When it comes to endgames, Avengers is not the only endgame that matters. There are endgames in chess whose complexity far surpasses the Marvel movie’s plot. Over the centuries, there have been many studies which attempt to demystify and assign an order to the chaos that is the chess endgame. One such attempt is the square rule.
What exactly is the square rule? To put it simply, it is a rule which allows one to deduce if, in an endgame, the King will be able to stop a pawn from promotion or not.
Imagine a pawn on any square, such as shown in the image(a white pawn). Imagine that both the white and black only have their kings(obviously) and white has a pawn. If white manages to promote that pawn into a queen, they will win the game. If black succeeds in capturing the pawn, they will avoid a defeat and draw the game. The same holds true if the situation is reversed and white has to defend against black.
The basic idea behind the square rule is simple. Anyone who knows this rule can avoid the tedious process of calculating moves and simply figure out the ending of such a game. The square rule works in the following way. First, we draw a diagonal from the square on which we have the pawn to the eighth rank of the board. Following that, then we use that diagonal to create a square. If the King is inside the square or if he can enter it, then it can stop the threat. If not, white is bound to win provided they do not make any blunders.
As we can see here, if it is white’s turn to move, the pawn will promote and there is nothing black can do to prevent this outcome. Every move starting from here till white gives black a checkmate will be visible to both the parties.
However, as we can see, if the king is in the square, even if white manages a promotion, black will simply capture on the next move. This game is a draw according to the square rule.
This brings the question of what happens if the pawn has a chance to move two squares, i.e. it has not moved from its position ever since the game began. The timing factor incorporates this in as well. We draw the square after the pawn has moved two squares, since if the king is in the square of a pawn which has not moved, it may not enter the square of a pawn which moves two places instead of one. Essentially, what this means is that if we want to draw a square for a pawn which can move two squares, we can draw a square for the pawn assuming it has already moved one square. The following picture illustrates this properly.