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  3. i don't understand a move...

After move 13 Na3 from white, i don't understand the computer suggestion and analysis (for Black). The computer suggests Nxe4... and i've tried to see what it meant but i still haven't got a clue. I've tried to count material being exchanged after the "good" move. Black is exchanging a knight and a rook for 2 pawns and a knight?
Could you have a look?

This one is tricky because it's a material sacrifice in order to get a massive attack against the white king. The computer is suggesting Nxe4 as a way to reveal the possibility of Rxf3. So Nxe4, dxe4, Rxf3, gxf3, followed by Qh4. Black's queen and bishop are focused on f2, white's kingside pawns are shattered, and the black rook is coming to f8. Meanwhile, all of white's pieces are huddled on the queenside doing nothing to defend.

These kinds of sacrifices are hard to see because you have to have a strong intuition that the attack will succeed - otherwise you're busted because you are down too much material.

Just look at the few sequences that engine offer (~10 moves further). White will need to give material back to avoid mate.

Thanks, that a lot clearer! How can we train such an intuition?

Wow, that's a great move. And people somehow claim that AlphaZero is the first engine to play entertaining chess, just look at variations like that!

It seems strange that Black has enough considering he only has a Bishop and then a Queen for attack (and White can even trade the bishops later). However Whites pieces are so misplaced that they can't actually prevent the black queen from taking the entire king side and then even bringing his knight exploiting a pin. Here's some sample variation:

Thanks BOT ! :)

this kind of move is typical brute force engine move ,i doubt that even Carlsen would play this way.

Fischer and Kasparov found far more difficult attacking moves. Even if you do not find 13...Nxe4!!, then it is easy to see that 13...Nd7? is a mistake as it loses central pawn d5.

I mean, seeing that Nxe4 followed by Rxf3 is an idea is not THAT difficult to see.
However it's not obvious at all why that is so good for Black. I could see myself trying this if I wanted a perpetual or so, but seeing that one just wins in the long run is beyond me. (without looking at the engine line of course) After all Black kinda only has two attacking pieces. If there's something I learned when playing chess is that two pieces are pretty much never enough to checkmate. However here Whites pieces are so awkwardly placed that it somehow just works out.

It is not just 2 pieces Ba7 and Qh4, also Ra8-f8 is ready to join the attack on the exposed king. It is hard to calculate to the end, but it is possible to sacrifice based on intuition, i.e. judging compensation sufficient.

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