Revisiting some old chess strategies: Utilizing ‘the Square’

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We are quite sure that all of you studied basic geometry in your school days. Among the first few theorems you studied, there was one that said: sum of any two sides of a triangle is greater than the third. You believed it to be universally true, didn’t you? Well, let me prove that it is not true for some parts of your chessboard!

two sides equal one

Let us consider the triangle formed by the squares a1, d4 and a7. If your King is sitting on a1, how many steps does it need to reach a7 walking along the a-file? Let us count: a2-a3-a4-a5-a6-a7, total 6 steps. Now let it go along the other two sides, a1-d4 and d4-a7, and count: b2-c3-d4-c5-b6-a7, total 6 steps again! Have I proved my point?

Some of you must be wondering what the point is in all this and others may be downright annoyed about such a silly proposition. But if you bear with us, we can tell you that keeping the above in mind can help you to tackle successfully many chess problems involving King and Pawn endings, either for a win or for a draw.

Take the simplest chess endings with a King and Pawn for both sides but positioned near opposite edges of the chessboard. You may have to follow a strategy of keeping options open for your King to move to either edge depending on the tactical plan of your opponent. The chess tactics for you will be to maintain a middle path till your opponent makes that critical move disclosing his plan and you can accordingly move your King to the required side.

middle of the road keeps options open

The above diagram shows the principle behind such tactics. The square a7 can be reached in same number of steps from either a4 or d4 but if you need to move midway to the other edge, you can move to h4 in three steps from d4 against seven steps from a4. We hope you understand the merit of such tactics. If you think carefully, you will realize that the concept of the square lies behind this chess tactics.

To make it clear with an example, we draw your attention to the endgame position described in Chess tactics in end games. For easy reference, the position is reproduced below where White with first move can snatch an ‘impossible’ draw!

White to move and draw

You can see the comments against the moves in the referred article – here we only show how the ‘square’ boundary changes with each move by Black Pawn. We also show how the White King’s area of effective influence ultimately comes in contact with his own pawn and intersects the ‘square’ of the Black pawn (indicating the possibility of capture) after his 3rd move (Fig. 3).

figure1   figure2
figure3   figure4
figure5   figure6

The triggering action was Black’s 3rd move (Fig. 4). This move disclosed Black’s intention to promote his pawn, so White King veered towards his own pawn (Fig. 5) to promote it likewise. Had Black captured the White pawn at this stage (3. … Kxc6) leaving his own pawn at h4, White King would move towards the Black pawn. White King would be able to step into the Square (refer Fig. 3) by playing 4. Kf4 and it would also be able to capture the Black pawn. White’s strategy ensured a draw either way.

Remember that the above chess tactics can be applied in many other endgame positions, not necessarily only the King and Pawn types. You only have to remember this type of chess tactics of moving the King along a diagonal.

 

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