Some time ago Sergey Yankovich wrote a generator for tablebases, also capable of generating 7-men endgames. As a metric he uses depth to mate, in short DTM. I have created all 5-men and a large bundle of 6-men. As a next challenge, I tried to generate the 7-men endgame KNNN vs. KNN. This engame has no value for practical play but it is of interest for chess enthousiasts like myself. The generation took about 36 days using a 2 TB external drive in RAID 0 from La Cie. The maximum memory requirement is about 3 GB, temporarily is 727 GB required for disk space. The final tablebase is about 10,7 GB large. This endgame has a DTM of 121, there are 7 positions with this maximum.

What I would be interested to know is whether this end-game is generally won or drawn. The fact that the max DTM is so large could suggest it is generally won. OTOH, the positions you show as wins all have the defending Knights separated from their King, making it conceivable that it can only be won for special cases like that, (after lengthy manouevring tightening the noose around one of the Knights), and that a more typical case where King and Knights protect each other and form a fortress, would be draw.

Does the generator provide statistics (e.g. % positions won with white or black to move)?

If not, another method would be to set up a position where black does not have any positional disadvantage (e.g. all white pieces in one corner, and the black KNN close to each other near the center), and see if it still probes as a win.

It would be good to see if the rule-of-thumb that one minor ahead in a pawnless ending is in general not enough for a win stays valid on adding more material. It might in this case, because all the pieces are equal. This makes it difficult to attack a defending Knight without offering a trade.

Does the generator provide statistics (e.g. % positions won with white or black to move)?

If not, another method would be to set up a position where black does not have any positional disadvantage (e.g. all white pieces in one corner, and the black KNN close to each other near the center), and see if it still probes as a win.

It would be good to see if the rule-of-thumb that one minor ahead in a pawnless ending is in general not enough for a win stays valid on adding more material. It might in this case, because all the pieces are equal. This makes it difficult to attack a defending Knight without offering a trade.

Yes, I have the statistics file.

Attachment: 7_KNNN-KNN.txt - Statistics 7_KNNN vs. KNN (12k)

OK, thanks! Looks like this is indeed a general draw: with black to move >96% of all positions are draw. That with white to move there is a large fraction of white wins is thus probably just because there are so many positions where a black knight is up for grabs.

So it seems the rule that one minor up is not enough for a (pawnless) win seems to hold in this case.

So it seems the rule that one minor up is not enough for a (pawnless) win seems to hold in this case.

> That with white to move there is a large fraction of white wins is thus probably just because there are so many positions where a black knight is up for grabs.

Indeed: at least one of white's pieces is under attack in 78.2% of the winning positions. Most of the attacks would be knight-to-knight and therefore reciprocal...

In the endings with 3 minor pieces vs. 2 minor pieces the only generally won cases that don't involve one side having more than one bishop of the same color seem to be kbbnknn and kbbnkbn. kbbnknn is no big surprise, given that kbbkn is a general win. There are some bizarre endings with same colored bishops. For example, kbbnkbb where Black has two bishops of the same color (while White has opposite colored bishops) contains winning lines of 220 moves to capture, even though the ending does not seem to be a general win.

However, rook + 2 minor pieces vs rook + minor piece seems to be a general win, one of the bigger surprises that has come out of 7-man databases.

2 rooks + minor piece vs 2 rooks seems to be close to a general win, at least it is won more often than most people expected.

Pawnless endings involving queens with one side having an extra minor piece don't seem to be general wins. In those endings, having the move is often more important than the extra piece, for example white to move in kqqkqqn wins about 50% of tje time.

However, rook + 2 minor pieces vs rook + minor piece seems to be a general win, one of the bigger surprises that has come out of 7-man databases.

2 rooks + minor piece vs 2 rooks seems to be close to a general win, at least it is won more often than most people expected.

Pawnless endings involving queens with one side having an extra minor piece don't seem to be general wins. In those endings, having the move is often more important than the extra piece, for example white to move in kqqkqqn wins about 50% of tje time.

Great news that there are more 7-man generator persons! It is an interesting but tiresome process.

Your max DTM and number of positions with this DTM coincied with Lomonosov 7-man tables. So both programs check each other results.

BTW. We just finished generation of all 4+3 DTM-tablebases. More information will be in the corresponding thread after processing of the statistics. In short total size of 525 endings is 63,2 TB (69564161276510 bytes). There are no new positions with largest DTM as compared to mate in 545 found several years ago.

Lomonosov tablebases are more compact than Sergey Yankovich tables. For example KNNN vs KNN occupies 4413656267 bytes, but I have no idea what block size is used for compression in Sergey Yankovich program.

Your max DTM and number of positions with this DTM coincied with Lomonosov 7-man tables. So both programs check each other results.

BTW. We just finished generation of all 4+3 DTM-tablebases. More information will be in the corresponding thread after processing of the statistics. In short total size of 525 endings is 63,2 TB (69564161276510 bytes). There are no new positions with largest DTM as compared to mate in 545 found several years ago.

Lomonosov tablebases are more compact than Sergey Yankovich tables. For example KNNN vs KNN occupies 4413656267 bytes, but I have no idea what block size is used for compression in Sergey Yankovich program.

has anyone processed an 8 man yet?

At least one 8-man tablebase (KBBBB/KRR) was generated in 2009 by Marc Bourzutschky & Yakov Konoval.

I would guess that is normally a win for the bishops. Is that right?

So does 4 bishops beat 2 rooks? I would say yes??

No, probably is only a general draw.

Yakov Konoval wrote: "As of early 2009 Marc generated the first 8men constellation - BBBBxRR. The bishops are 2 white- and 2 black-colour ones.

The 4 white same pieces (plus 2 black same pieces) reduce the tablebase size dramatically, the files are only about one half-length compare the full 7men base.

Time generation was about 4 days.

Although it seems the rooks can make an easy draw sacrificing for two same colour bishops, unexpectedly this exotic endgame is very complicated.

The maximal length is 64 (DTC) and this position is given as next game."

[Event "max win 64 DTC"]

[Site "?"]

[Date "2009.??.??"]

[Round "?"]

[White "BBBB"]

[Black "RR"]

[Result "1-0"]

[SetUp "1"]

[FEN "6r1/8/B4rB1/8/1B6/5k2/7B/K7 w - - 0 1"]

[PlyCount "127"]

1. Bh5+ $1 Ke3 2. Bbd6 $1 Rd8 3. Bc5+ $1 Kd2 4. Bae2 $1 Re6 5. Beg4 $1 Rc6 6.

Bf4+ $1 Kc3 7. Be5+ $1 Kd2 8. Bcd4 Rd5 9. Bb2 $1 Rb6 10. Bbc3+ $1 Ke3 11. Bf7

$1 Rd8 12. Ba2 $1 Rb5 13. Bf6 Rd6 14. Be7 $1 Ra6 15. Bcb4 $1 Rb8 16. Bbc5+ $1

Kd3 17. Bf3 $1 Kc2 18. Ba3 $1 Kc3 19. Bad6 $1 Rbb6 20. Bc5 $1 Rb5 21. Bh1 Rb8

22. Bed6 Rb5 23. Be4 Raa5 24. Ba3 $1 Kd4 25. Bf3 $1 Ra7 26. Bab4 $1 Ra4 27. Be1

$1 Kd3 28. Bd1 $1 Ra7 29. Beb4 $1 Rab7 30. Ba3 Kc3 31. Be2 Ra5 32. Bf3 $1 Rbb5

33. Be7 Ra7 34. Bfd5 Raa5 35. Bb2+ Kc2 36. Be4+ $1 Kd2 37. Bc6 Rb8 38. Bcd5 Kc2

39. Bba3 Kc3 40. Bed6 Rbb5 41. Be5+ Kd2 42. Bf4+ $1 Kc3 43. Bb2+ Kc2 44. Be4+

$1 Kd1 45. Kb1 Rb4 46. Bc2+ $1 Ke2 47. Bd6 $1 Rh4 48. Bba3 Rb5+ 49. Bab3 Rh3

50. Bd1+ Kf1 51. Bdb4 Rh4 52. Be7 Rc4 53. Ka1 Rc8 54. Bg4 Rc7 55. Bge6 Kf2 56.

Bbc4 Rh5 57. Bd8 Rh1+ 58. Kb2 Rg7 59. Bc5+ Kg3 60. Bd6+ Kf2 61. Bb6+ Ke1 62.

Kc1 Rg2 63. Bb4+ Rd2 64. Bxd2# 1-0

Yakov Konoval wrote: "As of early 2009 Marc generated the first 8men constellation - BBBBxRR. The bishops are 2 white- and 2 black-colour ones.

The 4 white same pieces (plus 2 black same pieces) reduce the tablebase size dramatically, the files are only about one half-length compare the full 7men base.

Time generation was about 4 days.

Although it seems the rooks can make an easy draw sacrificing for two same colour bishops, unexpectedly this exotic endgame is very complicated.

The maximal length is 64 (DTC) and this position is given as next game."

[Event "max win 64 DTC"]

[Site "?"]

[Date "2009.??.??"]

[Round "?"]

[White "BBBB"]

[Black "RR"]

[Result "1-0"]

[SetUp "1"]

[FEN "6r1/8/B4rB1/8/1B6/5k2/7B/K7 w - - 0 1"]

[PlyCount "127"]

1. Bh5+ $1 Ke3 2. Bbd6 $1 Rd8 3. Bc5+ $1 Kd2 4. Bae2 $1 Re6 5. Beg4 $1 Rc6 6.

Bf4+ $1 Kc3 7. Be5+ $1 Kd2 8. Bcd4 Rd5 9. Bb2 $1 Rb6 10. Bbc3+ $1 Ke3 11. Bf7

$1 Rd8 12. Ba2 $1 Rb5 13. Bf6 Rd6 14. Be7 $1 Ra6 15. Bcb4 $1 Rb8 16. Bbc5+ $1

Kd3 17. Bf3 $1 Kc2 18. Ba3 $1 Kc3 19. Bad6 $1 Rbb6 20. Bc5 $1 Rb5 21. Bh1 Rb8

22. Bed6 Rb5 23. Be4 Raa5 24. Ba3 $1 Kd4 25. Bf3 $1 Ra7 26. Bab4 $1 Ra4 27. Be1

$1 Kd3 28. Bd1 $1 Ra7 29. Beb4 $1 Rab7 30. Ba3 Kc3 31. Be2 Ra5 32. Bf3 $1 Rbb5

33. Be7 Ra7 34. Bfd5 Raa5 35. Bb2+ Kc2 36. Be4+ $1 Kd2 37. Bc6 Rb8 38. Bcd5 Kc2

39. Bba3 Kc3 40. Bed6 Rbb5 41. Be5+ Kd2 42. Bf4+ $1 Kc3 43. Bb2+ Kc2 44. Be4+

$1 Kd1 45. Kb1 Rb4 46. Bc2+ $1 Ke2 47. Bd6 $1 Rh4 48. Bba3 Rb5+ 49. Bab3 Rh3

50. Bd1+ Kf1 51. Bdb4 Rh4 52. Be7 Rc4 53. Ka1 Rc8 54. Bg4 Rc7 55. Bge6 Kf2 56.

Bbc4 Rh5 57. Bd8 Rh1+ 58. Kb2 Rg7 59. Bc5+ Kg3 60. Bd6+ Kf2 61. Bb6+ Ke1 62.

Kc1 Rg2 63. Bb4+ Rd2 64. Bxd2# 1-0

It is possible to generate some 8-man table with the pieces of the same type. It should not take more than a day (for Lomonosov tables). But producing really useful 8-man table is beyond reasonable efforts to do this at the current level of computer hardware. Even managing 7-man tables is a hard task for a while.

What can you say about this position?

(Black to move)

Most chess players will say it is draw. Black can't win having only one knight and no other pieces. White pawns will be delayed by the black knight.

Yes, all this is true.

But if we slightly move the e-pawn the situation changes.

There is no need in tablebases to see this. But it took some time for engines to discover mate (for example Houdini finds solution on depth 28.) This is the longest mate by black in KNPPP-KN ending.

2N5/K1k1n3/P7/8/8/8/2P1P3/8 b - - 0 1

(Black to move)

Most chess players will say it is draw. Black can't win having only one knight and no other pieces. White pawns will be delayed by the black knight.

Yes, all this is true.

But if we slightly move the e-pawn the situation changes.

2N5/K1k1n3/P7/8/8/4P3/2P5/8 b - - 0 1

There is no need in tablebases to see this. But it took some time for engines to discover mate (for example Houdini finds solution on depth 28.) This is the longest mate by black in KNPPP-KN ending.

Can anybody find a win for black here?!

Black moves and mates in 36 moves

K2k4/P7/2N1P3/4P3/2b5/8/8/8 b - - 0 1

Black moves and mates in 36 moves

Houdini *without* EGTB in 2 seconds ;).

39/47 0:01 0.00 1...Kc8 2.e7 Bf7 3.e8B Bxe8 4.Ne7+ Kc7 5.e6 Bb5 6.Nd5+ Kc8 7.Nb6+ Kc7 8.Nd5+ Kc8 (10.058.896) 8278 40/47 0:01 0.00 1...Kc8 2.e7 Bf7 3.e8B Bxe8 4.Ne7+ Kc7 5.e6 Bb5 6.Nd5+ Kc8 7.Nb6+ Kc7 8.Nd5+ Kc8 (13.305.037) 8512 40/75 0:01 -0.05++ 1...Kc7 (13.879.348) 8468 40/75 0:01 -0.15++ 1...Kc7 (13.896.576) 8463 37/75 0:01 -0.39++ 1...Kc7 (13.917.786) 8450 37/76 0:01 -1.27++ 1...Kc7 (13.951.089) 8434 37/76 0:01 -3.82++ 1...Kc7 (14.007.637) 8402 37/76 0:01 -11.04++ 1...Kc7 (14.027.603) 8389 37/76 0:02 -M36 1...Kc7 2.e7 Bf7 3.Nb4 Kc8 4.Nc6 Be8 5.Nd8 Bd7 6.Nb7 Kc7 7.Nd8 Bb5 8.Ne6+ Kc8 9.Nd8 Be8 10.Nb7 Kc7 11.Nd8 Bh5 12.Nc6 Bg6 13.e6 Be8 14.Nb8 Bb5 (19.721.390) 9100 38/76 0:02 -M36 1...Kc7 2.e7 Bf7 3.Nb4 Kc8 4.Nc6 Be8 5.Nd8 Bd7 6.Nb7 Kc7 7.Nd8 Bb5 8.Ne6+ Kc8 9.Nd8 Be8 10.Nb7 Kc7 11.Nd8 Bh5 12.Nc6 Bg6 13.e6 Be8 14.Nb8 Bb5 (20.068.867) 9118

I would like to have your Houdini :)

2 min is not enough for my one. Negative value appears only on depth 48.

2 min is not enough for my one. Negative value appears only on depth 48.

Amazing position. And incredible top engines can find the mate in 36 so fast. In one of the main lines the following position arise where whites can play e7-e8 promoting to a knight with check. As it happens e7-e8Q is equally good, but there might be other lines where under promotion helps the defence. Does your 7 man table base consider under promotion?

K2N4/P1k1P3/8/7b/8/8/8/8 w - - 19 28

It doesn't matter for this position but Lomonosov tablebases consider all under-promotions.

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