Progress on Blunder

[lithander]

Which gives 30. Now, 30 isn't the right answer. If we're following the above formula we'd need to square 30 and then divide it by 4. But as soon as we do this, we're no longer strictly computing the dot product. We're computing the dot product plus the dot product of those specific parts of the weight and feature vectors, squared. But that means our evaluation function model is now different, and so the partial derivative will be different as well. And there's no way to "fold" the squaring into each individual feature so we can keep using only the dot product since the operation of taking the square doesn't distribute like addition or multiplication, or division.

With your detailed explanation this makes total sense! Thanks for taking the time explaining this. Now I'm looking forward to see how you solved tuning such a two-step evaluation term in a mathematically sound way but you already promised a paper about this! No rush. I'm still busy with mobility and for that my approach is still working. I add mobility features like "there's a queen with 18 moves" to the vector and then after tuning I can either use the resulting coefficients directly via look-up table or apply some curve fitting to it.

[algerbrex]

With your detailed explanation this makes total sense! Thanks for taking the time explaining this.

Thanks, I'm glad that made things more clear!

Now I'm looking forward to see how you solved tuning such a two-step evaluation term in a mathematically sound way but you already promised a paper about this! No rush.

It actually wasn't as horrible as I thought it was going to be actually. The hardest part was going into the tuner and completely reworking the structure for collecting features.

As far as the math goes, I purposely made sure to make the formula simple so the new partials weren't too bad to compute. I'll definitely type it up in some LaTex with some code and make it look nice, since I know someone will actually be reading it now I was planning to work on it a bit over the weekend, and probably have it done some time early next week and post here about it.

I'm still busy with mobility and for that my approach is still working. I add mobility features like "there's a queen with 18 moves" to the vector and then after tuning I can either use the resulting coefficients directly via look-up table or apply some curve fitting to it.

Were you still using the approach from Minimal Chess, with the mobility PSQT, or do I understand that you're now using something more traditional?

[lithander]

Were you still using the approach from Minimal Chess, with the mobility PSQT, or do I understand that you're now using something more traditional?

I had that code from MinimalChess ported to Leorik pretty early. But it didn't help as much as it did in MinimalChess where including it didn't cause such a massive speed drop, proportionally. So I resolved to keep the eval simple (PSQT only) and worry about improving it later...

That time has finally come and I started from scratch: All pieces have between 0 and X legal moves. I looked into my set of FENs to just count (instead of think) what X is and learned that I need to add only 88 boolean features, total. Each feature would be about one specific Piece/Move combination e.g. component 834 of the feature vector being set to 1 means there is a white queen that can move to exactly 23 squares. Running that through the tuner I could look at the resulting weights and see something like this:

Code: Select all

Moves     0    1    2    3   4   5   6   7   8   9   10   11   12   13
======================================================================
Bishop = -27, -20, -12, -8, -2,  2,  5,  6,  8,  9,  12,  5,   12, -8

Now, each Bishop's material value should be modified by these CP values based on how mobile it is. If it can't move at all it loses 27 cp of it's worth. With 5 or more moves it gains a small bonus. If I use these modifiers verbatim I gain some good Elo already.

But it looks like you could approximate the values with a linear function, and I'm planning to try some curve-fitting to get rid of the noise from my too small dataset. But there's this interesting 5, 12, -8 in the end. That's nonlinear... is it just noise? But it would make sense that a bishop that has 14 moves is not a sign of a winning position. Neither is he protecting something nor attacking.

So that's the kind of thoughts I'm currently exploring! I'll post a complete writeup when I've settled on one implementation.

[algerbrex]

That time has finally come and I started from scratch: All pieces have between 0 and X legal moves. I looked into my set of FENs to just count (instead of think) what X is and learned that I need to add only 88 boolean features, total. Each feature would be about one specific Piece/Move combination e.g. component 834 of the feature vector being set to 1 means there is a white queen that can move to exactly 23 squares. Running that through the tuner I could look at the resulting weights and see something like this:

Code: Select all

Moves     0    1    2    3   4   5   6   7   8   9   10   11   12   13
======================================================================
Bishop = -27, -20, -12, -8, -2,  2,  5,  6,  8,  9,  12,  5,   12, -8

Now, each Bishop's material value should be modified by these CP values based on how mobile it is. If it can't move at all it loses 27 cp of it's worth. With 5 or more moves it gains a small bonus. If I use these modifiers verbatim I gain some good Elo already.

But it looks like you could approximate the values with a linear function, and I'm planning to try some curve-fitting to get rid of the noise from my too small dataset. But there's this interesting 5, 12, -8 in the end. That's nonlinear... is it just noise? But it would make sense that a bishop that has 14 moves is not a sign of a winning position. Neither is he protecting something nor attacking.

So that's the kind of thoughts I'm currently exploring! I'll post a complete writeup when I've settled on one implementation.

Interesting, thanks for sharing that!

Your approach is interesting. I'm not sure if it's novel, but it's novel to me The model I was using was to collect in my features vector the total number of average moves for white and multiply this per piece per game phase. Which seemed to work pretty well, I think it got like ~35 Elo.

I look forward to the write-up!

[algerbrex]

Another quick update.

I've been making good progress on Blunder 8.0.0, so I decided I'd do a quick sanity check to see the strength difference still between Blunder 7.6.0 and the dev version. Over about 1600 games, the dev version was weaker by ~30 Elo. Which isn't horrible, but did surprise me a little bit, since at this point I'm pretty confident 8.0.0's evaluation is superior to what I had in 7.6.0, and both versions basically have feature parity.

But it occurred to me that I forgot one of the biggest rules of thumb when improving your engine is not to neglect the search or evaluation for too long, as both are very interdependent (emphasis on the rule of thumb, as I'm sure there are plenty of counter-examples). I've spent a good bit of time writing a gradient descent tuner to maximize the Elo gain from the evaluation, but I've been a bit lazy with just being content with copying and pasting over the same search values used in 7.6.0.

And this has worked mostly fine of course, but I spent quite a long time tuning the search value parameters of 7.6.0 to work well with its specific evaluation. I remember in particular I squeezed a good ~50-60 Elo from optimizing the formula for null-move reductions and futility pruning margins.

So I suppose I shouldn't find it too shocking that when I put these exact same values into Blunder 8.0.0, with a very differently tuned evaluation, even one that's likely better, they'll perform sub-optimally.

So I'll likely spend the next couple of evenings working on re-optimizing some search values to work better with the new evaluation. In particular, I'll probably see if I can get away with being more aggressive with some pruning margins since I feel the evaluation is better. So far I'm not getting very promising results from any tweaking, but then again I would've said the same thing before I found success back with Blunder 7.6.0.

I've also looked back into the different methods for auto-tuning these search parameters using something like a genetic algorithm, CLOP, or Optuna for chess, as Texel Tuning has been working so nicely for me, it's been hard not to wish for an equally effective algorithm for tuning searches. I remember I tried all of these ideas in the past with minimal success, but I might revisit them a bit.

[algerbrex]

Wrote a short blog post on the major work I've done so far these past couple of weeks: https://algerbrex.github.io/2022/06/25/refactoring.html

Currently, Blunder 8.0.0 is 30 Elo stronger than Blunder 7.6.0 from quick bullet testing. Not super happy about the strength gain, it's still still progress in the right direction

I'll probably be releasing Blunder 8.0.0, depending on if these next few ideas I have are beneficial and if I can wrangle some elusive bugs.

[lithander]

I enjoyed the read!

My hope was that by the next round of Division 7 I could supply a version that would promote. But with a new version of Odonata and now Blunder to compete with the opponents will be quite a bit tougher than last time. Also I wonder when Erik will release a new version of MadChess. On his blog he wrote about a beta version of 3.1 already in march.

It’s a commonly known phenomena that the stronger an engine gets, the harder it can become to consistenly make progress, as many of the “obvious” improvments have already been implemented, meaning it takes many more hours of indepdent testing and experimenting to find progress. But of course, I find this to be the most rewarding period of an engines development, despite it’s difficulties.

I agree. To revisit a feature that you previously considered solved or working good enough and finding some ways to improve it further can feel very rewarding. And the harder the battle the sweeter the victory. On the other side lack of good progress for a long time can be frustrating. A lot of engines seem to get abandoned or start to stagnate in the Elo range that we are currently in and I think by now I have a good idea why that is!

[algerbrex]

I enjoyed the read!

Thanks! I'm going to try not to let the blog die, even if I only post once or twice a month, better than never. It provides even more motivation to know others read it to.

My hope was that by the next round of Division 7 I could supply a version that would promote. But with a new version of Odonata and now Blunder to compete with the opponents will be quite a bit tougher than last time. Also I wonder when Erik will release a new version of MadChess. On his blog he wrote about a beta version of 3.1 already in march.

Indeed so. I've done some very rough testing against Odonata 0.6.2, and it seems very strong, so a lot of progress has been made since the latest release.

As for Blunder, I've been able to make a bit more progress, but only once I realized my time controls were likely too short to see the full strength of my changes. The latest dev version after I made a couple more improvements actually appeared to be a regression against the version that was +30 Elo against 7.6.0. But after I extended the time control to 5+0.5s, the current dev version is now about +50 stronger than 7.6.0, which is more what I expected. And re-running the old test of 7.6.0 vs the other dev version also gave around +30 Elo. Going forward I'll likely prefer to start using time controls a bit longer, especially for search-related patches, as it seems more accurate.

So as it stands now, if I released Blunder 8.0.0 it'd be about 50 Elo stronger. No idea how that would translate to CCRL rating, although I expect less!

On the other side lack of good progress for a long time can be frustrating. A lot of engines seem to get abandoned or start to stagnate in the Elo range that we are currently in and I think by now I have a good idea why that is!

Unfortunately very true it can definitely be frustrating to cycle through many ideas with little to no improvement. I've had plenty of times where I've started with 5-10 "good" ideas, and at the end after testing, maybe 2 stick, and gain in total 15 Elo. But as you said all the sweeter when you find another breakthrough.

My next goal is to break 2700 on the CCRL, at which point I'll be pretty happy, considering I set my "final" goal 6 months ago to be breaking 2000+ Elo on the CCRL. Once I reach that point I'll likely need to revisit the drawing board to figure out where I might squeeze out the last little bit of Elo before I try my hand at giving Blunder a neural network. And then some form of parallelism.

[Chessqueen]

I enjoyed the read!

Thanks! I'm going to try not to let the blog die, even if I only post once or twice a month, better than never. It provides even more motivation to know others read it to.

My hope was that by the next round of Division 7 I could supply a version that would promote. But with a new version of Odonata and now Blunder to compete with the opponents will be quite a bit tougher than last time. Also I wonder when Erik will release a new version of MadChess. On his blog he wrote about a beta version of 3.1 already in march.

Indeed so. I've done some very rough testing against Odonata 0.6.2, and it seems very strong, so a lot of progress has been made since the latest release.

As for Blunder, I've been able to make a bit more progress, but only once I realized my time controls were likely too short to see the full strength of my changes. The latest dev version after I made a couple more improvements actually appeared to be a regression against the version that was +30 Elo against 7.6.0. But after I extended the time control to 5+0.5s, the current dev version is now about +50 stronger than 7.6.0, which is more what I expected. And re-running the old test of 7.6.0 vs the other dev version also gave around +30 Elo. Going forward I'll likely prefer to start using time controls a bit longer, especially for search-related patches, as it seems more accurate.

So as it stands now, if I released Blunder 8.0.0 it'd be about 50 Elo stronger. No idea how that would translate to CCRL rating, although I expect less!

On the other side lack of good progress for a long time can be frustrating. A lot of engines seem to get abandoned or start to stagnate in the Elo range that we are currently in and I think by now I have a good idea why that is!

Unfortunately very true it can definitely be frustrating to cycle through many ideas with little to no improvement. I've had plenty of times where I've started with 5-10 "good" ideas, and at the end after testing, maybe 2 stick, and gain in total 15 Elo. But as you said all the sweeter when you find another breakthrough.

My next goal is to break 2700 on the CCRL, at which point I'll be pretty happy, considering I set my "final" goal 6 months ago to be breaking 2000+ Elo on the CCRL. Once I reach that point I'll likely need to revisit the drawing board to figure out where I might squeeze out the last little bit of Elo before I try my hand at giving Blunder a neural network. And then some form of parallelism.

I wonder if the latest version of Blunder can win at least 2 games out of 100 against Vs Stockfish 3, I really do NOT expect more than 5 draws.

[Chessqueen]

I decided not to continue this match of 50 games, since it is obvious that Stockfish 3 is about 450 to 550 ratings point higher than Blunder.

Engine Score St Bl S-B
1: Stockfish-3-64-ja 24.0/25 ························· 1111111111111011111111111 24.00
2: Blunder-windows 1.0/25 0000000000000100000000000 ························· 24.00

25 games played / Tournament is finished
Name of the tournament: Stockfish-3015
Site/ Country: DESKTOP-OFQ3C0P, United States
Level: Blitz 3/2
Hardware: Intel(R) Core(TM) i7-4770 CPU @ 3.40GHz 3.40 GHz 16.0GB Memory
Operating system: Windows 10 Home Home Edition (Build 9200) 64 bit
PGN-File: C:\Program Files (x86)\Arena\Tournaments\Stockfish-2600.pgn
Website:
E-Mail Address:

[pgn][Event "Blunder-2650"]
[Site "DESKTOP-OFQ3C0P"]
[Date "2022.06.28"]
[Round "25"]
[White "Stockfish-3-64-ja"]
[Black "Blunder-windows"]
[Result "1-0"]
[BlackElo "2630"]
[ECO "D36"]
[Opening "QGD"]
[Time "07:40:32"]
[Variation "Exchange, Main Line, 9.Nf3 Re8 10.O-O Nf8 11.h3"]
[WhiteElo "2615"]
[TimeControl "180+2"]
[Termination "adjudication"]
[PlyCount "88"]
[WhiteType "program"]
[BlackType "program"]

1. c4 e6 2. Nc3 d5 3. d4 Nf6 4. cxd5 exd5 5. Bg5 c6 6. e3 Be7 {(Bf8-e7
Ng1-f3 Bc8-f5 Bf1-d3 Nf6-e4 Bg5xe7 Qd8xe7 O-O O-O Nc3-e2 Nb8-d7 Ra1-c1
Qe7-b4 b2-b3 Qb4-e7) -0.17/15 5} 7. Qc2 O-O {(O-O Ng1-f3 Be7-d6 Bf1-d3
h7-h6 Bg5-h4 Rf8-e8 O-O Bc8-g4 Bd3-e2 Nb8-d7 Bh4-g3 Bd6xg3 h2xg3 Ra8-c8)
-0.19/15 7} 8. Bd3 Nbd7 9. Nf3 {(Ng1-f3 h7-h6 Bg5-h4 Nd7-b6 O-O Bc8-g4
Nf3-e5 Bg4-e6 Rf1-e1 Kg8-h8 Bd3-f5 Nf6-d7 Bh4xe7 Qd8xe7 Bf5xe6 Qe7xe6
Ne5-d3 Nb6-c4 Nd3-f4 Qe6-e7 b2-b3) +0.56/19 9} Re8 {(Rf8-e8 O-O-O Nd7-f8
h2-h3 Nf8-g6 Kc1-b1) -0.09/15 7} 10. O-O {(O-O Nd7-f8 Nf3-e5 Nf6-g4 Bg5xe7
Qd8xe7 Ne5-f3 Nf8-g6 h2-h3 Ng4-f6 Rf1-d1 Bc8-e6 Rd1-c1 Qe7-c7 a2-a3 Be6-d7
Rc1-e1 b7-b6 Ra1-c1 c6-c5 Nc3-b5 Bd7xb5 Bd3xb5) +0.60/21 6} Nf8 {(Nd7-f8
Nf3-e5 a7-a5 f2-f4 Nf8-g6 Ra1-d1 Nf6-g4 Bg5xe7 Qd8xe7 Rd1-e1 Ng4-f6 Ne5xg6
h7xg6 f4-f5 g6xf5 Bd3xf5 Bc8xf5 Rf1xf5) -0.13/15 7} 11. h3 {(h2-h3 Bc8-e6
Bg5-f4 Nf8-g6 Bf4-h2 Be7-d6 Bh2xd6 Qd8xd6 Ra1-c1 b7-b6 a2-a3 Be6-d7 Rf1-d1
Ra8-c8 Qc2-b3 Re8-d8 Qb3-a4 Rc8-c7 Bd3xg6 h7xg6 Nf3-e5 Bd7-f5 Qa4-a6 c6-c5)
+0.60/22 24} Ng6 {(Nf8-g6 Nf3-e5 Be7-d6 f2-f4 Bd6-c7 Bd3-e2 a7-a6 Ra1-d1
Qd8-d6 Be2-f3 Qd6-d8 a2-a3) -0.26/14 5} 12. Ne5 {(Nf3-e5 Nf6-d7 Bg5xe7
Qd8xe7 Ne5-f3 Nd7-b6 Nc3-e2 Nb6-d7 Rf1-d1 Nd7-f6 Ne2-c3 Bc8-e6 a2-a3 Be6-d7
Ra1-c1 Ra8-d8 Qc2-b3) +0.60/21 11} Bd6 {(Be7-d6 f2-f4 Bd6-c7 Ra1-e1 Bc7-a5
Ne5xg6 h7xg6 f4-f5 Ba5xc3 Qc2xc3 g6xf5 Bd3xf5 Bc8xf5 Rf1xf5) -0.27/13 5}
13. f4 {(f2-f4 Bd6-b4 a2-a3 Bb4-e7 Ra1-e1 a7-a5 Qc2-b3 Ng6-f8 Rf1-f2 Nf8-d7
e3-e4 a5-a4 Nc3xa4 Nd7xe5 d4xe5 Nf6xe4 Bg5xe7 Re8xe7 Bd3xe4 d5xe4 Re1xe4)
+0.96/17 7} a6 {(a7-a6 h3-h4 Bd6-e7 Qc2-e2 Ng6-f8 h4-h5 Nf8-d7 Bg5xf6
Be7xf6 Ra1-d1 h7-h6 a2-a3 Nd7xe5 f4xe5) -0.29/14 5} 14. Rae1 {(Ra1-e1
Bd6-b4 a2-a3 Bb4-a5 b2-b4 Ba5-b6 Ne5-f3 Ng6-f8 Nc3-a4 Bb6-c7 Na4-c5 Nf8-g6
f4-f5 Ng6-f8 e3-e4 Bc7-g3 Re1-e2 h7-h6 Bg5xf6 Qd8xf6) +1.05/17 6} Bb4
{(Bd6-b4 h3-h4 Qd8-d6 Bg5xf6 Bb4xc3 b2xc3 g7xf6 h4-h5 f6xe5 h5xg6 h7xg6
f4xe5) -0.40/12 5} 15. a3 {(a2-a3 Bb4-a5 Qc2-a4 Ba5-c7 Bg5xf6 g7xf6 Ne5-f3
Qd8-d6 Qa4-c2 Kg8-h8 Qc2-b3 b7-b5 Qb3-c2 Bc8-d7 Bd3-f5 Kh8-g8 Bf5xd7 Qd6xd7
f4-f5 Ng6-e7) +1.05/19 9} Bd6 {(Bb4-d6 Ne5-f3 Bd6-b8 f4-f5 Ng6-f8 Bg5-f4
h7-h6 Bf4xb8 Ra8xb8 e3-e4 d5xe4 Nc3xe4 Nf8-d7) -0.55/13 5} 16. Nf3 {(Ne5-f3
Bd6-e7 f4-f5 Ng6-f8 Bg5-f4 Be7-d6 Bf4xd6 Qd8xd6 e3-e4 d5xe4 Nc3xe4 Nf6xe4
Bd3xe4 Nf8-d7 Be4-d3 Re8xe1 Rf1xe1 Nd7-f6 Qc2-c5 Qd6-f8 Nf3-e5 Nf6-d5
Bd3-e4 Qf8xc5 d4xc5) +0.96/18 6} Be7 {(Bd6-e7 f4-f5 Ng6-f8 Bg5-f4 Be7-d6
Bf4xd6 Qd8xd6 Qc2-d2 Nf8-d7 e3-e4 d5xe4 Nc3xe4 Nf6xe4 Re1xe4 Nd7-f6 Re4xe8+
Nf6xe8) -0.59/15 4} 17. Rc1 {(Re1-c1 Ng6-f8 Rf1-e1 a6-a5 Nf3-e5 Nf8-g6
Qc2-b3 Ra8-a7 Ne5-f3 Be7-d6 f4-f5 Ng6-e7 Qb3-c2 Nf6-d7 Bg5-f4 Bd6xf4 e3xf4
Nd7-f6 g2-g4 h7-h6 Nf3-e5 b7-b6 Qc2-b3) +0.96/19 9} Bd6 {(Be7-d6 Rf1-e1
b7-b5 Nf3-e5 Bc8-b7 Bd3-f5 c6-c5 d4xc5 Bd6xc5 Nc3xb5 a6xb5 Qc2xc5 Ng6xe5
f4xe5 Re8xe5 Qc5xb5 Re5xf5 Bg5xf6 Rf5xf6 Qb5xb7) -0.44/14 4} 18. Ne5
{(Nf3-e5 a6-a5 Rf1-e1 Bd6-e7 Qc2-b3 Ra8-a7 Ne5-f3 Be7-d6 Nf3-e5 Bd6-e7)
+0.96/19 6} Nf8 {(Ng6-f8 Rc1-d1 Nf8-g6 e3-e4 h7-h6 e4xd5 h6xg5 Ne5xf7
Kg8xf7 Bd3xg6+ Kf7-g8 Bg6xe8 Nf6xe8 f4xg5 Qd8xg5 d5xc6 b7xc6) -0.48/11 4}
19. Qb3 {(Qc2-b3 Bd6-e7 Rf1-f3 Ra8-a7 Rf3-f2 Nf8-d7 Bd3-b1 h7-h6 Bg5-h4
Nf6-h5 Bh4xe7 Qd8xe7 Qb3-c2 Nh5-f6 Rf2-f3 g7-g6 e3-e4 d5xe4 Nc3xe4 Nf6-d5)
+1.17/17 15} Be7 {(Bd6-e7 Rc1-e1 Be7-d6 Ne5-g4 Bc8xg4 h3xg4 Ra8-b8 Bg5xf6
Qd8xf6 g4-g5 Qf6-d8) -0.51/11 4} 20. Rfe1 {(Rf1-e1 a6-a5 Bg5-h4 Nf8-g6
Bh4-g5 Ra8-a7 Ne5-f3 Be7-d6 Nf3-e5 Bd6-e7) +0.96/17 6} Ng6 {(Nf8-g6 Ne5-f3
Nf6-h5 Bg5xe7 Ng6xe7 Nc3-a4 Ra8-b8 Na4-c5 Nh5-g3 Nc5xa6 Rb8-a8 Na6-c5
Ne7-g6 Nc5xb7) -0.52/13 4} 21. Na4 {(Nc3-a4 Nf6-d7 Bg5xe7 Re8xe7 Qb3-c2
Re7-e8 Ne5-f3 a6-a5 Qc2-f2 Qd8-f6 f4-f5 Ng6-e7 e3-e4 d5xe4 Bd3xe4 Re8-d8
Qf2-c2 b7-b5 Na4-c3 Nd7-b6 g2-g4 Ne7-d5 Nc3xd5 c6xd5) +1.01/18 6} b5
{(b7-b5 Na4-c5 Ng6xe5 f4xe5 Nf6-d7 Bg5xe7 Qd8xe7 Qb3-c2 Nd7xc5 Qc2xc5
Qe7xc5 Rc1xc5 Bc8-d7 Kg1-f2) -0.55/14 5} 22. Nc5 {(Na4-c5 Ng6xe5 f4xe5
Nf6-d7 Bg5xe7 Qd8xe7 Re1-f1 Nd7xc5 Rc1xc5 Qe7-g5 Rf1-f3 Bc8-d7 Qb3-c2
Qg5-h6 Qc2-f2 Re8-e7 Qf2-g3 Kg8-h8 Rf3-f4 Qh6-h5 Rf4-f1 Qh5-h6 e3-e4 Qh6-d2
e4xd5 Qd2xb2) +1.37/20 4} Nxe5 {(Ng6xe5 f4xe5 Nf6-d7 Bg5xe7 Qd8xe7 Qb3-d1
Nd7xc5 Rc1xc5 Qe7-g5 Rc5xc6 Bc8xh3 Qd1-f3 Bh3-d7 Rc6-c1 Ra8-c8 Rc1xc8
Re8xc8 Qf3xd5) -0.64/17 4} 23. fxe5 {(f4xe5 Nf6-d7 Bg5xe7 Qd8xe7 Re1-f1
Nd7xc5 Rc1xc5 Qe7-g5 Rf1-f3 Bc8-d7 Qb3-c2 Qg5-h5 Qc2-f2 Re8-c8 Qf2-g3
Kg8-h8 Rf3-f1 Bd7-e6 Rf1-c1 a6-a5 Qg3-f2 Be6-d7 Rc1-f1 Qh5-g5 Qf2-f4 Qg5xf4
Rf1xf4 Kh8-g8) +1.33/22 5} Nd7 {(Nf6-d7 Bg5xe7 Qd8xe7 Qb3-d1 Nd7xc5 Rc1xc5
Qe7-g5 Rc5xc6 Bc8xh3 Qd1-f3 Bh3-e6 Qf3-f4 h7-h6 Qf4xg5 h6xg5 Re1-f1 Re8-c8
Rc6-c5 Rc8xc5 d4xc5) -0.60/18 4} 24. Bxe7 {(Bg5xe7 Qd8xe7 Re1-f1 Kg8-h8
Qb3-c2 Nd7xc5 Qc2xc5) +1.53/23 6} Qxe7 {(Qd8xe7 Qb3-d1 Nd7xc5 Rc1xc5 Qe7-g5
Qd1-f3 Bc8-d7 Kg1-h2 h7-h6 e3-e4 Ra8-c8 e4xd5 c6xd5 Re1-f1 Bd7-e6 Qf3-g3
Qg5-d2 b2-b4 Rc8xc5 b4xc5) -0.54/18 4} 25. Rf1 {(Re1-f1 Nd7xc5 Rc1xc5
Qe7-g5 Rf1-f3 Bc8-d7 Rc5-c1 Kg8-h8 Qb3-c2 Bd7-e6 Qc2-c5 a6-a5 Qc5-d6 Qg5-h4
Bd3-f1 Re8-d8 Qd6-c7 Qh4-g5 Rc1xc6 Ra8-c8 Qc7-b6 Rc8xc6 Qb6xc6) +1.33/21 4}
Nxc5 {(Nd7xc5 Rc1xc5 Qe7-g5 Rf1-f3 Bc8-d7 Qb3-d1 Ra8-c8 Qd1-e1 Re8-e7 h3-h4
Qg5-h5 Rc5-c1 c6-c5 e5-e6 Re7xe6 Rc1xc5) -0.42/16 4} 26. Rxc5 {(Rc1xc5
Qe7-g5 Rf1-f3 Bc8-d7 Qb3-c2 Qg5-h5 Qc2-d2 Re8-c8 Rc5-c1 a6-a5 e3-e4 Qh5-h4
Rf3-f4 Qh4-g5 e4xd5 c6xd5 Rc1-f1 Bd7xh3 Bd3xh7+ Kg8-h8 Bh7-d3 Bh3-g4 Qd2-e1
Bg4-h5 Bd3xb5) +1.29/21 5} Qg5 {(Qe7-g5 Rf1-f3) -0.49/15 4} 27. Rf3
{(Rf1-f3 Bc8-d7 Qb3-c2 Qg5-h5 Qc2-d2 Qh5-h4 Rc5-c1 Re8-c8 Qd2-b4 Bd7-e6
Qb4-d6 Rc8-d8 Qd6-c5 Rd8-c8 Rc1-f1 Qh4-g5 Qc5-d6 Kg8-h8 Rf1-c1 Rc8-d8
Qd6-c7 Qg5-h4 Rc1xc6 Qh4-e1+ Bd3-f1 Qe1-d2) +1.45/22 7} Bb7 {(Bc8-b7 Qb3-c2
Qg5-h4 Rf3-f1 Ra8-d8 Qc2-d2 Re8-e7 Rc5-c1 Re7-e8 Qd2-e2 Qh4-g5 Bd3-f5 g7-g6
Bf5-b1 Qg5-g3 Rf1-f6) -0.57/16 5} 28. Rc2 {(Rc5-c2 Qg5-e7 Rc2-f2 Re8-f8
Qb3-c2 h7-h6 Qc2-c3 f7-f6 e5xf6 Rf8xf6 Rf3xf6 g7xf6 Bd3-b1 Ra8-e8 Bb1-g6
Re8-f8 Qc3-d3 Kg8-h8 b2-b4 Bb7-c8 Rf2-c2 Qe7-c7 Rc2-c1 Bc8-e6) +1.57/19 5}
g6 {(g7-g6 Qb3-b4 Ra8-c8 Rc2-c1 h7-h6 b2-b3 Re8-e6 Kg1-h2 Re6-e8 Rf3-f4
Rc8-d8 g2-g3 Rd8-d7 Qb4-d2) -0.46/14 4} 29. Qc3 {(Qb3-c3 Re8-e6 Rc2-f2
Ra8-f8 Rf3-f4 Qg5-e7 b2-b4 f7-f6 e3-e4 Kg8-g7 h3-h4 Kg7-g8 Bd3-c2 Rf8-f7
h4-h5 g6-g5 Rf4-f3 h7-h6 e4xd5 c6xd5) +1.69/19 4} Rac8 {(Ra8-c8 Qc3-b4
Re8-e7 Rc2-c1 Re7-e6 Rf3-f4 h7-h6 Kg1-h2 Re6-e8 Kh2-g1) -0.50/17 5} 30.
Rcf2 {(Rc2-f2 Rc8-c7 b2-b4 Bb7-c8 Qc3-c5 Re8-e7 Rf2-c2 Bc8-b7 g2-g3 Rc7-d7
Rc2-f2 Re7-e8 h3-h4 Qg5-e7 Qc5-b6 Qe7-e6 Kg1-g2 Rd7-e7 Qb6-c5 Qe6-d7 Kg2-g1
Qd7-g4 Qc5-d6 Qg4-e6 Qd6-c5 Qe6-g4) +1.85/22 4} Rc7 {(Rc8-c7 b2-b4 Bb7-c8
Qc3-c5 Bc8-b7 Qc5-d6 Rc7-e7 Qd6-f6 Qg5xf6 Rf3xf6 Re7-d7 Rf2-f1 Kg8-g7
Rf1-c1 h7-h6) -0.43/15 5} 31. Qc5 {(Qc3-c5 Qg5-e7 Qc5-b6 Qe7-d8 Rf3-f6
Rc7-e7 Qb6-c5 Qd8-a5 Qc5-c1 Re8-f8 b2-b4 Qa5-d8 Qc1-c5 Rf8-e8 Rf2-f1 Re7-d7
Bd3-e2 Rd7-e7 Qc5-c2 Re7-c7 Be2-g4 Bb7-c8 Rf6xc6 Rc7xc6 Qc2xc6 Bc8xg4
h3xg4) +1.93/22 12} Rce7 {(Rc7-e7 b2-b4 Re7-c7) -0.52/14 3} 32. b4 {(b2-b4
Re7-c7 Rf3-f4 Bb7-c8 Qc5-b6 Qg5-d8 h3-h4 Bc8-e6 h4-h5 Rc7-c8 Qb6xa6 Qd8-g5
h5xg6 h7xg6 Qa6-a7 Qg5-e7 Qa7-b6 Qe7-c7 Qb6-a6 Qc7-e7 Rf4-f6) +1.93/22 10}
Rc7 {(Re7-c7 Kg1-h2 Rc7-e7 Rf2-f1 Re7-c7 Qc5-d6 Qg5-e7 Rf3-f6 Re8-d8 Qd6xe7
Rc7xe7 Kh2-g3 Kg8-g7) -0.60/17 6} 33. g3 {(g2-g3 Qg5-e7 Qc5-b6 Qe7-d8
Rf3-f6 Rc7-e7 Qb6-c5 a6-a5 e3-e4 Re7-d7 b4xa5 Re8-e7 Kg1-h2 d5xe4 Bd3xe4
Rd7xd4 Be4xc6 Bb7xc6 Qc5xc6 Rd4-d5 Rf6-d6 Rd5xd6 Qc6xd6 Re7-d7 Qd6-b6
Rd7-d3 Qb6xd8+ Rd3xd8) +1.77/22 10} Rce7 {(Rc7-e7 Qc5-c1 Re7-c7 Kg1-g2
Bb7-c8 Rf2-c2 Bc8-d7 e3-e4 Qg5xc1 Rc2xc1 Bd7-e6 Rf3-f6 d5xe4 Bd3xe4 Re8-d8)
-0.34/15 3} 34. Kg2 {(Kg1-g2 Re7-d7 h3-h4 Qg5-e7 Qc5-c3 Qe7-f8 Rf3-f6
Qf8-h6 Rf6-f4 Rd7-e7 Qc3-c5 Re7-d7 Qc5-b6 Qh6-g7 e3-e4 Kg8-h8 Bd3-c2 Rd7-e7
Rf4-f6 Re7-d7 Kg2-g1 Rd7-e7 Bc2-d3) +2.14/20 4} Rc7 {(Re7-c7 Qc5-d6 Rc7-e7
Qd6-f6 Qg5xf6 Rf3xf6 Kg8-g7 Rf2-f1 Re7-d7 Rf1-c1 h7-h6 Rf6-f2 h6-h5 Rf2-f6)
-0.56/17 3} 35. h4 {(h3-h4 Qg5-d8 h4-h5 Bb7-c8 h5xg6 h7xg6 Rf2-f1 Qd8-e7
Qc5-c2 Qe7-g5 Qc2-f2 Re8-e7 Rf3-f6 Bc8-g4 e3-e4 Bg4-e6 Rf1-h1 d5xe4 Bd3xe4
Rc7-c8 Rf6-f4 Be6-g4 Qf2-c2 Bg4-h5 Qc2-c5 Re7-d7 Qc5-c3 Qg5-h6 Be4xc6
Qh6-g5 Rf4-f6) +2.14/19 3} Qg4 {(Qg5-g4 Qc5-d6 Rc7-e7 Qd6-f6 Re7-d7 Rf2-f1
Re8-e6 Qf6-f4 Qg4xf4 Rf3xf4 h7-h5 Rf4-f6 Rd7-e7 Kg2-f3 Bb7-c8 Rf6-f4 Re7-c7
Rf1-c1 Re6-e8) -0.56/19 4} 36. Rf4 {(Rf3-f4 Qg4-e6 Rf4-f6 Qe6-c8 h4-h5
Re8-e6 Rf6-f4 Qc8-f8 Qc5-c1 Qf8-g7 e3-e4 d5xe4 Bd3xe4 Rc7-d7 h5xg6 h7xg6
Qc1-c5 Qg7-f8 Qc5-c3 Qf8-h6 Qc3-b3 Bb7-c8 Rf4-h4 Qh6-g7 Qb3-e3 Kg8-f8
Qe3-c3) +2.38/20 2} Qd1 {(Qg4-d1 Qc5-c3 Qd1-h5 Rf4-f6 Rc7-e7 Bd3-e2 Qh5-h6
Rf2-f1 Re8-f8 Be2-g4 Rf8-d8 e5-e6 f7xe6 Rf6xe6 Rd8-e8 Re6-e5 Kg8-h8)
-0.75/17 6} 37. Qd6 {(Qc5-d6 Rc7-e7 Bd3-e2 Qd1-c1 Be2-g4 c6-c5 b4xc5 Qc1xe3
Bg4-d7 f7-f5 e5xf6/ep Re7-f7 c5-c6 Bb7-c8 Bd7xe8 Qe3xe8 Qd6xd5 Bc8-e6
Qd5-d6 Qe8-c8 d4-d5 Be6-f5 Rf4-b4 h7-h5 Qd6-e5 Bf5-h3+ Kg2-h2) +7.47/17 1}
Rce7 {(Rc7-e7 Bd3-c2 Qd1-e1 Rf4-f3 a6-a5 Rf3xf7 Re7xf7 Rf2xf7 Kg8xf7
Bc2xg6+ h7xg6 Qd6-f6+ Kf7-g8 Qf6xg6+ Kg8-f8 Qg6-f6+ Kf8-g8 Qf6-g6+)
-0.25/15 4} 38. Be2 {(Bd3-e2 Qd1-c1 Be2-g4 a6-a5 Bg4-d7 Bb7-c8 Bd7xc8
Qc1xa3 b4xa5 Qa3xa5 Bc8-d7 Qa5-d8 Bd7xc6 f7-f5 Qd6-c5 b5-b4 Qc5xb4 Re8-f8
Qb4-b5 Re7-e6 Bc6xd5) +8.28/18 1} Qc1 {(Qd1-c1 Be2-g4 Qc1xe3 Bg4-d7 Re7xe5
Rf4xf7 Qe3-e4+ Kg2-h2 Re5-e6 Bd7xe6) -4.61/16 9} 39. Bg4 {(Be2-g4 Qc1xa3
Bg4-d7 Qa3xb4 Qd6xb4 Re7xd7 Rf4-f6 Re8-e7 h4-h5 Rd7-c7 Qb4-d6 Re7-d7 Qd6-c5
Rd7-e7 e5-e6 Bb7-c8 e6xf7+ Re7xf7 h5xg6 Rf7xf6 Rf2xf6) +8.80/18 1} Qxe3
{(Qc1xe3 Bg4-d7 f7-f5 Bd7xe8 Re7xe8 Qd6-d7 Re8-b8 Qd7-c7 Rb8-e8 Qc7xb7
Qe3-c1 Qb7xa6 Qc1-c3 h4-h5 Qc3-c1) -4.92/17 11} 40. Bd7 {(Bg4-d7 Bb7-c8
Bd7xc8 f7-f5 e5xf6/ep Re7-f7 Qd6xc6 Qe3-e1 Bc8xa6 Re8-d8 Ba6xb5 Qe1-e3
Rf2-e2 Qe3xa3 Re2-e8+ Rd8xe8 Qc6xe8+ Rf7-f8 f6-f7+ Kg8-g7 Qe8-e5+ Kg7-h6
Qe5-e7 Kh6-g7 Qe7-f6+ Kg7-h6) +10.34/18 1} f5 {(f7-f5 Bd7xe8 Re7xe8 Qd6-d7
Re8-b8 Qd7-c7 Rb8-f8 Qc7xb7 Qe3xa3 Qb7xc6 Qa3xb4 Qc6xd5+ Kg8-h8 Qd5-e6
a6-a5 Rf2-c2 Qb4-e1 Rc2-c7 a5-a4) -5.08/18 8} 41. Bxe8 {(Bd7xe8 Re7xe8
h4-h5 Qe3xf2+ Rf4xf2 Bb7-c8 h5xg6 h7xg6 Qd6xg6+ Kg8-f8 Qg6xc6 Bc8-e6 Qc6xa6
Be6-d7 Qa6-d6+ Re8-e7 Qd6xd5 Bd7-e6 Qd5xb5 Re7-d7 a3-a4 Kf8-f7 Qb5-b6
Be6-d5+ Kg2-f1 Bd5-e6 a4-a5 Be6-c4+ Kf1-e1 Bc4-e6) +15.87/16 1} Rxe8
{(Re7xe8 Qd6-d7 Re8-b8 Qd7-c7) -5.25/16 3} 42. h5 {(h4-h5 Bb7-c8 h5xg6
Re8-e6 g6xh7+ Kg8xh7 Qd6-c7+ Kh7-g6 Qc7xc8 Re6xe5 d4xe5 Qe3xe5 Qc8-g8+
Qe5-g7 Qg8-e8+ Qg7-f7 Rf4-g4+ Kg6-f6 Rf2xf5+ Kf6xf5 Rg4-f4+ Kf5-g5 Qe8xf7
Kg5-h6 Qf7-f6+ Kh6-h5 Qf6xc6) +20.76/16 1} Bc8 {(Bb7-c8 h5xg6 Bc8-e6 Qd6xc6
Re8-e7 Qc6-a8+ Kg8-g7 Qa8-d8 Re7-f7 g6xf7 Be6xf7 Rf4xf5 Qe3-e4+ Kg2-h2
Bf7-g8) -9.78/13 8} 43. hxg6 {(h5xg6 Qe3-e4+ Rf4xe4 d5xe4 Qd6xc6 Re8-f8
e5-e6 Kg8-g7 e6-e7 Rf8-g8 e7-e8Q Rg8xe8 Qc6xe8 h7xg6 Qe8xc8 Kg7-h7 Rf2-c2
f5-f4 g3xf4 g6-g5 Qc8-d7+ Kh7-g6 Rc2-c6+) +95.42/18 20} Qxf4 {(Qe3xf4
Rf2xf4 Bc8-e6 Qd6xc6 Re8-e7 Rf4-h4 Kg8-h8 g6xh7 Re7xh7 Rh4xh7+ Kh8xh7
Qc6xe6 Kh7-g7 Qe6xa6 Kg7-h7 Qa6xb5) -13.43/15 8} 44. Rxf4 {(Rf2xf4 Bc8-e6
Qd6xc6 Re8-e7 Qc6-a8+ Kg8-g7 g6xh7 Kg7xh7 Qa8-f8 Be6-f7 Rf4-h4+ Bf7-h5
Qf8xe7+ Kh7-g8 Rh4xh5 f5-f4 Rh5-g5+ Kg8-h8 Qe7-g7+) +M10/16 1} Be6 {(Bc8-e6
Qd6xc6 Kg8-f8 g6xh7 Kf8-e7 Qc6xe8+ Ke7xe8 Rf4-h4 Ke8-d7 h7-h8Q Kd7-c7
Rh4-h7+ Be6-d7 Qh8-a8 f5-f4 Qa8-a7+ Kc7-c6 Qa7xd7+ Kc6-b6 Qd7-e6+) -M10/16
7 Arena Adjudication} 1-0[/pgn]