NULP

(Number of Unique Legal Positions in chess endgames)

Number of Chess endgames

This table shows the actual number of possible endgames and ESMs (endgame + side to move) in standard Chess, for up to 32 pieces.

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
254,243,14822,379,9758,486,29644,755,675
263,783,48426,163,4597,565,65052,321,325
272,178,31928,341,7784,356,63856,677,963
28 613,65528,955,4331,226,68157,904,644
29 83,62529,039,058 167,25058,071,894
30 6,09029,045,148 12,10558,083,999
31 15529,045,303 31058,084,309
32 129,045,304 158,084,310
© 2013–2014 Kirill Kryukov
Available under the CC BY 3.0 License