The strongest passer

[Lyudmil Tsvetkov]

[D]r4rk1/2nqbppp/1nb1p3/p2pP3/PppP1B2/1P3N1P/2PQBPP1/R2NR1K1 b 0 1

Above is a position I posted 2 years ago.

At that point, no engine was able to offer a solution.

So, please, engine programmers, and enthusiasts, switch on your engines and tell me how black wins this?

PS. Please note, that again, as the position was composed by myself, or actually stems from a game of mine, I am not 100% certain black is winning this, but close to 98%.

[Lyudmil Tsvetkov]

OK, I will anticipate things a bit, as I have now some free time to post, but will still await intriguing engine output.

The point is that, if black does not find quick counterplay, and the position on the queen side gets blocked, white can actually win by attacking on the king side, where it has a substantial advantage.

So black must do something quickly, and the most reasonable thing is to sacrifice a piece on a4, getting 2 connected passers for it. I think the right way to sacrifice is Ba4, and not Na4, but still the position is sufficiently complicated to be completely certain.

At some point, after Ba4, you might get the following position:

[d]r4rk1/2nqbppp/4p3/p2pP3/n1pP1B2/1pP2N1P/3QBPP1/R2NR1K1 w - - 0 1

which I think should strongly favour black.

And the key to it all is the black passer on b3 - this is the strongest possible passer in chess.

What is so peculiar about the b3 passer?
Well, most engines would give passer bonus for b3, and also connected passer bonus additionally, but that is not enough. The b3 passer is due significantly more bonus, I would say some 50cps above all usual bonus points.

Why so?

Well, the reason is simple: b3 connects to a larger own pawn chain, f7-e6-d5-c4, which considerably decreases the enemy pieces' chances to detain this passer, as well as the own pieces' chances to organize quickly and bring up reserves, trying to promote it.

As said, and as supported by Carl, the longer chain, although this time pointed away from the enemy king, has the power to neutralise the enemy pieces' efficiency and boost the own pieces' efficiency in the process.

That means, black has time to improve, while white can not possibly do so.

In terms of specific eval, the b3 passer, as you see, is a passer, defended by an own pawn, c4, which own pawn is in turn defended by another own pawn, d5. That means, b3 is a passer, connecting to a larger own chain, which is sufficient evidence to assign an additional 50cps bonus.

Do you think 50cps is something to sneeze at?
Hardly, if it changes a lost position to a draw, and a draw to a win.
Again, this is one of the subtler positional terms engines hate to implement.

So again, I would give 50cps bonus for any passer defended by a pawn that is in turn defended.
A bit strange definition, but I think not difficult to implement, moreover that such positions are relatively frequent, if you know how to use them.

The bonus would be due both for the middlegame and the endgame, supposedly equal values, but not larger in the endgame, as longer chains are valid mainly in the middlegame. So contrary to most passers, this type of passer might be stronger in the middlegame.

So, for the time being, I leave it at that, very interested in any engine output, even if just for the sake of statistics, and especially in high-end machines output with stronger engines.

Any engine seeing a win for black after Ba4 or Na4, or at least in the second posted diagram?

[velmarin]

And the key to it all is the black passer on b3 - this is the strongest possible passer in chess.

Hi Lyudmil,

What are the exact movements to take the pawn on b3.

[lantonov]

SF latest dev version (17/02/2015) is clearly struggling here and can find nothing but a draw:

29 0.00 311.9M 3:51.67 Rfd8 Ne3 Qe8 Ng4 Qf8 h4 Kh8 Bg5 Rd7 Bxe7 Rxe7 Ne3 Qb8 Ng4 Qf8
29 0.00? 223.4M 2:44.31 Qd8 h4?
28 +0.05 182.7M 2:12.80 Qd8 Bg5 Bb7 Qf4 Bxg5 Nxg5 h6 Nf3 Ba6 Ne3 Qe7 Rac1 Rfd8 Qg3 Qf8 Qf4 Rac8 Qg3 Kh8 Qf4 Qe7 Qg3 Kh7 Rcd1 Kg8 Ng4 Kh8 Ne3 cxb3
27 +0.05 42.7M 0:31.05 Bb7 Bg5 Ba6 Qf4 Bxg5 Qxg5 h6 Qg3 Rac8 Rc1 Kh8 Ne3 Rfd8 Qh4 Qe8 Ng4 Qf8 Rcd1 Rb8 Qg3 Rdc8 Rc1 Qe7 Qf4 Kh7 Rcd1 cxb3
26 +0.05 25.2M 0:18.13 Bb7 Bg5 Ba6 Qf4 Bxg5 Qxg5 h6 Qg3 Rac8 Rc1 Kh8 Ne3 Rfd8 Qh4 Qe8 Ng4 Qf8 Rcd1 Rb8 Qg3 Rdc8 Rc1 Qe7 Qf4 Kh7 Rcd1 cxb3
25 +0.05 18.5M 0:13.25 Bb7 Bg5 Ba6 Qf4 Bxg5 Qxg5 h6 Qg3 Rac8 Rc1 Kh8 Ne3 Rfd8 Qh4 Qe8 Ng4 Qf8 Rcd1 Rb8 Qg3 Rdc8 Rc1 Qe7 Qf4 Kh7 Rcd1 cxb3
24 +0.06 12.1M 0:08.70 Bb7 Bg5 Ba6 Qf4 Bxg5 Qxg5 h6 Qg3 Rac8 Rc1 Kh8 Ne3 Rfd8 Qh4 Qe8 Ng4 Qf8 Qg3 Qe7 Qf4 Kh7 Ra1 Qd7 Qc1
23 +0.06 5.13M 0:03.74 Bb7 Bg5 Ba6 Bxe7 Qxe7 Rc1 h6 Qf4 Rfc8 Ne3 Qf8 Ng4 Rab8 Qg3 Kh8 Qf4 Kh7 Rcd1 Ra8 Rc1 Rd8 Ne3 Qe7 Ng4 Bb7
22 +0.06 3.15M 0:02.27 Bb7 Bg5 Ba6 Bxe7 Qxe7 Rc1 h6 Qf4 Rfc8 Ne3 Qf8 Ng4 Rab8 Qg3 Kh8 Qf4 Kh7 Rcd1 Ra8 Rc1 Rd8 Ne3 Qe7 Ng4 Bb7 Rcd1
21 +0.06 2.15M 0:01.53 Bb7 Bg5 Ba6 Bxe7 Qxe7 Rc1 h6 Qf4 Rfc8 Ne3 Qf8 Ng4 Rab8 Qg3 Kh8 Qf4 Kh7 Rcd1 Kg8 Rc1 Bb7 Ne3 Qe8 bxc4 Qxa4
20 +0.07 780192 0:00.58 Bb7 Bg5 Ba6 Bxe7 Qxe7 Ne3 h6 Ng4 Rfc8 Qf4 Qf8 Qg3 Kh8 Ne3 Qe7 Nd2 Rd8 f4 c3 Nf3 Bxe2 Rxe2
19 +0.07 482869 0:00.36 Bb7 Bg5 Ba6 Bxe7 Qxe7 Ne3 h6 Ng4 Rfc8 Qf4 Qf8 Qg3 Kh8 Ne3 Qe7 Nd2 Rd8 f4 c3 Nf3 Bxe2 Rxe2
18 +0.08 119584 0:00.11 Bb7 Bg5 Ba6 Bxe7 Qxe7 Ne3 h6 Ng4 Rfc8 Qf4 Qf8 Qg3 Kh8 Ne3 Qe8 Nd2 Qc6 bxc4 Bxc4
17 +0.08 7877 0:00.00 Bb7 Bg5 Rfc8 Bxe7 Qxe7 Qf4 Ba6 Rc1 Qe8 Qg3 h6 Ne3 Kh8 Ng4 Qf8 Qf4 Rd8 Ne3 Kg8 Qg3
16 +0.08 5440 0:00.00 Bb7 Bg5 Rfc8 Bxe7 Qxe7 Qf4 Ba6 Rc1 Qe8 Qg3 h6 Ne3 Kh8 Ng4 Qf8 Qf4 Rcb8 Ra1
15 +0.08 4542 0:00.00 Bb7 Bg5 Rfc8 Bxe7 Qxe7 Qf4 Ba6 Rc1 Qe8 Qg3 h6 Ne3 Kh8 Ng4 Qf8 Qf4 Rcb8
14 +0.08 3529 0:00.00 Bb7 Bg5 Rfc8 Bxe7 Qxe7 Qf4 Ba6 Rc1 Qe8 Qg3 h6 Ne3 Kh8 Ng4 Qf8 Qf4
13 +0.08 2676 0:00.00 Bb7 Bg5 Rfc8 Bxe7 Qxe7 Qf4 Ba6 Rc1 Qe8 Qg3 h6 Ne3 Kh8 Ng4 Qf8
12 +0.08 2027 0:00.00 Bb7 Bg5 Rfc8 Bxe7 Qxe7 Qf4 Ba6 Rc1 Qe8 Qg3 h6 Ne3 Kh8 Ng4
11 +0.08 1512 0:00.00 Bb7 Bg5 Rfc8 Bxe7 Qxe7 Qf4 Ba6 Rc1 Qe8 Qg3 h6 Ne3 Kh8
10 +0.08 1071 0:00.00 Bb7 Bg5 Rfc8 Bxe7 Qxe7 Qf4 Ba6 Rc1 Qe8 Qg3
9 +0.08 838 0:00.00 Bb7 Bg5 Rfc8 Bxe7 Qxe7 Qf4 Ba6 Rc1 Qe8
8 +0.08 648 0:00.00 Bb7 Bg5 Rfc8 Bxe7 Qxe7 Qf4 Ba6 Rc1
7 +0.08 497 0:00.00 Bb7 Bg5 Rfc8 Bxe7 Qxe7 Qf4 Ba6
6 +0.08 378 0:00.00 Bb7 Bg5 Rfc8 Bxe7 Qxe7 Qf4
5 +0.08 285 0:00.00 Bb7 Bg5 Rfc8 Bxe7 Qxe7
4 +0.08 208 0:00.00 Bb7 Bg5 Rfc8 Bxe7
3 +0.08 143 0:00.00 Bb7 Bg5 Rfc8
2 +0.08 88 0:00.00 Bb7 Bg5
1 +0.08 41 0:00.00 Bb7

I was certain that your solution is a sac on a4 with N or B in order to make b4 a passer before reading your second post.

[velmarin]

After
[D]r4rk1/2nqbppp/4p3/p2pP3/nppP1B2/5N1P/2PQBPP1/R2NR1K1 w - - 0 3

[Lyudmil Tsvetkov]

And the key to it all is the black passer on b3 - this is the strongest possible passer in chess.

Hi Lyudmil,

What are the exact movements to take the pawn on b3.

For example, a line like Ba4 ba4 Na4 c3 b3, do not say it is obligatory or optimal, but might occur.

[lantonov]

After Bxa4 SF thinks that White is about half a pawn ahead, with many fail-lows and fail-highs though. White generally avoids the position with the b3 passer.

35 +0.51? 916.0M 11:37.27 bxa4 Nxa4?
35 +0.57! 894.3M 11:19.79 bxa4!
34 +0.45? 827.2M 10:24.50 bxa4 Nxa4?
34 +0.51! 811.2M 10:12.47 bxa4!
33 +0.51! 794.6M 10:00.28 bxa4!
33 +0.45? 785.0M 9:53.00 bxa4 Nxa4?
32 +0.51 713.7M 8:58.59 bxa4 Nxa4 h4 Nb6 Ne3 a4 Ng4 b3 Bh6 Ne8 cxb3 axb3 Rxa8 Nxa8 Bg5 Nb6 Rb1 Bxg5 Qxg5 Kh8 Nd2 Qa7 Qe3 Qa2 h5 h6 Bd1 Kg8 Bxb3 cxb3 Rxb3 Nc4 Nxh6+ Kh8
32 +0.54? 664.0M 8:21.47 bxa4 Nxa4?
32 +0.62! 640.9M 8:04.27 bxa4!
32 +0.52! 640.5M 8:03.92 bxa4!
32 +0.46! 638.9M 8:02.65 bxa4!
31 +0.40 548.8M 6:54.80 bxa4 Nxa4 Bg5 Nb6 h4 Nb5 Ne3 Bxg5 hxg5 Nc3 Nd1 Ne4 Qf4 a4 Nd2 Rfd8 Nxe4 dxe4 c3 a3 cxb4 Qxd4 Ne3 Nd5 Nxd5 exd5 Ra2 Re8 Rea1 Qxe5 Qxe5 Rxe5 Rxa3 Rxa3 Rxa3 Rxg5
31 +0.39? 437.5M 5:29.99 bxa4 Nxa4?
31 +0.48? 352.3M 4:26.41 bxa4 Nxa4?
31 +0.54? 312.0M 3:55.95 bxa4 Nxa4?
30 +0.60 258.2M 3:11.24 bxa4 Nxa4 h4 Nb6 Ne3 a4 Ng4 b3 Bh6 Ne8 cxb3 axb3 Rxa8 Nxa8 Bg5 Nb6 Rb1 Bxg5 Qxg5 Kh8 Nd2 Qa7 h5 Qa2 Qe7 Rg8 Qb4 Na4 Bd1 Nb2 Bxb3 cxb3 Qxb3 Qxb3 Nxb3 Nc4 Nc5 Nc7 Ne3 Nxe3
30 +0.58? 227.0M 2:47.58 bxa4 Nxa4?
30 +0.66! 218.4M 2:41.20 bxa4!
30 +0.57! 217.6M 2:40.64 bxa4!
30 +0.51! 216.2M 2:39.58 bxa4!
29 +0.44 214.0M 2:37.92 bxa4 Nxa4 h4 Nb6 Ne3 a4 Ng4 b3 Bh6 Ne8 cxb3 axb3 Rxa8 Nxa8 Bg5 Nb6 Ra1 Bxg5 Qxg5 f5 exf6 Nxf6 Nxf6+ Rxf6 Qe3 Qc7 Qc3 Nd7 Ng5 Nb6
29 +0.71! 186.4M 2:17.63 bxa4!
29 +0.48? 184.4M 2:16.09 bxa4 Nxa4?
29 +0.63! 179.6M 2:12.49 bxa4!
29 +0.53? 160.9M 1:58.64 bxa4 Nxa4?
29 +0.54? 139.8M 1:43.41 bxa4 Nxa4?
29 +0.60? 120.5M 1:29.41 bxa4 Nxa4?
28 +0.76? 69.7M 0:50.74 bxa4 Nxa4?
28 +0.87! 67.7M 0:49.33 bxa4!
28 +0.67? 66.3M 0:48.19 bxa4 Nxa4?
28 +0.73! 63.8M 0:46.39 bxa4!
27 +0.67! 59.4M 0:43.22 bxa4!
26 +0.60 58.9M 0:42.83 bxa4 Nxa4 h4 Nb6 Ne3 a4 Ng4 b3 Bh6 Ne8 cxb3 axb3 Rxa8 Nxa8 Bg5 Bxg5 Qxg5 f5 exf6 Nxf6 Nfe5 Qc7 Nxf6+ Rxf6 Rb1 Nb6 Qh5 Qe7 Qg4 Qc7
26 +0.77! 54.6M 0:39.88 bxa4!
26 +0.61? 52.3M 0:38.13 bxa4 Nxa4?
26 +0.82? 35.4M 0:25.84 bxa4 Nxa4?
26 +0.90! 33.9M 0:24.74 bxa4!
26 +0.81! 33.5M 0:24.49 bxa4!
26 +0.74! 33.3M 0:24.34 bxa4!
25 +0.68 30.6M 0:22.42 bxa4 Nxa4 h4 Nb6 Ne3 a4 h5 a3 h6 g6 Bd1 Na4 Ng4 Nc3 Nf6+ Bxf6 exf6 Ne8 Be5 Qd8 Ng5 Nxf6 Bf3 a2 Kf1 Ra4 Qf4 Nfe4 Bxe4 Nxe4 Nxe4 dxe4 Bd6
25 +0.82? 23.8M 0:17.60 bxa4 Nxa4?
25 +0.90! 23.5M 0:17.36 bxa4!
25 +0.81! 23.4M 0:17.27 bxa4!
25 +0.74? 21.3M 0:15.80 bxa4 Nxa4?
24 +0.81? 15.2M 0:11.42 bxa4 Nxa4?
24 +0.90? 12.7M 0:09.61 bxa4 Nxa4?
24 +0.96? 11.4M 0:08.77 bxa4 Nxa4?
23 +1.02 10.0M 0:07.75 bxa4 Nxa4 h4 Nb6 Ne3 a4 h5 a3 h6 g6 Bd1 Na4 Ng4 Nc3 Bg5 Ne8 Nf6+ Nxf6 exf6 Bd6 Ne5 Bxe5 dxe5 a2 Bg4 Qa4
23 +0.88! 9.34M 0:07.19 bxa4!
23 +0.77? 8.57M 0:06.64 bxa4 Nxa4?
23 +0.91? 7.12M 0:05.64 bxa4 Nxa4?
23 +1.01? 6.74M 0:05.39 bxa4 Nxa4?
23 +1.07? 6.35M 0:05.13 bxa4 Nxa4?
22 +1.13 5.75M 0:04.69 bxa4 Nxa4 h4 Nb6 h5 a4 h6 g6 Ne3 a3 Bg5 b3 cxb3 cxb3 Ng4 Ne8 Reb1 b2 Ra2 Bxg5 Nxg5 Qe7 Qe3 Nc4 Qf4
22 +0.94! 5.59M 0:04.56 bxa4!
22 +0.87? 5.07M 0:04.14 bxa4 Nxa4?
22 +0.96? 4.60M 0:03.83 bxa4 Nxa4?
22 +1.02? 4.33M 0:03.64 bxa4 Nxa4?
21 +1.08 3.42M 0:02.97 bxa4 Nxa4 h4 Nb6 h5 a4 h6 g6 Ne3 a3 Bd1 Nb5 Ng4 Nc3 Bg5 Ne4 Qf4 Qd8 Bxe7 Qxe7 Rxe4 dxe4 Nf6+ Kh8 Qxe4 Nd5 Nxd5 exd5 Qxd5
20 +0.91 3.01M 0:02.64 bxa4 Nxa4 h4 Nb6 h5 a4 h6 g6 Ne3 a3 Bd1 Nb5 Ng4 Nc3 Nf6+ Bxf6 exf6 Qd8 Ng5 Nxd1 Rexd1 b3 Be5 b2 Ra2
19 +0.78 2.76M 0:02.44 bxa4 Nxa4 h4 Nb6 h5 a4 h6 g6 Bg5 a3 Ne3 b3 Ng4 b2 Ra2 Ne8 Rb1 Bxg5 Nxg5 Qa4 Ne3 Qb5 c3
18 +0.83 1.86M 0:01.78 bxa4 Nxa4 h4 Nb6 h5 a4 h6 g6 Ne3 a3 Ng4 b3 cxb3 cxb3 Nf6+ Bxf6 exf6 Nc4 Ne5 Nxd2
17 +0.83 1.03M 0:01.11 bxa4 Nxa4 h4 Nb6 h5 a4 h6 g6 Ne3 a3 Ng4 b3 cxb3 cxb3 Qd3 b2 Ra2 Nc4 Nf6+ Bxf6 exf6 Qd8 Qc2
16 +0.85 697544 0:00.80 bxa4 Nxa4 h4 Nb6 h5 a4 h6 g6 Ne3 a3 Reb1 a2 Rc1 Nb5 Ng5 Nc3 Ng4 Nxe2+ Qxe2 Bxg5 Bxg5
15 +0.86 574412 0:00.69 bxa4 Nxa4 h4 Nb6 h5 a4 h6 g6 Ng5 a3 Qe3 Nb5 Ra2 Nc7 f3 Nb5
14 +0.96 396474 0:00.53 bxa4 Nxa4 Qc1 Nb6 Bd2 a4 Rb1 b3 Nc3 a3 cxb3 a2 Nxa2 Rxa2 bxc4 Nxc4
13 +1.23 153317 0:00.25 bxa4 Nxa4 h4 Rfb8 Qc1 b3 cxb3 Rxb3 Nd2 Rbb8 Qc2 Nb6 Nc3 Bxh4 Reb1 Be7
12 +1.12 111106 0:00.19 bxa4 Nxa4 Bg5 Bxg5 Qxg5 Nb6 Ne3 h6 Qh4 Nb5 Ng4 b3 Nf6+ gxf6 exf6
11 +1.06 59373 0:00.11 bxa4 Nxa4 Qc1 Nb6 Bd2 a4 Qb1 Qb5 Ne3 a3 Qa2 h6
10 +1.23 24951 0:00.05 bxa4 Nxa4 Rf1 Rfb8 h4 b3 cxb3 Rxb3 Qc1 Rab8 Ne3
9 +1.20 13557 0:00.03 bxa4 Nxa4 h4 Nb6 h5 h6 Bxh6 a4 Bf4 a3
8 +1.22 7895 0:00.02 bxa4 Nxa4 Rf1 Rfb8 Qc1 b3 cxb3 Rxb3
7 +1.53 2448 0:00.00 bxa4 Nxa4 h4 h6 Qc1 b3 Ne3
6 +1.31 1647 0:00.00 bxa4 Nxa4 g3 h6 h4 c3
5 +1.88 580 0:00.00 bxa4 Nxa4 Ne3 b3 cxb3
4 +1.57 276 0:00.00 bxa4 Nxa4 Qc1 b3 cxb3 cxb3
3 +1.81 170 0:00.00 bxa4 Nxa4 c3 bxc3 Nxc3 Nxc3 Qxc3
2 +1.73 98 0:00.00 bxa4 Nxa4
1 +1.73 56 0:00.00 bxa4 Nxa4

[Lyudmil Tsvetkov]

SF latest dev version (17/02/2015) is clearly struggling here and can find nothing but a draw:

29 0.00 311.9M 3:51.67 Rfd8 Ne3 Qe8 Ng4 Qf8 h4 Kh8 Bg5 Rd7 Bxe7 Rxe7 Ne3 Qb8 Ng4 Qf8
29 0.00? 223.4M 2:44.31 Qd8 h4?
28 +0.05 182.7M 2:12.80 Qd8 Bg5 Bb7 Qf4 Bxg5 Nxg5 h6 Nf3 Ba6 Ne3 Qe7 Rac1 Rfd8 Qg3 Qf8 Qf4 Rac8 Qg3 Kh8 Qf4 Qe7 Qg3 Kh7 Rcd1 Kg8 Ng4 Kh8 Ne3 cxb3
27 +0.05 42.7M 0:31.05 Bb7 Bg5 Ba6 Qf4 Bxg5 Qxg5 h6 Qg3 Rac8 Rc1 Kh8 Ne3 Rfd8 Qh4 Qe8 Ng4 Qf8 Rcd1 Rb8 Qg3 Rdc8 Rc1 Qe7 Qf4 Kh7 Rcd1 cxb3
26 +0.05 25.2M 0:18.13 Bb7 Bg5 Ba6 Qf4 Bxg5 Qxg5 h6 Qg3 Rac8 Rc1 Kh8 Ne3 Rfd8 Qh4 Qe8 Ng4 Qf8 Rcd1 Rb8 Qg3 Rdc8 Rc1 Qe7 Qf4 Kh7 Rcd1 cxb3
25 +0.05 18.5M 0:13.25 Bb7 Bg5 Ba6 Qf4 Bxg5 Qxg5 h6 Qg3 Rac8 Rc1 Kh8 Ne3 Rfd8 Qh4 Qe8 Ng4 Qf8 Rcd1 Rb8 Qg3 Rdc8 Rc1 Qe7 Qf4 Kh7 Rcd1 cxb3
24 +0.06 12.1M 0:08.70 Bb7 Bg5 Ba6 Qf4 Bxg5 Qxg5 h6 Qg3 Rac8 Rc1 Kh8 Ne3 Rfd8 Qh4 Qe8 Ng4 Qf8 Qg3 Qe7 Qf4 Kh7 Ra1 Qd7 Qc1
23 +0.06 5.13M 0:03.74 Bb7 Bg5 Ba6 Bxe7 Qxe7 Rc1 h6 Qf4 Rfc8 Ne3 Qf8 Ng4 Rab8 Qg3 Kh8 Qf4 Kh7 Rcd1 Ra8 Rc1 Rd8 Ne3 Qe7 Ng4 Bb7
22 +0.06 3.15M 0:02.27 Bb7 Bg5 Ba6 Bxe7 Qxe7 Rc1 h6 Qf4 Rfc8 Ne3 Qf8 Ng4 Rab8 Qg3 Kh8 Qf4 Kh7 Rcd1 Ra8 Rc1 Rd8 Ne3 Qe7 Ng4 Bb7 Rcd1
21 +0.06 2.15M 0:01.53 Bb7 Bg5 Ba6 Bxe7 Qxe7 Rc1 h6 Qf4 Rfc8 Ne3 Qf8 Ng4 Rab8 Qg3 Kh8 Qf4 Kh7 Rcd1 Kg8 Rc1 Bb7 Ne3 Qe8 bxc4 Qxa4
20 +0.07 780192 0:00.58 Bb7 Bg5 Ba6 Bxe7 Qxe7 Ne3 h6 Ng4 Rfc8 Qf4 Qf8 Qg3 Kh8 Ne3 Qe7 Nd2 Rd8 f4 c3 Nf3 Bxe2 Rxe2
19 +0.07 482869 0:00.36 Bb7 Bg5 Ba6 Bxe7 Qxe7 Ne3 h6 Ng4 Rfc8 Qf4 Qf8 Qg3 Kh8 Ne3 Qe7 Nd2 Rd8 f4 c3 Nf3 Bxe2 Rxe2
18 +0.08 119584 0:00.11 Bb7 Bg5 Ba6 Bxe7 Qxe7 Ne3 h6 Ng4 Rfc8 Qf4 Qf8 Qg3 Kh8 Ne3 Qe8 Nd2 Qc6 bxc4 Bxc4
17 +0.08 7877 0:00.00 Bb7 Bg5 Rfc8 Bxe7 Qxe7 Qf4 Ba6 Rc1 Qe8 Qg3 h6 Ne3 Kh8 Ng4 Qf8 Qf4 Rd8 Ne3 Kg8 Qg3
16 +0.08 5440 0:00.00 Bb7 Bg5 Rfc8 Bxe7 Qxe7 Qf4 Ba6 Rc1 Qe8 Qg3 h6 Ne3 Kh8 Ng4 Qf8 Qf4 Rcb8 Ra1
15 +0.08 4542 0:00.00 Bb7 Bg5 Rfc8 Bxe7 Qxe7 Qf4 Ba6 Rc1 Qe8 Qg3 h6 Ne3 Kh8 Ng4 Qf8 Qf4 Rcb8
14 +0.08 3529 0:00.00 Bb7 Bg5 Rfc8 Bxe7 Qxe7 Qf4 Ba6 Rc1 Qe8 Qg3 h6 Ne3 Kh8 Ng4 Qf8 Qf4
13 +0.08 2676 0:00.00 Bb7 Bg5 Rfc8 Bxe7 Qxe7 Qf4 Ba6 Rc1 Qe8 Qg3 h6 Ne3 Kh8 Ng4 Qf8
12 +0.08 2027 0:00.00 Bb7 Bg5 Rfc8 Bxe7 Qxe7 Qf4 Ba6 Rc1 Qe8 Qg3 h6 Ne3 Kh8 Ng4
11 +0.08 1512 0:00.00 Bb7 Bg5 Rfc8 Bxe7 Qxe7 Qf4 Ba6 Rc1 Qe8 Qg3 h6 Ne3 Kh8
10 +0.08 1071 0:00.00 Bb7 Bg5 Rfc8 Bxe7 Qxe7 Qf4 Ba6 Rc1 Qe8 Qg3
9 +0.08 838 0:00.00 Bb7 Bg5 Rfc8 Bxe7 Qxe7 Qf4 Ba6 Rc1 Qe8
8 +0.08 648 0:00.00 Bb7 Bg5 Rfc8 Bxe7 Qxe7 Qf4 Ba6 Rc1
7 +0.08 497 0:00.00 Bb7 Bg5 Rfc8 Bxe7 Qxe7 Qf4 Ba6
6 +0.08 378 0:00.00 Bb7 Bg5 Rfc8 Bxe7 Qxe7 Qf4
5 +0.08 285 0:00.00 Bb7 Bg5 Rfc8 Bxe7 Qxe7
4 +0.08 208 0:00.00 Bb7 Bg5 Rfc8 Bxe7
3 +0.08 143 0:00.00 Bb7 Bg5 Rfc8
2 +0.08 88 0:00.00 Bb7 Bg5
1 +0.08 41 0:00.00 Bb7

I was certain that your solution is a sac on a4 with N or B in order to make b4 a passer before reading your second post.

Thanks for the output, Lyudmil.

With moves like Bb7 black is hardly going to win any time soon.

What about the second diagram I posted?

[Lyudmil Tsvetkov]

After Bxa4 SF thinks that White is about half a pawn ahead, with many fail-lows and fail-highs though. White generally avoids the position with the b3 passer.

35 +0.51? 916.0M 11:37.27 bxa4 Nxa4?
35 +0.57! 894.3M 11:19.79 bxa4!
34 +0.45? 827.2M 10:24.50 bxa4 Nxa4?
34 +0.51! 811.2M 10:12.47 bxa4!
33 +0.51! 794.6M 10:00.28 bxa4!
33 +0.45? 785.0M 9:53.00 bxa4 Nxa4?
32 +0.51 713.7M 8:58.59 bxa4 Nxa4 h4 Nb6 Ne3 a4 Ng4 b3 Bh6 Ne8 cxb3 axb3 Rxa8 Nxa8 Bg5 Nb6 Rb1 Bxg5 Qxg5 Kh8 Nd2 Qa7 Qe3 Qa2 h5 h6 Bd1 Kg8 Bxb3 cxb3 Rxb3 Nc4 Nxh6+ Kh8
32 +0.54? 664.0M 8:21.47 bxa4 Nxa4?
32 +0.62! 640.9M 8:04.27 bxa4!
32 +0.52! 640.5M 8:03.92 bxa4!
32 +0.46! 638.9M 8:02.65 bxa4!
31 +0.40 548.8M 6:54.80 bxa4 Nxa4 Bg5 Nb6 h4 Nb5 Ne3 Bxg5 hxg5 Nc3 Nd1 Ne4 Qf4 a4 Nd2 Rfd8 Nxe4 dxe4 c3 a3 cxb4 Qxd4 Ne3 Nd5 Nxd5 exd5 Ra2 Re8 Rea1 Qxe5 Qxe5 Rxe5 Rxa3 Rxa3 Rxa3 Rxg5
31 +0.39? 437.5M 5:29.99 bxa4 Nxa4?
31 +0.48? 352.3M 4:26.41 bxa4 Nxa4?
31 +0.54? 312.0M 3:55.95 bxa4 Nxa4?
30 +0.60 258.2M 3:11.24 bxa4 Nxa4 h4 Nb6 Ne3 a4 Ng4 b3 Bh6 Ne8 cxb3 axb3 Rxa8 Nxa8 Bg5 Nb6 Rb1 Bxg5 Qxg5 Kh8 Nd2 Qa7 h5 Qa2 Qe7 Rg8 Qb4 Na4 Bd1 Nb2 Bxb3 cxb3 Qxb3 Qxb3 Nxb3 Nc4 Nc5 Nc7 Ne3 Nxe3
30 +0.58? 227.0M 2:47.58 bxa4 Nxa4?
30 +0.66! 218.4M 2:41.20 bxa4!
30 +0.57! 217.6M 2:40.64 bxa4!
30 +0.51! 216.2M 2:39.58 bxa4!
29 +0.44 214.0M 2:37.92 bxa4 Nxa4 h4 Nb6 Ne3 a4 Ng4 b3 Bh6 Ne8 cxb3 axb3 Rxa8 Nxa8 Bg5 Nb6 Ra1 Bxg5 Qxg5 f5 exf6 Nxf6 Nxf6+ Rxf6 Qe3 Qc7 Qc3 Nd7 Ng5 Nb6
29 +0.71! 186.4M 2:17.63 bxa4!
29 +0.48? 184.4M 2:16.09 bxa4 Nxa4?
29 +0.63! 179.6M 2:12.49 bxa4!
29 +0.53? 160.9M 1:58.64 bxa4 Nxa4?
29 +0.54? 139.8M 1:43.41 bxa4 Nxa4?
29 +0.60? 120.5M 1:29.41 bxa4 Nxa4?
28 +0.76? 69.7M 0:50.74 bxa4 Nxa4?
28 +0.87! 67.7M 0:49.33 bxa4!
28 +0.67? 66.3M 0:48.19 bxa4 Nxa4?
28 +0.73! 63.8M 0:46.39 bxa4!
27 +0.67! 59.4M 0:43.22 bxa4!
26 +0.60 58.9M 0:42.83 bxa4 Nxa4 h4 Nb6 Ne3 a4 Ng4 b3 Bh6 Ne8 cxb3 axb3 Rxa8 Nxa8 Bg5 Bxg5 Qxg5 f5 exf6 Nxf6 Nfe5 Qc7 Nxf6+ Rxf6 Rb1 Nb6 Qh5 Qe7 Qg4 Qc7
26 +0.77! 54.6M 0:39.88 bxa4!
26 +0.61? 52.3M 0:38.13 bxa4 Nxa4?
26 +0.82? 35.4M 0:25.84 bxa4 Nxa4?
26 +0.90! 33.9M 0:24.74 bxa4!
26 +0.81! 33.5M 0:24.49 bxa4!
26 +0.74! 33.3M 0:24.34 bxa4!
25 +0.68 30.6M 0:22.42 bxa4 Nxa4 h4 Nb6 Ne3 a4 h5 a3 h6 g6 Bd1 Na4 Ng4 Nc3 Nf6+ Bxf6 exf6 Ne8 Be5 Qd8 Ng5 Nxf6 Bf3 a2 Kf1 Ra4 Qf4 Nfe4 Bxe4 Nxe4 Nxe4 dxe4 Bd6
25 +0.82? 23.8M 0:17.60 bxa4 Nxa4?
25 +0.90! 23.5M 0:17.36 bxa4!
25 +0.81! 23.4M 0:17.27 bxa4!
25 +0.74? 21.3M 0:15.80 bxa4 Nxa4?
24 +0.81? 15.2M 0:11.42 bxa4 Nxa4?
24 +0.90? 12.7M 0:09.61 bxa4 Nxa4?
24 +0.96? 11.4M 0:08.77 bxa4 Nxa4?
23 +1.02 10.0M 0:07.75 bxa4 Nxa4 h4 Nb6 Ne3 a4 h5 a3 h6 g6 Bd1 Na4 Ng4 Nc3 Bg5 Ne8 Nf6+ Nxf6 exf6 Bd6 Ne5 Bxe5 dxe5 a2 Bg4 Qa4
23 +0.88! 9.34M 0:07.19 bxa4!
23 +0.77? 8.57M 0:06.64 bxa4 Nxa4?
23 +0.91? 7.12M 0:05.64 bxa4 Nxa4?
23 +1.01? 6.74M 0:05.39 bxa4 Nxa4?
23 +1.07? 6.35M 0:05.13 bxa4 Nxa4?
22 +1.13 5.75M 0:04.69 bxa4 Nxa4 h4 Nb6 h5 a4 h6 g6 Ne3 a3 Bg5 b3 cxb3 cxb3 Ng4 Ne8 Reb1 b2 Ra2 Bxg5 Nxg5 Qe7 Qe3 Nc4 Qf4
22 +0.94! 5.59M 0:04.56 bxa4!
22 +0.87? 5.07M 0:04.14 bxa4 Nxa4?
22 +0.96? 4.60M 0:03.83 bxa4 Nxa4?
22 +1.02? 4.33M 0:03.64 bxa4 Nxa4?
21 +1.08 3.42M 0:02.97 bxa4 Nxa4 h4 Nb6 h5 a4 h6 g6 Ne3 a3 Bd1 Nb5 Ng4 Nc3 Bg5 Ne4 Qf4 Qd8 Bxe7 Qxe7 Rxe4 dxe4 Nf6+ Kh8 Qxe4 Nd5 Nxd5 exd5 Qxd5
20 +0.91 3.01M 0:02.64 bxa4 Nxa4 h4 Nb6 h5 a4 h6 g6 Ne3 a3 Bd1 Nb5 Ng4 Nc3 Nf6+ Bxf6 exf6 Qd8 Ng5 Nxd1 Rexd1 b3 Be5 b2 Ra2
19 +0.78 2.76M 0:02.44 bxa4 Nxa4 h4 Nb6 h5 a4 h6 g6 Bg5 a3 Ne3 b3 Ng4 b2 Ra2 Ne8 Rb1 Bxg5 Nxg5 Qa4 Ne3 Qb5 c3
18 +0.83 1.86M 0:01.78 bxa4 Nxa4 h4 Nb6 h5 a4 h6 g6 Ne3 a3 Ng4 b3 cxb3 cxb3 Nf6+ Bxf6 exf6 Nc4 Ne5 Nxd2
17 +0.83 1.03M 0:01.11 bxa4 Nxa4 h4 Nb6 h5 a4 h6 g6 Ne3 a3 Ng4 b3 cxb3 cxb3 Qd3 b2 Ra2 Nc4 Nf6+ Bxf6 exf6 Qd8 Qc2
16 +0.85 697544 0:00.80 bxa4 Nxa4 h4 Nb6 h5 a4 h6 g6 Ne3 a3 Reb1 a2 Rc1 Nb5 Ng5 Nc3 Ng4 Nxe2+ Qxe2 Bxg5 Bxg5
15 +0.86 574412 0:00.69 bxa4 Nxa4 h4 Nb6 h5 a4 h6 g6 Ng5 a3 Qe3 Nb5 Ra2 Nc7 f3 Nb5
14 +0.96 396474 0:00.53 bxa4 Nxa4 Qc1 Nb6 Bd2 a4 Rb1 b3 Nc3 a3 cxb3 a2 Nxa2 Rxa2 bxc4 Nxc4
13 +1.23 153317 0:00.25 bxa4 Nxa4 h4 Rfb8 Qc1 b3 cxb3 Rxb3 Nd2 Rbb8 Qc2 Nb6 Nc3 Bxh4 Reb1 Be7
12 +1.12 111106 0:00.19 bxa4 Nxa4 Bg5 Bxg5 Qxg5 Nb6 Ne3 h6 Qh4 Nb5 Ng4 b3 Nf6+ gxf6 exf6
11 +1.06 59373 0:00.11 bxa4 Nxa4 Qc1 Nb6 Bd2 a4 Qb1 Qb5 Ne3 a3 Qa2 h6
10 +1.23 24951 0:00.05 bxa4 Nxa4 Rf1 Rfb8 h4 b3 cxb3 Rxb3 Qc1 Rab8 Ne3
9 +1.20 13557 0:00.03 bxa4 Nxa4 h4 Nb6 h5 h6 Bxh6 a4 Bf4 a3
8 +1.22 7895 0:00.02 bxa4 Nxa4 Rf1 Rfb8 Qc1 b3 cxb3 Rxb3
7 +1.53 2448 0:00.00 bxa4 Nxa4 h4 h6 Qc1 b3 Ne3
6 +1.31 1647 0:00.00 bxa4 Nxa4 g3 h6 h4 c3
5 +1.88 580 0:00.00 bxa4 Nxa4 Ne3 b3 cxb3
4 +1.57 276 0:00.00 bxa4 Nxa4 Qc1 b3 cxb3 cxb3
3 +1.81 170 0:00.00 bxa4 Nxa4 c3 bxc3 Nxc3 Nxc3 Qxc3
2 +1.73 98 0:00.00 bxa4 Nxa4
1 +1.73 56 0:00.00 bxa4 Nxa4

After h4, black plays Nb6, followed by a4,a3, Qa4

[d]r4rk1/2n1bppp/1n2p3/3pP3/qppP1B1P/p4N2/2PQBPP1/R2NR1K1 w - - 0 1
It is not clear to me how white is going to stop the 2 black passers, as b3 threatens.

It is also not clear to me what can white achieve on the king side, I think nothing, as the valuable d3 square, where Be2 might go to attack the black king, is under the control of the d5 pawn, part of the longer chain.

It is not an easy position, but I think black should win this.

It might be interesting to see a longer search with Louis' 16-core...

[lantonov]

The second diagram strongly favours Black and SF thinks this too:

27 -1.06 177.6M 2:15.59 Ne3 Nb6 Reb1 a4 Bd1 a3 Bxb3 cxb3 Rxb3 Nc4 Qd3 Nxe3 Bxe3 Rfb8 Rxb8+ Rxb8 Bg5 h6 Bxe7 Qxe7 c4 dxc4 Qxc4 Rb2 Qa4 Nb5 d5 exd5 Qa8+ Qf8 Qxd5 Nc3 Qd3 Ne2+ Kf1
26 -1.07 146.8M 1:51.05 Ng5 Nb6 Qc1 a4 Qb1 Bxg5 Bxg5 a3 Bh5 h6 Bh4 Nb5 Re3 a2 Qc1 Na4 Rg3 Kh7 Be2 Rg8 f4 Qa7 Re3 Rgb8 Bf2 Qe7 Rg3 Qa3 Qd2 b2 Nxb2 Nxb2
26 -0.98? 131.3M 1:39.14 Ng5 Nb6?
26 -0.96? 121.8M 1:31.70 Ng5 Nb6?
26 -0.90? 108.0M 1:21.27 Ng5 Nb6?
25 -0.84 101.8M 1:16.47 Ng5 Nb6 Qc1 a4 Qb1 Bxg5 Bxg5 a3 Bh5 h6 Bh4 Nb5 Re3 a2 Qc1 Na4 Rg3 Kh7 Be2 Rg8 f4 Qa7 Re3 Rgb8 Bh5 Rf8 Qd2 Naxc3 Rxc3 Qxd4+ Qxd4 Nxd4
25 -0.85? 100.9M 1:15.69 Ng5 Nb6?
25 -0.77! 99.3M 1:14.47 Ng5!
25 -0.87! 98.6M 1:13.86 Ng5!
25 -0.93! 98.4M 1:13.64 Ng5!
24 -0.99 91.6M 1:08.51 h4 Nb6 h5 a4 Nh2 a3 h6 g6 Ng4 Qd8 Nf6+ Bxf6 exf6 Nb5 Bg5 Na4 Bf3 b2 Nxb2 axb2 Rxa4 Rxa4 Qxb2 Qa5 Bd2
24 -1.03? 84.2M 1:02.34 Ne3 Nb6?
24 -0.97? 72.8M 0:53.84 Ne3 Nb6?
23 -0.91 63.7M 0:47.08 Ne3 Nb6 Reb1 a4 Bd1 a3 Bxb3 cxb3 Rxb3 Nc4 Qc2 Nxe3 Bxe3 Rfb8 Ng5 Bxg5 Bxg5 Rxb3 Qxb3 Nb5 Bd2 Qc6 Ra2 h6 Qb4 g5 Qe7
23 -0.84? 44.9M 0:31.91 Ne3 Nb6?
23 -0.73! 42.0M 0:29.89 Ne3!
23 -0.74! 37.7M 0:26.83 Ne3!
23 -0.81? 31.8M 0:22.67 Ne3 Nb6?
22 -0.74 25.9M 0:18.55 Ne3 Nb6 h4 a4 Ng4 a3 Bg5 Qd8 Bxe7 Qxe7 h5 b2 Ra2 h6 Rb1 Rfb8 Nf6+ gxf6 Qxh6 Qf8 Qf4 fxe5 Qxe5 Nb5
22 -0.70? 21.8M 0:15.80 Ne3 Nb6?
22 -0.60? 18.1M 0:13.24 Ne3 Nb6?
22 -0.54? 15.1M 0:11.16 Ne3 Nb6?
21 -0.48? 11.7M 0:08.83 Ne3 Nb6?
20 -0.41 10.6M 0:08.05 Ne3 Nb6 Ng4 a4 Bg5 Qd8 Bxe7 Qxe7 h4 a3 h5 b2 Ra2 f5 exf6 gxf6 Bf1 Nb5 Be2 Qg7 Nh6+ Kh8
20 -0.31! 10.3M 0:07.77 Ne3!
20 -0.47? 7.97M 0:06.11 Ne3 Nb6?
20 -0.26? 6.32M 0:04.91 Ne3 Nb6?
20 -0.18! 6.15M 0:04.78 Ne3!
20 -0.28! 6.11M 0:04.75 Ne3!
20 -0.34? 5.73M 0:04.49 Ne3 Nb6?
19 -0.28? 4.91M 0:03.94 Ne3 Nb6?
18 -0.22! 4.19M 0:03.41 Ne3!
18 -0.32? 4.14M 0:03.34 Ne3 Nb6?
18 -0.25! 3.93M 0:03.20 Ne3!
18 -0.34! 3.92M 0:03.20 Ne3!
18 -0.40! 3.92M 0:03.20 Ne3!
17 -0.46 3.81M 0:03.10 Ne3 Nb6 Ng4 a4 Bh6 Ne8 Bxg7 Nxg7 Nf6+ Bxf6 exf6 Nf5 g4 Qd8 gxf5 Qxf6 fxe6 fxe6 Qg5+ Qxg5+ Nxg5 a3 Nxe6 Rf5 Nc5
16 +0.14 1.32M 0:01.17 h4 Nb6 h5 a4 h6 g6 Ne3 a3 Ng4 b2 Rad1 Na4 Bg5 a2 Bxe7 Qxe7 Nf6+ Kh8 Ng5
15 +0.04 1.12M 0:01.02 h4 Rfb8 h5 h6 Be3 b2 Rb1 Rb3 Bxh6 gxh6 Qxh6 Nb5 Ng5 Bxg5 Qxg5+ Kh7 Ne3 Qd8
14 +0.20 834219 0:00.81 h4 Rfb8 Bg5 b2 Rb1 Bxg5 hxg5 Rb3 Nxb2 Nxc3 Ra1 Nxe2+ Qxe2 a4 Nd1 Qd8
13 +0.24 437780 0:00.53 h4 Rfb8 Bg5 b2 Rb1 Bxg5 Nxg5 h6 Nf3 Nb5 h5 Qb7 Rxb2 Nxb2 Nxb2
12 +0.44 256672 0:00.36 h4 Rfb8 h5 h6 Be3 b2 Rb1 Rb3 Bxh6 Nb5 Bf4 Nbxc3 Nxc3
11 +0.77 115748 0:00.17 h4 Nb6 h5 h6 Bxh6 gxh6 Qxh6 a4 Ng5 Bxg5 Qxg5+ Kh7 h6 f5 exf6
10 +0.42 96661 0:00.14 Bg5 Bxg5 Qxg5 b2 Rb1 Rab8 Qd2 Rb3 Rxb2 Nxb2
9 +0.64 25675 0:00.05 g3 Rfb8 h4 h6 Nb2 Nxb2 Qxb2 a4 Nd2
8 +0.82 10890 0:00.02 h4 Rfb8 Ne3 b2 Rad1 h6 g4 Ba3
7 +0.70 8221 0:00.02 h4 Rfb8 Nb2 Nxb2 Qxb2 a4 Red1
6 +0.91 2039 0:00.00 Ne3 Nb6 Bg5 Bxg5 Nxg5 h6
5 +0.93 1460 0:00.00 Ne3 Nb6 Nf1 a4 Ne3
4 +1.05 679 0:00.00 Rb1 h6 Nb2 Nxb2
3 +1.27 423 0:00.00 Nb2 Nxb2 Qxb2
2 +1.52 186 0:00.00 Rb1 f6
1 +1.27 39 0:00.00 Nb2 Nxb2
0 #

But as I wrote in the previous post SF avoids this position. I see that other engines (Komodo) avoid the b3 passer position too.