Student: What is the winning technique with an extra piece? Teacher: The same as it is in most instances when you’re ahead in material: exchange pieces and avoid complications. This emphasizes your advantage because if you trade efficiently unit for unit, your extra piece is likely to be the only meaningful survivor. Your extra thing will then be able to steal the other guy’s remaining things, and you’ll be ahead by more and more things until your juggernauting things can force checkmate.