For amateurs to become better chess players, they: * Learn basic endings like KKR * Review their tournament length games for where they made sub-par moves *

For amateurs to become better chess players, they: * Learn basic endings like KKR * Review their tournament length games for where they made sub-par moves * Learn tactics like pin and fork * Replay grandmaster games * Do two to mate chess problems, and other such problems * Learn strategies like best placement of pieces, proper pawn structure etc. * Learn openings (when one is more advanced) Some of these can be reasoned out or explained step-by-step. Some can not - like doing chess problems. How does that make one a better player? In some ways it does not make sense, but in some ways it does - after doing many chess problems, I start "seeing" two to mates when they appear on the board, whereas I may have missed them before. When you do dozens, or hundreds, or thousands (Polgar book) of these two to mate problems, and redo them until you can see two to mates within seconds, your brain gets good at pattern matching, and you become more adept at seeing two to mates when they appear on the board during games. One interesting thing is the first time you see a two-to-mate, it may take a few minutes, maybe even 20 minutes to find it. After subsequent review it may take a few seconds. Do this thousands of times, and it shifts from rational analysis to pattern matching.