Why Bd7+??

[Jack Lad]

[d] 8/2p5/7p/8/kn2K1B1/8/P1N5/8 w - - 0 1
Here white can win with 1. Nxb4 Kxb4 2. Kd3 1-0

However does your engine prefer to play 1. Bd7+? instead which only draws?

[Alessandro Scotti]

Hamsters considers Bd7+ only to depth 6, then goes for Nxb4.

[YL84]

Hi,
Alessandro could you explain from your point of view why your engine can avoid Bd7 ? Also I don't understand why Bd7+ is a draw? Below is the analysis of my chess engine which is not so strong, but maybe I could improve this type of endgame play if I understand something

yves


"depth 1 score 325 temps 75 nbnod 25 B_F :24 : c2b4
"depth 2 score 325 temps 90 nbnod 96 B_F :8,42614977317636 : c2b4 a4b4
"depth 3 score 324 temps 94 nbnod 451 B_F :7,08069875108501 : g4d7 a4a5 c2b4
"depth 4 score 324 temps 97 nbnod 1124 B_F :5,09335287822724 : g4d7 a4a5 c2b4 a5b4
"depth 5 score 350 temps 106 nbnod 3321 B_F :4,65978642003607 : g4d7 a4a5 c2b4 a5b4 a2a4
"depth 6 score 347 temps 124 nbnod 7215 B_F :3,96642571038029 : g4d7 a4a5 c2b4 a5b4 a2a4 c7c5
"depth 7 score 349 temps 197 nbnod 22606 B_F :3,9644320353851 : g4d7 a4a5 c2b4 a5b4 a2a4 c7c5 e4f3
"depth 8 score 340 temps 299 nbnod 44448 B_F :3,48667566271774 : g4d7 a4a5 c2b4 a5b4 a2a4 c7c5 d7c6 b4a5
"depth 9 score 346 temps 525 nbnod 104890 B_F :3,39828555623006 : g4d7 a4a5 c2b4 a5b4 a2a4 b4a5 e4d3 a5b6 d3c2
"depth 10 score 345 temps 940 nbnod 195597 B_F :3,13158410720704 : g4d7 a4a5 c2b4 a5b4 a2a4 c7c5 d7c6 h6h5 e4f4 c5c4
"depth 11 score 357 temps 2242 nbnod 551260 B_F :3,19624366806894 : g4d7 a4a5 c2b4 a5b4 a2a4 b4a5 d7c6 a5b6 c6d5 c7c6 d5c4
"depth 12 score 354 temps 4623 nbnod 1080190 B_F :2,99881621185192 : g4d7 a4a5 c2b4 a5b4 a2a4 b4a5 d7c6 a5b6 c6d5 c7c6 d5c4 b6b7
"depth 13 score 358 temps 15578 nbnod 3346822 B_F :3,08230394939709 : g4d7 a4a5 c2b4 a5b4 a2a4 b4a5 e4d4 h6h5 d7b5 a5b6 b5d3 h5h4 d3c2
"depth 14 score 351 temps 35005 nbnod 7130584 B_F :2,95020164483738 : g4d7 a4a5 c2b4 a5b4 e4f5 b4a3 d7e6 a3b4 f5g6 h6h5 g6h5 c7c6 h5h4 b4a5
"depth 15 score 358 temps 99197 nbnod 23637366 B_F :3,02815076809459 : g4d7 a4a5 c2b4 a5b4 e4f5 b4a3 d7e6 a3b4 f5g6 c7c6 g6h6 b4a3 h6g7 a3b4 e6d7

[Dirt]

[d] 8/2p5/7p/8/kn2K1B1/8/P1N5/8 w - - 0 1
Here white can win with 1. Nxb4 Kxb4 2. Kd3 1-0

However does your engine prefer to play 1. Bd7+? instead which only draws? :roll:

Time to finally switch to Nxb4 on my Athlon 1700+:

Toga 1.3.1
22:11

Fruit 5/11/03 (with 5 piece TB)
4:45

Times on a modern processor would be close to one third of this, so Fruit should find the right move at long time controls. The tablebases probably are most of the difference.

[Alessandro Scotti]

Hi,
Alessandro could you explain from your point of view why your engine can avoid Bd7?

No (*), but knowing Hamsters it's almost certainly for the wrong reason!

(*) I am a patzer and no longer try to understand why an engine picks a move. I can guarantee there is no special knowledge for this position though!

[Mike S.]

The 6-piece ending after 1.Bd7+ Ka5 2.Nxb4 Kxb4 is an instructive tablebase draw... White cannot keep the remaining pawn against the advancing black pawns (+king heading for the a pawn). Surprisingly though, White can win if the bishop is on g4 instead of being on d7. I'd say this is extremely difficult to distuingish form a human viewpoint and I would hesitate to assign "??" to 1.Bd7+.

For this position, I have 4-piece tbs. only and it takes a while before the score for Bd7+ drops (D945 3.4 GHz, 256 MB hash):

Analysis by Rybka 2.3.2a 32-bit :

1.Bd7+ Ka5 2.Nxb4
+- (2.27) Depth: 5 00:00:00
1.Nxb4 Kxb4 2.Be2
+- (2.53) Depth: 5 00:00:00
1.Nxb4 Kxb4 2.Be2 Ka3
+- (2.33) Depth: 6 00:00:00 2kN
1.Nxb4 Kxb4 2.Be2 c5 3.Kd5
+- (2.19) Depth: 7 00:00:00 4kN
1.Bd7+ Ka5 2.Nxb4 Kxb4 3.Bc6 h5
+- (2.40) Depth: 7 00:00:00 5kN

(...)

1.Bd7+ Ka5 2.Nxb4 Kxb4 3.Bc6 Ka3 4.Bd5 c5 5.Bb3 h5 6.Kf4 h4 7.Be6 Kb4
+- (2.03) Depth: 19 00:00:12 1749kN, tb=933
1.Bd7+ Ka5 2.Nxb4 Kxb4 3.Bc6 Ka3 4.Bd5 c5 5.Bb3 h5 6.Kf4 h4 7.Be6 Kb4
+- (2.03) Depth: 20 00:00:16 2371kN, tb=1980
1.Bd7+ Ka5 2.Nxb4 Kxb4 3.Bc6 Ka3 4.Bd5 c5 5.Bb3 h5 6.Kf4 h4 7.Be6 Kb4
+- (2.03) Depth: 21 00:00:19 2808kN, tb=2844
1.Bd7+ Ka5 2.Nxb4 Kxb4 3.Bc6 Ka3 4.Bd5 c5 5.Bb3 h5 6.Bf7 h4 7.Be6 Kb4
± (0.81) Depth: 22 00:00:34 5048kN, tb=5039
1.Nxb4 Kxb4 2.Kd3 Ka3 3.Be6 h5 4.Kc2 h4 5.Kb1 c5 6.Ka1 c4 7.Bxc4 h3
± (1.17) Depth: 22 00:00:36 5427kN, tb=6251
1.Nxb4 Kxb4 2.Kd3 Ka3 3.Be6 h5 4.Kc2 h4 5.Kb1 c5 6.Ka1 c4 7.Bxc4 h3
± (1.17) Depth: 23 00:00:41 6131kN, tb=7991
1.Nxb4 Kxb4 2.Kd3 Ka3 3.Be6 h5 4.Kc2 h4 5.Kb1 c5 6.Ka1 c4 7.Bxc4 h3
± (1.17) Depth: 24 00:00:47 7131kN, tb=10815
1.Nxb4 Kxb4 2.Kd3 Ka3 3.Be6 h5 4.Kc2 h4 5.Kb1 c5 6.Ka1 c4 7.Bxc4 h3
± (1.31) Depth: 25 00:00:56 8648kN, tb=14596

And for comparison, multi-pv(2) after depth 23:

Analysis by Rybka 2.3.2a 32-bit :

1. ± (1.31): 1.Nxb4 Kxb4 2.Kd3 Ka3 3.Be6 h5 4.Kc2 h4 5.Kb1 c5 6.Ka1 c4 7.Bxc4 h3
2. ² (0.30): 1.Bd7+ Ka5 2.Nxb4 Kxb4 3.Bc6 Ka3 4.Bd5 c5 5.Kf4 h5 6.Be6 Kb4 7.Kg5 c4

Rybka doesn't assign a clear 0.00 draw score to Bd7+ but I think that may be because of the alternative 2.Ne3 or other knight moves except NxN (although the pv doesn't show it yet).

[Jack Lad]

The 6-piece ending after 1.Bd7+ Ka5 2.Nxb4 Kxb4 is an instructive tablebase draw... White cannot keep the remaining pawn against the advancing black pawns (+king heading for the a pawn). Surprisingly though, White can win if the bishop is on g4 instead of being on d7. I'd say this is extremely difficult to distuingish form a human viewpoint and I would hesitate to assign "??" to 1.Bd7+.

Thanks for the analysis Mike.

There is actually only one ? for the move - the next one is for the question. The problem seems to be that engines cannot see that Ka3 draws after Bc6 or c5 draws after a4 or Kd3.
[d] 8/2pB4/7p/8/1k2K3/8/P7/8 w - - 0 1

Interestingly if the h pawn is on h7 instead then black can hold the draw in the original position.
[d] 8/2p4p/8/8/kn2K1B1/8/P1N5/8 w - - 0 1

[Jack Lad]

[d] 8/5B1p/8/8/1k6/2p5/P1K5/8 b - - 0 1

Here black can play h6 to draw however if the pawn is already on h6 then black is in zugzwang.

[YL84]

Hi,
Alessandro you are too modest, for your engine and for yourself
It seems that viewing this combination is difficult for engines also, unless a high search depth is reached !
yves