THEMATIC CHESS TRAININGBOOK 8 - POSITIONAL SACRIFICESUnlike tactical sacrifices, so-called positional sacrifices are an investment of material that usually doesn't bring immediate benefits but translates into certain positional advantages whose fruits 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 enabling a square as a strong point, displacing the opponent's pawn structure or creating some kind of weakness in the enemy position.The student should bear in mind that, when solving the exercises, they are not asked to decipher all the moves in the game or position (which are sometimes included until the end, for documentation purposes), but only those that, say, lead to an advantage for one side or to equality when it comes to saving an inferior position. There are exceptions (and here the guidance of an instructor or the student's own common sense is important), because if the first move or two produce such a judgment, the solver can be expected to come up with additional concrete lines that enrich the solution. Chess is not a mathematical science and allows for a variety of interpretations.Only one formula is known for progressing in chess: play as many games as possible, together with theoretical study and analysis of the games themselves. The ideal complement to this formula is, as many great masters recommend, for the player to develop and perfect their tactical and strategic skills by solving numerous exercises, specially selected for their usefulness. Like the ones we offer here