The Exchange Sacrifice

Petrosian:

The exchange sacrifice (provided it is a real sacrifice) belongs to the complicated weapons. It occurs in games by players of various strength. My opinion is that the main problem, when one makes such a decision, is first of all of a psychological character. Our knowledge of the relative strength of chess pieces is acquired at our very first steps in chess. A beginner is taught during his very first lessons that the strength of pieces is measured by Pawns.

When a player makes his choice [of move] this involuntary knowledge reduces his vision; he mechanically rejects moves which put a stronger piece under the attack of a weaker one. This is the greatest psychological difficulty in the course of a chess game. - Petrosian's Legacy, p.68

Kasparov:

A key role in the reconsideration of the limits of the possible employment of the exchange sacrifice was played by Petrosian. Many made sacrifices -- one can name a whole galaxy of brilliant masters who have demonstrated the triumph of mind over matter. For example, Alekhine and Tal had a highly creative approach to the evaluation of the comparative strength of pieces on the board. But the combinations of Alekhine and Tal are usually associated with the rapid development of the initiative or a direct attack on the King.

Petrosian introduced the exchange sacrifice for the sake of 'quality of position', where the time factor, which is so important in the play of Alekhine and Tal, plays hardly any role. Even today, very few players can operate confidently at the board with such abstract concepts. Before Petrosian no one had studied this. By sacrificing the exchange 'just like that', for certain long term advantages, in positions with disrupted material balance, he discovered latent resources that few were capable of seeing and properly evaluating. - My Great Predecessors III, p.12

Both comments were made in the respective introductions to Reshevsky - Petrosian, 1953 Zurich Candidates Tournament.