Long analysis of some opening positions

[Ajedrecista]

Hello:

Both predicted score and centipawns evaluation can be calculated from the Lc0 formula:

Technical Explanation of Leela Chess Zero

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cp = 111.714640912 * tan(1.5620688421 * Q)
score = (Q + 1)/2  // 0 =< score =< 1
Q = 2*score - 1  // -1 =< Q =< 1

pawns = cp/100 = 1.11714640912 * tan(1.5620688421 * Q)
pawns = 1.11714640912 * tan(1.5620688421 * (2*score - 1))

score = 0.5 + (0.5/1.5620688421)*atan(pawns/1.11714640912)

Computing Taylor series of pawns around score = 0.5 and the same for score around pawns = 0:

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pawns ~ 1.745059597*(2*score - 1) // When score is close to 50%
score ~ 0.5 + 0.2865231655*pawns // When pawns are close to 0

In other words, a rate of change of circa 3.49 cp for each 1% in score (~ 7 Elo) when score is close to 50%; and a rate of change of circa 0.2865% in score (~ 2 Elo) for each cp when cp are close to 0.

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Once said that, I am curious about Zaitsev (9. ... Bb7), Chigorin (9. ... Na5) and Breyer (9. ... Nb8) variations of the Spanish Opening:

1. e4 e5 2. Nf3 Nc6 3. Bb5 a6 4.Ba4 Nf6 5.O-O Be7 6.Re1 b5 7.Bb3 d6 8.c3 O-O 9.h3

Current analysis of chessdb.cn Chess Cloud Database Query Interface returns the following evals:

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   Move      Evals from white POV
9. ... Bb7          +14 cp
9. ... Na5          +16 cp
9. ... Re8          +16 cp
9. ... h6           +23 cp
9. ... Bd7          +27 cp
9. ... a5           +34 cp
9. ... Nb8          +36 cp
9. ... Be6          +38 cp
9. ... Nd7          +38 cp

Though I think that those are SF evals, which might be different from Lc0 evals.

Regards from Spain.

Ajedrecista.

[OneTrickPony]

Move Evals from white POV
9. ... Bb7 +14 cp
9. ... Na5 +16 cp
9. ... Re8 +16 cp
9. ... h6 +23 cp
9. ... Bd7 +27 cp
9. ... a5 +34 cp
9. ... Nb8 +36 cp
9. ... Be6 +38 cp
9. ... Nd7 +38 cp

Interesting, 9...Na5 has a reputation of being by far the worst out of the 3 major lines (with Bb7/Re8 being the best).
I will run some of those. It will take a while as I usually let it run overnight when there is nothing else to run connected to my business.

[OneTrickPony]

Zaitsev variation:

[pgn]1.e4 e5 2.Nf3 Nc6 3.Bb5 a6 4.Ba4 Nf6 5.O-O Be7 6.Re1 b5 7.Bb3 d6 8.c3 O-O 9.h3 Bb7 10.d4 Re8 11.Nbd2 Bf8[/pgn]

1. 37 [+54.01] 12.a3 h6 13.Bc2 Nb8 14.b3 Nbd7 15.Bb2 Rb8 16.Rb1 g6 17.b4 Nh5 18.c4 Nf4 19.cxb5 axb5 20.Nb3 Ba8 21.Qd2 h5 22.dxe5 Bh6 23.Kf1 Nxe5 24.Nxe5 dxe5 25.Qxd8 Rbxd8 26.Red1 f6 27.Nc5 Bf8 28.Nd7 Be7 29.Rbc1 Kf7 30.Bb3+ Kg7 31.g3 Nxh3 32.Rxc7 Ng5 33.f4 Nxe4 34.fxe5 fxe5 35.Bxe5+ Kh6 36.Bf7 Rf8 37.Nxf8 Rxd1+ 38.Ke2 Rd2+ 39.Ke1 Bd6 40.Bf4+ Bxf4 41.gxf4 Rd8 42.Nxg6 Nf6 43.Nh4 Be4 44.Rc5 Rd3 45.Rxb5 Rxa3 46.Be6 Ra6 47.Re5 Ra4 48.b5 Bh7 49.Ng2 Rb4 50.Ke2 Ne4 51.Ke3
2. 37 [+54.00] 12.Bc2 g6 13.d5 Nb8 14.b3 c6 15.c4 Nbd7 16.Nf1 a5 17.Ne3 cxd5 18.Nxd5 Ba6 19.Bg5 h6 20.cxb5 Bxb5 21.Bd3 Rb8 22.Nxf6+ Nxf6 23.Bxf6 Qxf6 24.Rc1 Qe6 25.h4 Be7 26.g3 Kg7 27.Bxb5 Rxb5 28.Re3 Rc8 29.Rec3 Rxc3 30.Rxc3 a4 31.Qd3 Rb4 32.Kg2 axb3 33.axb3 Bd8 34.Rc6
3. 37 [+53.83] 12.d5 Nb8 13.Nf1 Nbd7 14.Ng3 h6 15.Nh2 c6 16.Ng4 cxd5 17.exd5 Nc5 18.Nxf6+ Qxf6 19.Bc2 g6 20.a4 Qh4 21.Be3 Rec8 22.axb5 axb5 23.Rxa8 Rxa8 24.b3 Qe7 25.Qd2 Ra2 26.Rb1 Qc7 27.Qd1 h5 28.Rc1 f5 29.c4 bxc4 30.b4 Na6 31.Bb3 Rb2 32.Bxc4 Nxb4 33.Bd2 Qb6 34.Be3 Qd8 35.Ne2 Ba6
4. 37 [+53.81] 12.a4 exd4 13.cxd4 h6 14.Ba2 Nb4 15.Bb1 c5 16.d5 Nd7 17.Ra3 c4 18.Nd4 Qf6 19.N2f3 Nc5 20.b3 Nbd3 21.Bxd3 cxd3 22.axb5 Nxe4 23.b4 Bxd5 24.Qxd3 axb5 25.Qxb5 Rxa3 26.Bxa3 Re5 27.Qb8 Re7 28.Bc1 Ng5 29.Rxe7 Nxf3+ 30.Nxf3 Qxe7 31.Be3 Qb7 32.Qxb7 Bxb7 33.Nd4 Be7 34.b5 Kf8 35.Nf5 h5 36.Bf4 g6 37.Nxd6 Bxd6 38.Bxd6+ Ke8 39.Kh2 Bd5 40.b6
5. 37 [+50.28] 12.Ng5 Re7 13.d5 Na5 14.Bc2 h6 15.Ngf3 c6 16.b4 Nc4 17.Nxc4 bxc4 18.dxc6 Bxc6 19.Nd2 d5 20.exd5 Qxd5 21.Ne4 Nxe4 22.Qxd5 Bxd5 23.Bxe4 Bxe4 24.Rxe4 Rc8 25.f4 exf4 26.Rxe7 Bxe7 27.Bxf4 Bf6 28.Rc1 Rd8 29.a4 Rd5 30.Kf2 Kf8 31.Ke2 Ke7 32.Bd2 Rd3 33.Be1 Ke6 34.b5
6. 37 [+52.82] 12.Re2 h6 13.Bc2 Nb8 14.a4 Nbd7 15.Re1 Rb8 16.b4 Ba8 17.Bb2 Qc8 18.axb5 axb5 19.Ra5 c6 20.Qa1 Bb7 21.c4

275M nodes, 90GB of RAM, JHortos J96-28 net (also 6max Syzygy but that search managed to get one TB hit).

Not surprisingly 12.a3 is the main move. I think 12.a4 is more or less analyzed down to draw. I am surprised to see 12.d5 being as close eval wise. I always considered 12.a3 to be a better move. I am surprised we don't see more of Zaitsev at the top level chess btw. It results in interesting complex positions and doesn't seem to be worse than Berlin/Marshall/Open.