"Morozevich is a bright player; I like how he plays. This is active chess: only forward! Sometimes luck is on his side, sometimes it is not. It is not boring to watch his games." – Kramnik

Mathematical precision is not something to be scorned and is not incompatible with either the human element nor art. It is a form of beauty all on its own. And computer evaluations not only don't destroy the human ability to understand pragmatism under the stress of completion but can actually enhance our admiration for those who are able to come oh so close to perfection under difficult circumstances. At least it does to some of us. As far as using computers, I find that it has increased and not diminished my ability to calculate. Perhaps it’s the poor use of computers that has caused the contrary. One should learn to properly use the tools available before criticizing them.

<Once> a game of chess has been played, it changes status. It stops being a struggle between two people and becomes public property. Then it's perfectly legitimate to analyse it, discuss it, find better moves.

It's the same for a work of art - a painting, a book, a film. Once it is out there, the public will take over ownership of it. They will form theories about it, discuss it, may even write a sequel or two.

George Lucas doesn't seem to understand this when he constantly changes the storyline to star wars. Han shot first - that belongs to the fans now. And no amount of fancy editing in the later versions will change that.

And, as you say, there is nothing wrong with using computers as tools to aid our analysis of a chess game.

What I object to is the use of computers to criticise someone who did not have the benefit of computers at the time. In objective terms 32...d2 is a better move than 32....0-0-0 because it wins more material and mates more quickly.

But I still maintain that 32....0-0-0 is a more pragmatic move to play OTB. Its gains might not be as great as 32...d2, but it needs less calculation. And what we don't know is how much time Moro had to make that move.

And if we want to learn and improve our own play, it sometimes pays to try to understand why a strong player didn't play a move that the computer recommends.

When i went through the game, on move 32 I just spotted the move d2 in a second, thinking why Moro didn't play it, and then took another about 15 seconds to calculate that it was completely safe and couldn't harm his king before he mates him (with his two (or one) queens).

There is one group of people who think that GMs should always play the objectively best move and that we can criticise them if they don't. Then there is another group of people who think that GMs should play a reasonable second best move if it is a pragmatic choice.

Then there are a couple of side issues to spice things up. Some folk don't like computers. And some folk don't like it when we are a little too free with our criticisms of players who are much stronger than we are.

So when you asked your interesting question you sparked off a few of these old debates. Nothing directed at you, just unfinished business.

There's another point here. One of the raison-d'etres of this site is that we want to learn and improve our play. So when someone with the strength of Moro passes over 32...d2 (which I am sure he would have seen) and plays 32...0-0-0 instead, we really ought to ask why.

So do I but only to a point.

<...And, as you say, there is nothing wrong with using computers as tools to aid our analysis of a chess game...>

I agree with both of you on this though I don't use one.

<...What I object to is the use of computers to criticise someone who did not have the benefit of computers at the time...>

This is where I also have a problem, I see kibitzers that tear strong GMs to pieces on different pages and it's almost funny because somebody like me (that actually managed to draw with and beat some GMs in active play) can't touch these players overall.

<...I don't subscribe to the school of thought which says that computers are bad. But nor do I believe that we should slavishly trust in them. We need to think for ourselves, using computers where they are heplful.>

<: Instead of 32...0-0-0, why black didn't play d2? It seems even more efficient, and still safe for his king.>

To which <Once> replied: <Probably because Moro isn't a computer.> and goes on to discuss the human elements of chess, like a ticking clock, issues of clear calculation, an easy calculated win (which conserves energy over long tournaments, or at least allows one to enjoy winning a won game without losing your mind)... His response was by and large as perfect as could be. No insults, just strong reasons why a super-GM would take an easier/slower win than a quicker/harder-to-calculate win.

Post match analysis - with or without computers - will often unearth better moves than those played. Incidentally, that's one of the reasons that prevents me from posting any of my feeble OTB efforts on this or any other site!

And this searching for truth is a good thing. It helps us all to learn and gets us closer to "chess truth" about a position and a game.

But when we find something that was missed OTB we should really resist the temptation to think (or claim) that we are better than the players or that they were eejits for not spotting it. We operate in a very different environment to the players.

So I'm cool with spotting and pointing out the improvements. I'm also comfortable with the sensible use of computers. It's what <King Death> calls monday morning quarterbacks (lovely phrase!) that I feel uneasy.

You have a good point there. Those of us that are old enough to remember life prior to ubiquitous electronic calculators are probably not nearly as good now with simple arithmetic as we were before the advent of calculators. The same may happen with chess engines. I know that I am often reluctant to trust my instincts and calculations until I've checked them out with a computer but in my case that lack of confidence is well founded since I am not, never was, and never will be a strong player. So for me using computers to provide meaningful analysis (at least I hope that some of them are meaningful!) is a necessity and not a choice. I envy strong players like yourself and others on this site who are capable of providing insightful analysis without the help of computers.

But I think that using computers and reviewing their analyses in detail has actually improved my chess capabilities since I come up with ideas based on my human evaluation of the resulting positions and more and more often (although, alas, not too often) I find that my ideas turn out to be correct. So maybe (hopefully) your fears are unfounded. And, equally hopefully, my perception of my improved chess capabilities is not unfounded.

Let's also remember that use of computers to analyze chess is a relatively new phenomenon since only until fairly recently have sufficiently powerful computers and sufficiently capable chess engines been available at a reasonable price to the chess playing masses. I suspect that we are a long way from figuring out the best way to use computers in this task and hopefully we will do that without reducing our ability to work things out for ourselves.

Chess is finite game. The number of moves of any game is finite. So you can, in principle, check out for yourself if a given move can force a win or not. If the position is such that there is no way to force a win, then there is no intrinsic advantage to the move the computer suggests. (Remember the computer evaluates on the basis of an evaluation function that is defined by the programmer, a man. Its parametrization comes from our chess lore and the practical experience programming chess engines the programmer may have.)

My answer to your first question is "Not Necessarily". A lot depends on the chess engine used, the depth that it was allowed to search, and the "cleverness" of the engine's heuristics in selecting which branches of the search tree it searches. And, regardless of the circumstances, any engine is quite capable of making mistakes.

Chess engines are different and some are simply better than others in evaluating the position resulting from the candidate moves they investigate. All things being equal, the deeper an engine is allowed to search the more confident we should be that it will find the "best" move since it will have looked at more potential positions. But all things are never equal. No chess engine, regardless of how powerful a computer it runs in, can look at all the moves in its search tree at the depth required to establish confidence in its evaluation in a reasonable amount of time. So engines restrict (prune) the branches of the search tree that they look at in depth according to some heuristics (a.k.a. "guesses"). The more aggressive an engine prunes its search tree, the deeper it can search in the same amount of time (and therefore increase our confidence in its final evaluation of the position). But at the same time it increases the chances the branch of their search tree that contains the "best" move will not be looked at, so the quality of its search depends on the quality of its "guesses". So search engine developers must perform a number of tradeoffs and determine what approaches work best in the majority of positions.

Oh, yes, the majority of positions. Chess engines currently tend to excel in tactically complex open and semi-open positions, and they tend to do less well in strategically complex closed positions and endgames. To make it even harder to generalize, if two engines are used to analyze a position, the first one might find the "best" move and the second one may not. And, if they are given a different position to analyze, the second engine may find the "best" move and the first one may not. So whenever possible, I try to analyze a position using at least 3 different engines, and average their evaluations to reduce one engine's possible evaluation bias.

To try to answer your second and third questions, IMO the "best" move is the one that will cause the player on the move to reach the position's most likely conclusion in the smallest number of moves. I phrased my answer that way because as you pointed out in some positions a win can be demonstrated, in some positions a win is likely but not capable of being demonstrated, and some positions are just dead drawn and it's not reasonable to downgrade a human or a computer for their inability to find a winning move in that position, assuming equally good play from their opponent.

But I'm not really satisfied with that definition myself. If two moves give the same result, but one of the moves causes that result to be delayed one or more moves, is it proper to consider one move "better" than the other? After all, the end result was the same. And, if you enjoy making your opponent suffer (yes, there are some chess-playing sadists out there), you might even be able to argue that the move that prolongs the inevitable result the longest is the "best" move.

As you also pointed out the criteria for determining the "best" move can also include esthetics And as <Once> pointed out, the criteria can also include practicality. So Morozevich's 32...0-0-0 was arguably better practically than 32...d2 even though the latter may have lead to a win in a smaller number of moves. Not implying at all that Morozevich might have a sadistic streak in him; no, not at all. He was just being practical.

And what about a player who in a lost position plays a move that leads to complications that are the most likely to lead his opponent astray even though it's not the "best" move in the sense that the "best" move would delay the otherwise inevitable loss the longest (the flip side of my definition of "best" move)? Kind of like the horizon effect affecting chess engines. And what if as a result of that less than "best" move one's opponent goes astray and a certain loss is transformed into a draw or even a win? Who would then argue that the move actually played wasn't "better" than the objectively "best" move?

There is more than one game of chess. First and (probably) foremost there is the struggle. Two people over the board trying to beat each other. And here the best move is the one that wins. That might not be the absolute best move in theoretical terms. But chess is a struggle, a fight, a sport.

If you are winning, keep it simple. If you are losing, look for ways to complicate. And don't care too much about the "best" move.