Imagine you are playing a game, and early on you win an extra rook. What should be your strategy? Some players want to use their extra piece to play for a quick checkmate—but this approach is unnecessarily risky. In a complex attacking game, both sides have chances to win, even the side that is down in material.
In fact, Paul Morphy, the world’s top chess player in the mid-1800s, would often play with “rook odds”: his opponents would start the game with an extra rook.
To their amazement, Morphy would usually win. How could he pull this off? The answer is that there were still enough pieces on the board that Morphy could use his queen, bishops, knights, pawns, and remaining rook to coordinate a decisive attack. We can see this from the final position of one of his rook odds games he played as white:
Morphy used his knight, bishops, and rook to chase black’s king to the edge of the board, eventually checkmating with a pawn. What teamwork!
So, what is the optimal strategy for the side with the extra rook? Simply to trade off pieces! To illustrate this, imagine that Morphy’s opponent managed to swap off queens, bishops, knights, and the remaining rook.
Black is still only ahead by one rook, but we are looking at an entirely different position. Even a novice player would not have trouble winning a couple of white’s pawns with the rook, promoting a pawn to a queen, and going for checkmate.
We can further understand the power of trading while ahead with a sports analogy: imagine you are playing 5-on-4 basketball. Does the other side have any likelihood to win? They probably have some chance. If those four guys are skilled, they even have a big chance.
Now let’s say you can swap out player for player: 4 on 3, 3 on 2, 2 on 1… you can see how the advantage of your extra player grows because the opposing side has less of a team to counter you. By the time you get to 1 on 0, you are guaranteed to win!
Moral of the story: When you are up in material, trade-off! Which each piece swap you make, the position simplifies, and your advantage grows.