Geometry of the Chessboard: 3 Indispensable Patterns
Most students will tell you the shortest route between two points is a straight line, although ‘for the kings on the chessboard this is only valid for the diagonals’, wrote GM Karsten Müller and IM Frank Lamprecht on their monumental work ‘Fundamental Chess Endings’ (Gambit). Indeed, the geometry of the chessboard guards lots of secrets on its squares.
I could bet you’ve heard of the Rule of the Square, but what about Bahr’s Rule? Here I present you with three indispensable patterns to internalize in order to improve your ending technique and conquer that half point which will eventually give you a better position on the final standings.
Under the diagrams you see the FEN which serves to copy the positions directly to your chess software and study them by yourself, when confronted with complex positions you can make click on it to follow the explanation of every example in a chessboard window full of extra comments.
Many players fail to finish their opponents off in a knight and bishop vs king ending just out laziness, the technique required on this final isn’t particularly hard to achieve (at home). What you need is to learn the next pattern and its successful knight manoeuvre: Nf7-e5-d7-c5-b7. As you may have noticed this reminds of a ‘W’.
Sure, mating the enemy king isn’t the easiest task in the world but if you practice the position a couple of (dozen) times you will find it simple enough to master it and win every time it arises on the board. I encourage you to make click on the FEN and study the technique along with the commentaries.
Surely enough you’ve already found yourself immersed to the neck in the following position at either side of the board failing to find the path to success. The geometry of the chessboard doesn’t allow alternatives: were the white king outside of the winning zone then the draw is inevitable.
On the contrary, should His Majesty enjoy the gardens of paradise inside the winning zone on its turn to play then White would be capable of delivering mate by allowing Black to queen. 1.Qf2+ Kb1 2.Kb4 a1Q 3.Kb3!
The Bähr’s Rule
I hadn’t heard of this rule before reading Müller-Lamprecht’s work and I can tell you that this easily alleviates the weight of the job in positions like the one presented in the following diagram. It works when two pawns are blocked along the a/h-file and the attacking side counts on a passed pawn.
Draw a diagonal starting at the enemy pawn towards its camp until you reach the c/f-file, from that point on turn the diagonal towards your first rank, whether the passed pawn is on or below the line then you’ll win thanks to the sacred geometry of the chessboard.