"Equal trades of pieces" are not inherently equal.
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This is a pretty simple tip, much simpler than it sounds, that should be able to get you at least a few comebacks and simple victories.
Learn to recognize when a piece is good (powerful) or bad (weak), and NEVER trade a "good" piece for a "bad" (or...less good) one.
This game is a good showing of that (see move 13). Also a good showing of what is perhaps the worst move I've ever seen, though that's unrelated.