An absolutely incredible engine game!

Today I'm showing you a game played between Leela Chess Zero against itself, but restricted to 200 nodes (half-moves) of analysis per player. Another way of saying it is that Leela cannot calculate more than 200 positions in total for both players. This means that in order for a side to win, it must outcalculate the incredible BT4 network, which is considered to be the best network right now.

If you guys are new here, LeelaChessZero is a network designed to emulate the play of Alphazero. Both Leela and Alphazero calculate only a few thousand or, on stronger hardware, a few million nodes (a node basically means a position or a half-move) at most, whereas Stockfish and many other engines prefer to calculate many millions/billions of nodes per second. Think of stockfish as a calculating beast, whereas Leela understands what to calculate. This understanding is both an asset and a hindrance. Some chess moves are just so unintuitive for Leela that it gets missed, and sometimes the position is so deep Stockfish cannot calculate far enough because of lack of understanding. Leela's network is basically its brain, which tries to find out the best possible move using a search algorithm called Monte Carlo tree search.

The game started from a so-called setup opening (I forced them to play the Italian game). They did not really have a choice, but 1 e4 e5 2 Nf3 Nc6 3 Bc4 was the opening I chose.

When I played Leela with just 10 nodes vs. itself, it started to just play the same line/game over and over. At that point I learned that it's absolutely necessary to put in something called temperature. This means Leela won't always pick the best move (for the first 10 moves) to stop playing the same exact game over and over again. 

The game continued with Bc5 a4 a5 h3 d6

One thing I have learned about such structures is that this a4/a5 benefits Black more. This is because if White somehow gets in c3-d4, Black can sometimes take on d4, and if cxd4 gets an outpost on b4. At the same time though, White might get a massive center.

7 0-0 h6 8 c3 Qf6!?

From this point, both sides have been moving their pawns more than their pieces (odd, but the moves are understandable). Now Black decided to play Qf6 and h6 (stopping Bg5), trying to control the d4 pawn break. Somehow, my engines are saying White can actually play d4 anyway, but Leela opts for another move.

Na3 

Leela wants to go Nb5 and d4, so Black decides to immediately chop off the knight with the bishop.

Bxa3 Rxa3 Qg6 threatening h3 and e4, you cannot protect both, so 10 Kh2 Qxe4 11 d4!

Suddenly Whites' threats are very real. Black has an exposed queen in the center and Blacks central pawns are now big weaknesses. White is not winning, somehow, but will easily win back the pawn with moves like Re1 and Bb5. 

Qf5! 12 Bb5 Bd7 13 Re1 Nge7 14 dxe5 dxe5

15 Bd3 Qf6 16. b4!

Leela "sacrifices" a pawn, although it's more of a distraction tactic to distract Black from the defense of e5. According to Stockfish at high depth, White should have played b4 instead of Bd3 because Black in this case can defend with Qd6!

Qd6! 17 Kg1!

Black threatened to go e4+

Bf5 18 Bxf5 Nxf5 19 b5 Qxd1 20 Qxd1 Nd8 (perhaps Rd8! was better) 21 Nxe5

White has a big initiative in the center with the rook and knight. c4 and Rad3 come to (my) mind, with an infiltration on d7. Perhaps White threatens to go Rd7 with a fork.

Ne6! 

Apparently the point of Ne6 is not to defend the c7 pawn against a rook infiltration but to meet g4 with Nd6 b6 0-0-0!

Ra2 (threat of Ba3) 0-0! Ba3 Rfd8

It seems Black has actually defended quite well. He has the open file and is very solid. It doesn't seem like the imbalances are the ones that tip this game into victory for one of the players; instead, it's probably going to be an endgame blunder!

Rad2! (Keeping control of the file) Rxd2 Rxd2 f6?! (Apparently Nd6 sacrificing a pawn was better?) Nc4

To me it seems like Black's position is very solid, although the engines give this as +0.8 for White. I guess that a5 is somewhat hanging in this position, so the next move is obvious but does leave weaknesses behind.

b6 27 Rd7 Rd8 28 Rxd8 Nxd8. White lost the advantage; instead of Rd7, White should have played Rd5, but there the situation would have still been complicated.

How do you play this endgame? Black has a great weakness on c7, so I'm thinking of Bc1 Bf4 or Ne3 Nd5. White also has weaknesses on c3 and a4, but here White has better piece activity to attack Black's pawns than Black has to attack White's pawns. 

g4 Nh4 Ne3! blacks c7 pawn is targeted with nd5 perhaps. Ne6 Nd5 Ng6 

Black probably wants Kf7 and Ne7

Kf1 Kf7 c4?! White pushes but allows Ne5:

Ne5!

Now the position becomes quite wild. White's c4 is hanging and must push to c5 to weaken Black's pawn structure, but Black has a hidden countershot here! Can you find it?

c5 Nc4! cxb6!! cxb6 Bc1

White is going defenseive. Bc1 is passive and White must defend a4 too.

Nc3 Nd3! Be3 Nxe3 fxe3

In this endgame, Black has a weakness on b6, but after Ke6, Nc5, or Nb2, Nd5 isn't, let's say, effective.

Ke6 Ke2 Nc5

This position is actually completely lost for White. White's knight must sit passively to constantly defend the a4 pawn, and eventually White will be in a zugzwang, a compulsion to move, where every move you can make worsens your position.

41 e4 Ke5 42 Ke3 g5! White is in zugzwang! 

43 Nd5 Nxa4 44 Kd3 Kc5+ 45 Kc4 Nd7 46 Nc3

...a4! distracting the knight! Black has the b6 pawn defended, and White is losing!

47 Nxa4 Kxe4 48 Nc3+ Ke5 (stopping white from playing Kd5) 49 Nd5

Black is almost in zugzwang too! But black is still winning with the extra kingside pawn:

f5! gxf5 Kxf5 Kd4 h5!

Ke3 Ke5! Ne7 Nf6 Nc8 Nd5+ Kf3 Kd4

Black puts his pawns on h5 and g5, where they cannot be touched by the White king, and prepares to take the b5 pawn next. If White ever plays h4, it's met by g4!, where Black's knight controls the f4 square.

Nd6 Nf6! (not Kc5 Ne4+) Nf7 Nh7 

Black just defends the pawn: the b5 pawn is going to be very easy to target!

Nd6 Kc5 Nc8 Kxb5 Ke4 Kc5 Nxb6? (Black is desperate, but two pawns and a knight vs. a pawn is very lost! Kxb6 Kf5 

h4 Kg6 g4 and White lost in a few moves.

What does this game show, you might be asking? Well, my favorite thing this game shows is that Leela is really good at understanding the position, but with restraints on how much it can calculate, you can often get tactical masterpieces as the winning moves are unintuitive to find (or require deeper calculation).

I will definitely post more of these kinds of blog posts! If you liked it, please make sure to like the blog post so I'll get more motivated to continue! Bye for now.