What are the winning chances of every pieces? (6men egtb)

Question

Is there a site or document which shows what the winning chances are of every "Specific Pieces vs. Specific Pieces" endgame?

e.g. What are the winning chances of Rook & Bishop vs 2 Knights?

Answer 1

I don't know a single source tabulating the winning percentages for all 6-piece endings, but at least some amount of summarizing information can probably be found scattered throughout Nunn's Secrets of ... Endings series of books, which are essentially translations from tablebase to human-usable information. But there is a spreadsheet available from Tamplin's chess endgame site, 3-5 Man Results and Maximals, that contains the percentage winning statistics across all < 6-man endgames. A sample of the data:

Endgame     wtm(=)  btm(=)      wtm(1-0)    btm(1-0)        wtm(0-1)    btm(0-1)

KK          100.00  100.00      0.00        0.00            0.00        0.00
KBK         100.00  100.00      0.00        0.00            0.00        0.00
KNK         100.00  100.00      0.00        0.00            0.00        0.00
KPK         23.49   41.91       76.51       58.09           0.00        0.00
KQK         0.00    10.32       100.00      89.68           0.00        0.00
KRK         0.00    9.97        100.00      90.03           0.00        0.00

...

KRNKP       1.53    17.10       98.45       78.39           0.01        4.51
KRNKQ       41.12   19.71       35.44       2.10            23.43       78.19
KRNKR       63.29   93.60       36.63       3.24            0.07        3.16

...

The first, third and fifth numerical columns give the percentage of white-to-move positions that are, respecitively, draws, white wins or black wins. And the other columns give similar information for the black-to-move positions. I'd think it unlikely that a similar table for 6-man positions doesn't already exist out there in the ether somewhere, but I don't know where such is located.

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EDIT: Sure enough, the second edition of Nunn's Secrets of Pawnless Endings (and not the first edition which predated available 6-man tablebases) does go at least partly toward what you're after. There is a summary table (pp. 325-329) that, while not providing the numerical detail of the table above, does include for each 6-man piece combination at least an indication of whether it is generally won or drawn (presumably based on whether a majority of positions are theoretically won or not, as above), along with information about the longest win and longest reciprocal zugzwang for each ending.

To use your example, Nunn notes that KRBKNN is generally a win for White, while the longest win is 223 moves from the following position:

[fen "1K6/5BR1/2n5/2n2k2/8/8/8/8 w - - 0 1"]

Some of the endings also get discussed in the text. For instance, Nunn gives an optimal line from the above position and attempts to give annotations that make the very complex play involved understandable. (Partial spoiler: 1.Kc8! is the only winning move at the start.)

Answer 2

On ETD's encouragement, an addendum to his excellent answer.

http://kirill-kryukov.com/chess/discussion-board/viewtopic.php?f=6&t=6941#p76732 provides a spreadsheet with w/d/l statistics for most common piece combinations from 6-men nalimov tablebases. Screenshot of a part of the spreadsheet below (might have to zoom in..).

EDIT 2018: For up to 7 men, Syzygy tables (also with win percentages) are available: https://syzygy-tables.info/

Answer 3

This is end game theory... Usually this comparison is not done in middle game tactics or openings (obviously).

However, my best advice for you is to read about end game books, which completely cover scenarios of rook &bishop vs 2 Knights and MANY MANY other scenarios.

If you want a suggestion, read Domination in 2,545 end game studies. You won't be disappointed and you will find what you want, that I assure you.