NULP

(Number of Unique Legal Positions in chess endgames)

Number of endgames in Chess with any starting position

These numbers are computed using exact set of Chess pieces, but without assuming any fixed starting position.

PiecesEndgamesEndgames
Cumulative		ESMsESMs
Cumulative
2 1 1 1 1
3 5 6 10 11
4 30 36 55 66
5 110 146 220 286
6 365 511 715 1,001
7 1,001 1,512 2,002 3,003
8 2,520 4,032 5,005 8,008
9 5,720 9,752 11,440 19,448
10 12,190 21,942 24,310 43,758
11 24,309 46,251 48,618 92,376
12 46,233 92,484 92,340 184,716
13 83,817 176,301 167,634 352,350
14 146,094 322,395 291,978 644,328
15 244,350 566,745 488,700 1,133,028
16 393,114 959,859 785,898 1,918,926
17 606,777 1,566,6361,213,554 3,132,480
18 899,592 2,466,2281,798,689 4,931,169
191,279,689 3,745,9172,559,378 7,490,547
201,749,075 5,494,9923,497,43610,987,983
212,294,793 7,789,7854,589,58615,577,569
222,889,02110,678,8065,777,05521,354,624
233,477,15014,155,9566,954,30028,308,924
243,980,87118,136,8277,960,45536,269,379
254,291,44322,428,2708,582,88644,852,265
264,297,60526,725,8758,593,73153,445,996
273,914,64030,640,5157,829,28061,275,276
283,160,51533,801,0306,319,57567,594,851
292,172,55535,973,5854,345,11071,939,961
301,210,77037,184,3552,420,55074,360,511
31 490,05037,674,405 980,10075,340,611
32 122,76037,797,165 245,02575,585,636
© 2013–2014 Kirill Kryukov
Available under the CC BY 3.0 License