How do you 'calculate' compensation in chess

Question

Here is another very difficult subject for me that I can't even begin to understand [ incidentally, although I've been playing chess for over 50 years, my current ELO rating is only 1300, hence these questions.]

The idea of 'compensation' comes up all the time in master games.

• How do you calculate it?
• It seems to be a comparison between material and position. But what positional element is the material equivalent of a pawn; the exchange; a piece; even the queen?
• Can the idea of compensation even be adequately quantified at all?
  Given a position where, for example, one player sacrify a pawn to improve the position of a knight, would two GM's, say, Carlson and Giri, even agree as to whether the player has adequate compensation for the pawn, given their vastly different playing styles?

Answer 1

Introduction:

Your goal in the chess game, is to win. Having more points is good, only when it helps you win the game (e.g. check-mate your opponent) If sacrificing material improve your chances to win the game, then it is the right thing to do.

Compensation in Wikipedia

Compensation includes:

• Better pawn structure.
• The "two bishops", which refers to having bishops of both colors while your opponent does not. Almost all modern players consider having both bishops as an advantage, although historically there has been great debate as to how much of an advantage they constitute. The two bishops are most likely to show their power in the endgame.
• Better piece activity and/or better development (common in gambits).
• Having the enemy king open to future attack, either due to a loss of pawn cover or being trapped in the center of the board is often excellent compensation.
• Passed pawns are often decisive in the endgame.
• Connected and/or protected passed pawns are even more deadly.
• Control over key squares, diagonals, files, or ranks.

Summary:

There are several types of compensation.
The answer to Is the sacrifice worth the compensation? might depend on two factors:

• Is the compensation very straight forwards? (if so - it is clear to be good)
• The specific player profile (e.g. some players prefer open positions, and some closed positions) - if the new position after the sacrifice will be more suitable for the player - he'll have clear plan how to continue/win