Practical Chess Notebooks 8: Positional Sacrifices
 Unlike tactical sacrifices, so-called positional sacrifices are an investment of material that does not usually bring immediate benefits, but which translates into certain positional advantages that the player will reap in the medium or long term, and which are based more on positional factors than on a combinatorial sequence. These factors can be the qualification of a square as a strong point, the displacement of the opponent's pawn structure or the creation of some kind of weakness in the enemy's position. When solving the exercises, the student is not asked to decipher all the moves of the game or the position (which are sometimes included until the end for documentation purposes), but only those that, for example, lead to an advantage for one of the sides or to equality, when it is a question of saving an inferior position. There are exceptions (and here the guidance of an instructor or the common sense of the student himself is important), because if the first one or two moves produce such a judgment, it is to be expected that the solver will present additional concrete lines that enrich the solution. Chess is not a mathematical science and allows for a variety of interpretations. To progress in chess, there is only one formula: participate in as many tournaments as possible, along with theoretical study and analysis of the games themselves. The ideal complement to this formula is, as many Grandmasters recommend, for the player to develop and perfect his tactical and strategic skills by solving numerous exercises, specially selected for their usefulness. Like the ones we offer you here.