The number of winning, drawing and losing sub-7-man position

[guyhaw]

I wonder if anyone has coralled Nalimov's position-counts to total up the number of sub-7-man winning, drawing and losing positions.

If so, may I ask you to save me quite a bit of work. Thanks - G

[guyhaw]

The sub-7-man (s7m) EGTs, by my reckoning, contain values and depths for some 3,409,699,385,208 chess positions: that's 3.4*10^12 for short!

These are the legal positions, counted in Nalimov terms, and do not include what he calls 'broken positions', e.g., with the sntm in check.

Maybe others have similar figures.

g

[Kirill Kryukov]

For a long time I've been curious to know the number of unique legal positions (NULP) in various 8x8 chess endgames. (See this 4x4 chess page for exact meaning I put into "legal" and "unique", although in 8x8 chess the casting and en-passant rights will have to be considered too). Unfortunately I'm still not aware of any such numbers reported by anyone. This kind of number is, I believe, very important to know, as it would allow to compare the results from independent researchers. Now everyone counts positions in their own ways.

Then, based on counting strictly unique legal positions, we can count wins, draws and losses (or positions with particular metric value), and again the numbers will be comparable between independent solving projects.

As far as I recall, there are 462 unique legal 2-piece positions in 8x8 chess. However already for 3 pieces the number is unknown at present, to the best of my knowledge. If anyone will try to compute the NULP values for 3 or more pieces in 8x8 chess, that would be very interesting and important. (I may do this myself eventually, if no one steps up, but it won't be soon).

[Kirill Kryukov]

I myself am also guilty of sloppy counting, which I did for 3x3 chess: I never knew the number of unique legal positions until someone else computed it last month (54,826,983).

[guyhaw]

These are the figures I just retrieved from some work which I must have done years ago and forgotten about.

They are based on my decanting of Nalimov's figures into spreadsheets, and then into a summary spreadsheet. Therefore they should be basically Nalimov's figures - which follow a nomenclature for endgames, and almost full use of symmetry.

There are three caveats:
1) Nalimov counts '2' for positions which have both Kings on the long diagonal but are not diagonally symmetric.
- - - - - e.g., wK on a1, bK on c3, wQ on a8 or h1 ... that's two positions for Nalimov rather than one.
2) Nalimov has not computed any EGTs for 5-1(p) endgames involving a lone King
3) Nalimov has not included castling rights in his EGTs ... a simple add-on to existing EGTs if anyone would care to volunteer!


2-man: 462 wtm; 462 btm and 924 in all

3-man: 173,574 wtm; 198,588 btm and 372,162 in all

4-man: 60,633,085 wtm; 74,913,901 btm and 135,546,986 in all

5-man: 11,497,269,141 wtm; 14,536,367,740 btm and 26,033,636,881 in all

6-man:
- - - - - (3-3, no Pawns): 133,485,689,894 wtm, 158,608,269,192 btm and 292,093,959,086 in all
- - - - - (4-2, no Pawns): 141,924,532,148 wtm, 215,534,429,312 btm and 357,458,961,460 in all
- - - - - (3-3p, 1+ Ps): 535,915,028,728 wtm, 656,519,458,061 btm and 1,192,434,486,789 in all
- - - - - (4-2p, 1+Ps): 657,633,052,885 wtm, 883,909,368,035 btm and 1,541,542,420,920 in all
- - - - - 5-1 and 5-1p: no figures available

So that's, for sub-7-man (s7m) positions counted:
- - - - - 1,480,516,379,917 wtm, 1,929,183,005,291 btm and 3,409,699,385,208 in all


PS: There are 906,952 type A zugs in s7m-chess which is 0.0000265992% of the s7m chess positions!
- - - - - cf http://centaur.reading.ac.uk/view/creat ... fault.html and in particular http://centaur.reading.ac.uk/4518/

Additions and corrections welcome.

g

[Kirill Kryukov]

Thanks for summing up the Nalimov's numbers. Indeed these numbers are/were available from the Nalimov's stat files, but are not terribly interesting for me because of the caveats you mentioned. If I ever compute tablebase for normal chess, my numbers will be impossible to compare with Nalimov's, because of counting the positions differently. So the question for the real reference position count in 8x8 chess endgames remains open for now. But of course this is much better than nothing.