Compensation in chess

As a lowly [and very weak] club player [elo 1300---and that's on a good day!], one of the many areas of chess that I find baffling is the idea of 'compensation'. How can you quantify a positional advantage? What, for example, would be good positional compensation for a pawn; or the exchange; or a minor piece; or a rook? Presumably, the only acceptable compensation of the queen is the win of the game.

Can anyone enlighten me?

Many thanks

Dave H

You can't quantify it, it's more like intuition based on experience (trial, error, reading, analyzing). In close cases, even very strong players can disagree about whether or not there is compensation. Unsurprisingly engines can get it wrong too.

Starting with the basics though, I suppose it's worth mentioning a rule of thumb for the opening that a tempo is worth 1/3rd of a pawn. So if you sacrifice a pawn in the opening, but you have 2 or 3 more pieces developed than the opponent, then in most cases that's fine.

Other elements that compensate for material could be e.g. piece activity, king safety, and initiative.

One way you might think about it, is asking why is a queen worth more than a rook? Why is a rook worth more than a knight? Their values of attack and defense are the same (they can only capture one piece per move just like any other piece). The value comes from mobility and the number of squares a piece can control. A highly mobile piece like the queen, that can control many squares, has a higher probability of being useful, creating tactics, defending key squares, etc. So if you lose a rook... but your rook was stuck in a corner, you didn't really lose 5 points of material... at least not in the short term. If the game had gone on for 50 moves, sure, that rook would have probably been worth every bit of 5. But in the short term it can be as if you lost nothing... as long as your remaining pieces are more active than the opponent's then you have compensation. That's another basic idea.

Way to general of a statement.

Compensation for something big like a whole bishop or knight is rare. Compensation for a pawn happens all the time, at least in calculation (and so the player chooses not to win the pawn for now).

Compensation for a knight or a bishop isn't that rare really. It does happen all the time - for example during an attack where the opponent is cramped and can't get his pieces to defend, or when the King's pawn cover is compromised and the king is unsafe. Yet another option is in cases which involve a far-advanced pawn (or several!) - or where an advantage in development is really overwhelming. 

All of these cases presuppose that you don't have an immediately forced way to recover the material or do more damage - but unforced play can continue for quite a while with one player having more than full compensation for a whole piece - In many cases also a whole rook (for example, the knight captured it in the corner and part of the compensation is that it isn't clear if the knight can get out - or if the knight even has the time to get out of the corner, and may be captured back, together with some pawns at least). 

What is rare, is when the presence of several advanced pawns, combined with mating threats, provide compensation for a queen - or more! There are some brilliant examples of that happening, including from the 19th century...

Those are great examples of positional compensation that don't involve forcing moves. I probably shouldn't have said "rare."

Probably not... :-) And this is why we love chess - when "other considerations", that elusive, mysterious - even scary concept triumphs over raw materials. 

One can imagine an attack raging on, when some "piles of raw materials" lie gracelessly at some neglected corner of the chess board...

It is possible to have compensation for a full queen if your pieces are extremely developed (and all your opponent's pieces are stuck on the back rank), your opponent's king is under brutal attack (even if there is no short forced combination present yet), and  you also have some other major positional advantage (e.g., advanced or connected passed pawns, huge space advantage). (This type of compensation is not likely to happen in a real game.) For a piece or a rook, you need a bit less compensation than that.

I like compensation from forced lines.  I.e., concrete return.  Either mate or eventual surplus of material won for my "fake" sacrifice.

A material sacrifice for an aggressive positional advantage?  That's Tal magic.

I'm afraid that if I were to try it, my opponent would keep the booty and slowly neutralize, and then I lose from an over-optimistic assessment of my chances.

Of course a positional advantage can be quantified; any engine will do that when sacrificing material. For humans it's not so easy. I'm afraid that it depends very much on the given position and there are no abstract rules available. I suppose it's mainly intuition gained by experience (but I'm not a strong player. For a master it may be different.)

I once sacrificed a knight in a tournament for fun, but with some (insufficient) compensation. However, I soon brought my pawns to the centre, and with five Black pawns storming down the centre, the pawn mass was very deadly. My opponent had underestimated the pawns earlier.

Never did I expect my opponent to sacrifice back a piece to destroy my pawn masses.

That game eventually resulted in a draw.