Today’s column is about sacrifices and the exchange in particular. If you’re shown a chess position cold, then the first thing you do normally is to count the pieces just to check that the material is fairly balanced. But the relative activity is at least as important. The “joy of innumeracy” might turn out to be a valuable (in)ability in many chess positions! | Pictured: Lu Miaoyi at the 2023 Rapid and Blitz World Championships. | Photo: Lennart Ootes