Help understanding engine evaluation in a position.

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JayeshSinhaChess
 
 This is the final position from a game I played recently. 3I0 blitz. The opponent resigned and to be fair the position does look crushing. That being said I still think the opponent could have played on.
 
I put this in the engine and it evaluates the final position at around -3.18. However I wanted to see what the continuation would have been, as even though the position seems to be crushing, I don't see a clear win.
 
The engine suggests Kf1 as the move for White, which seems obvious. However then I would personally have played Qd5. The evaluation at point dips to 2.63.
 
The engine suggests Qg6 for black and the evaluation jumps to nearly 3.7
 
So why is Qg6 objectively such a good move, so much better than Qd5. I am sure GMs would have found Qg6, but why? Qg6 seems a counter intuitive move, as it takes the queen away from where the bluk of the action is taking place.
 
So what is the thought process you have to go through to find Qg6. What are you looking for. In that position what are the tick boxes that you look to fill before settling on a move and which of those conditions does Qg6 achieve and Qd5 fails.
SmithyQ

 Not only is Black a pawn up, he has a massive activity advantage and White's King is now misplaced on f1.  Black should strive to maximize his activity and generate further attacking chances, which means keeping the Queens on.

Qd5 is a fine move, but after say Nc4, Black either needs to move his Queen again to avoid a Queen trade, costing a tempo, or allow a Queen trade, reducing his attacking chances.  White can also trade the strong Bishop on d6 if Black aims to keep Queens on.  Still a much better position for Black, but compared to one move earlier, likely better for White.

That said, Qg6 does not jump out as a super-obvious move, and I'm not sure nitpicking over Qd5 or Qg6 is an efficient use of time in game.  A won game is a won game, whether it's +3 or +2.5, and computers often prefer tactical, complex positions when a simpler continuation is less 'optimal' but much simpler to win (ie, it might 20 extra moves in the endgame, but you are up a piece so it is 20 easy moves to find).  Trading Queens in a pawn-up endgame with almost no counterplay for White is not the worst decision in the world.  That's my quick take at least.

JayeshSinhaChess

You call it nitpicking but in those numbers somewhere lies the whole essence of chess. You do 2 moves which are okay instead of great and an engine crushes you.

SmithyQ

The higher the evaluation goes, though, the less practical it becomes.  An engine may evaluate a very tricky Queen endgame as +12 because it can expertly calculate all the checks and avoid perpetual checks while evaluating a Queen trade as only +2 because the opponent can resist mate for 20 moves … but it’s a trivial pawn ending.  Practically speaking, it makes no sense to prefer the Queen endgame, even if the comp calls trading Queens a ‘blunder’. 

When the evaluation is tighter, differences matter.  When the game is completely one-sided, they matter much less.  Or, said another way, I’m far more critical of my play and my accuracy when the game is undecided than when one side has a huge advantage.

It's also possible in the position you posted there's a hidden tactic that Qg6 exposes that I simply do not see. 

MitSud
I reckon what SmithyQ said before is correct, Qg6 continued the attack better than Qd5 and the engine just prefers to continue its attack wether you can trade queen into a better position or not. Maybe it calculated some attacking line where you can be guaranteed of winning at lead another pawn or a piece, engines like their material.
MitSud
That said I don’t think the engine eval matters that much to players of our level, it can help us with tactics we missed through the game, but not our understanding of the game, that’s where finding a stronger player is helpful (to analyse with), I’ve only been playing chess seriously for under a year, and the engine has not been useful at this beginner - intermediate level.
JayeshSinhaChess

No I agree that when I am up 5 pieces, what does it matter if I blunder 2 of them. Still an easy win 3 pieces up.

 

However in the OP, the position is crushing, but there is no clear win. Make two moves that seem reasonable and suddenly the evaluation has changed from -3 to -1.5, and its game on again. Its about finding bulls' eye with every move and GMs and engines do that. I am sure a gm would have found Qg6 in the position.

Clavius

I checked a few lines with Stockfish8.  Black has a strong attack but is only one pawn up so unless the follow-up is strong white could conceivably untangle his pieces and fight for a draw. The three best lines for Black after 12.Kf1 are not decisively different from each other.  The strength of 12...Qg6 appears to lie in keeping the queen away from harassment by white's minor pieces while putting some pressure on the g-file.  Also worth noting is the move 8...Qxg2.  Well played game on your part though white resigned too easily.