-9 : 154363 (4.40325%)
13-8 : 6624 (0.18895%)
14-7 : 484 (0.01381%)
15-6 : 45 (0.00128%)
16-5 : 8 (0.00023%)
21 pieces: 2828982 (80.69763%)
11-11: 2250349 (64.19193%)
12-10: 688523 (19.64034%)
13-9 : 23410 (0.66778%)
14-8 : 1208 (0.03446%)
15-7 : 91 (0.00260%)
16-6 : 12 (0.00034%)
22 pieces: 2963593 (84.53745%)
12-11: 2939748 (83.85726%)
13-10: 105884 (3.02038%)
14-9 : 3457 (0.09861%)
15-8 : 238 (0.00679%)
16-7 : 14 (0.00040%)
23 pieces: 3049341 (86.98344%)
12-12: 2588201 (73.82927%)
13-11: 556138 (15.86402%)
14-10: 12699 (0.36224%)
15-9 : 538 (0.01535%)
16-8 : 30 (0.00086%)
24 pieces: 3157606 (90.07173%)
13-12: 3150329 (89.86415%)
14-11: 61283 (1.74812%)
15-10: 1458 (0.04159%)
16-9 : 65 (0.00185%)
25 pieces: 3213135 (91.65572%)
13-13: 2895348 (82.59074%)
14-12: 398980 (11.38103%)
15-11: 5470 (0.15603%)
16-10: 155 (0.00442%)
26 pieces: 3299953 (94.13223%)
14-13: 3304023 (94.24832%)
15-12: 28341 (0.80844%)
16-11: 372 (0.01061%)
27 pieces: 3332736 (95.06737%)
14-14: 3147068 (89.77113%)
15-13: 253581 (7.23348%)
16-12: 1349 (0.03848%)
28 pieces: 3401998 (97.04309%)
15-14: 3409665 (97.26180%)
16-13: 9584 (0.27339%)
29 pieces: 3419249 (97.53518%)
15-15: 3306438 (94.31721%)
16-14: 165355 (4.71680%)
30 pieces: 3471793 (99.03402%)
16-15: 3478566 (99.22722%)
31 pieces: 3478566 (99.22722%)
16-16: 3505641 (99.99954%)
32 pieces: 3505641 (99.99954%)
number of legal moves
0: 362969 ( 0.120810%)
1: 1901144 ( 0.632774%)
2: 3227039 ( 1.074083%)
3: 3854679 ( 1.282985%)
4: 3895138 ( 1.296452%)
5: 3336736 ( 1.110594%)
6: 2527280 ( 0.841176%)
7: 1578942 ( 0.525533%)
8: 1239264 ( 0.412475%)
9: 1157109 ( 0.385130%)
10: 1300595 ( 0.432888%)
11: 1567137 ( 0.521603%)
12: 1956493 ( 0.651196%)
13: 2347169 ( 0.781228%)
14: 2747363 ( 0.914428%)
15: 3082120 ( 1.025848%)
16: 3397649 ( 1.130868%)
17: 3558553 ( 1.184423%)
18: 3695055 ( 1.229856%)
19: 4084960 ( 1.359632%)
20: 11079764 ( 3.687771%)
21: 4609116 ( 1.534091%)
22: 6498866 ( 2.163072%)
23: 5235286 ( 1.742504%)
24: 5213817 ( 1.735359%)
25: 6087465 ( 2.026142%)
26: 6764006 ( 2.251321%)
27: 8378343 ( 2.788634%)
28: 9980915 ( 3.322032%)
29: 9931608 ( 3.305621%)
30: 12766369 ( 4.249138%)
31: 10953417 ( 3.645718%)
32: 11799492 ( 3.927324%)
33: 11976241 ( 3.986153%)
34: 11745485 ( 3.909349%)
35: 11517842 ( 3.833580%)
36: 11265806 ( 3.749693%)
37: 11320813 ( 3.768002%)
38: 11108824 ( 3.697443%)
39: 9968670 ( 3.317956%)
40: 9234100 ( 3.073463%)
41: 8228753 ( 2.738845%)
42: 8035540 ( 2.674536%)
43: 6902513 ( 2.297422%)
44: 5780526 ( 1.923981%)
45: 4896690 ( 1.629807%)
46: 4143691 ( 1.379180%)
47: 3376168 ( 1.123718%)
48: 2741597 ( 0.912509%)
49: 2124692 ( 0.707179%)
50: 1633024 ( 0.543533%)
51: 1238356 ( 0.412172%)
52: 932955 ( 0.310523%)
53: 672173 ( 0.223725%)
54: 475931 ( 0.158408%)
55: 335011 ( 0.111505%)
56: 229579 ( 0.076413%)
57: 156671 ( 0.052146%)
58: 104128 ( 0.034658%)
59: 67974 ( 0.022624%)
60: 43594 ( 0.014510%)
61: 27511 ( 0.009157%)
62: 17910 ( 0.005961%)
63: 11101 ( 0.003695%)
64: 6342 ( 0.002111%)
65: 3980 ( 0.001325%)
66: 2281 ( 0.000759%)
67: 1354 ( 0.000451%)
68: 853 ( 0.000284%)
69: 437 ( 0.000145%)
70: 292 ( 0.000097%)
71: 215 ( 0.000072%)
72: 145 ( 0.000048%)
73: 100 ( 0.000033%)
74: 62 ( 0.000021%)
75: 28 ( 0.000009%)
76: 30 ( 0.000010%)
77: 22 ( 0.000007%)
78: 20 ( 0.000007%)
79: 17 ( 0.000006%)
80: 24 ( 0.000008%)
81: 12 ( 0.000004%)
82: 15 ( 0.000005%)
83: 12 ( 0.000004%)
84: 15 ( 0.000005%)
85: 13 ( 0.000004%)
86: 9 ( 0.000003%)
87: 5 ( 0.000002%)
88: 6 ( 0.000002%)
89: 7 ( 0.000002%)
90: 10 ( 0.000003%)
91: 8 ( 0.000003%)
92: 5 ( 0.000002%)
93: 7 ( 0.000002%)
94: 4 ( 0.000001%)
95: 2 ( 0.000001%)
96: 3 ( 0.000001%)
97: 3 ( 0.000001%)
98: 6 ( 0.000002%)
99: 7 ( 0.000002%)
100: 7 ( 0.000002%)