Wednesday, December 5, 2007

Calculating Your Endgame

The following endgame occurred.

I am Black.

White had just played:

42. Kd4 (see 1st diagram on left)

Now here's the question:

Should Black swap rooks by playing 42....Rxc5?

Give yourself a few minutes to think this over before proceeding to the answer below.

Before swapping Rooks, it is important to calculate first if the resulting pawn race is a win for Black or not.

What do you do after the White King recaptures with 43. Kxc5? How do you stop any of the White pawns from strolling up the board? Is there enough time to stop any of these pawns? If so, how?

Let's first consider the line 42. ... Rxc5

White naturally recaptures with 43. Kxc5 (see 2nd diagram on left)

Now we come to an important decision. What should Black play next?

When looking at endgames, it is important to calculate your tempi carefully. In endgames like this where it's down to a pawn race, every tempo is worth its weight in gold.

At the current position, only 2 of Black's pawns can Queen without being hindered by Black's King. The d and g pawn. Let's look at the g-pawn. It takes 5 tempi to get the g-pawn to Queen and 4 tempi for the d-pawn to Queen. It takes White 5 tempi for either the a or b pawn to Queen. With that in mind. Let's proceed.

We have a look first at 43... Ke4. This tempo is a wasted move. Why?

Look at your pawns after 43.... Ke4. 44. a4. Black needs 4 more pawn moves for the d-pawn to Queen. White's a-pawn also needs 4 moves to Queen. In other words, Black's pawn Queens then White's pawn Queens and the resulting endgame is a headache as both sides try to fight for an advantage. The position becomes messy as Black is trying to manouevre the Black Queen into a position so that he can trade off White's Queen or attack the remaining White pawn and White will do its utmost to keep up with annoying checks on the Black King to force a draw. It's not much fun and gives you an immense headache in the process. Black is probably winning but it's difficult.

But it secures the d-pawn, you say.

Well, does the d-pawn need securing? Is there any reason to be afraid of Kxd5? The answer is no. The simple reason is that this is a pawn race. White can ill afford a King move so any other move other than the pawn move results in a precious loss of tempo and letting Black queen first. So put your mind at ease. White will not take your d-pawn.

What about 43... d4 then?

Well, what about it? White is now forced to play 44. Kxd4 and again we have 2 pawns queening one after another and a prolonged fight ensues.

No. There has to be a simpler and quicker method to end White's misery. And there is.

Look at the White King. What is the problem with the White King's position?

Yes, it happens to rest on a diagonal belonging to a potential Queening square. The g1 square.

In other words, if I push my g-pawn I would Queen with check, gaining a precious tempo before White can queen (see 3rd diagram on left).

This tempo is enough to secure Black's win.

43 .... g5 (let's say White pushes the b-pawn although the end result doesn't really matter if the a-pawn was pushed).
44. b4 g4
46. b5 g3
46. b6 g2
47. b7 g1=Q+ (see last diagram on left)

Now White is lost.

If White captures the d-pawn with
48. Kxd5 Qg2+ (see the green arrows) secures the b-pawn

If White plays
48. Ke6 Qb6+ (see the red arrows) secures the b-pawn again

If White plays
48. Kc6 Qa7 (see the yellow arrows) results in White having to waste more tempi and Black's d-pawn simply races up the board while the Queen sacrifices itself for White's b-pawn leading to a simple win.

So the final answer to all of this is:

Yes, Black should play 42... Rxc5

Unfortunately, this is where where I erred. As I was short on time, I made things difficult for myself (this was a blitz game). I did not swap Rooks and played 42... Rd1+. I was lucky that my opponent blundered in time pressure and the game was subsequently won. However, I am still unhappy with the fact that I made the wrong move and gave myself unnecessary headaches in the process. I must work on my endgame technique more.

I hope that by showing you all of my blunders, I am helping you to make less mistakes as well.


  1. Hi there, i just dropped by after reading one of your comments over at chessloser's blog. You've got some great posts. I added you to my blogroll and feedreader. I'll make sure and stop by more often.

    Take care!


  2. I took me 15-20 seconds to be certain the ending was won. I began by imagining Rxc5 Kxc5.

    Black's f- and g-pawns and White's a- and b-pawns are unstoppable. Black's g-pawn queens with check first, in five steps.

    Black moves first. So imagine now a Black queen on g1 and a White pawn on b2... then a a Black queen on g1 and a White pawn on a2... in both cases the win is trivial.

    Picking the right candidates first is mostly about experience, but I think 'counting' would help you evaluate variations faster than 'calculating'. Note how I never did a "He moves here then I move there then he moves there", and how I handled the a-pawn variation.

  3. I'm actually trying to work on my middlegame thought process. When I rush to calculate variations I find the right answer more slowly if ever at all because the most important move is often the first move. Both Aagard and Silman seem to encourage *really looking* at the position before calculation, so I imagine there's some truth to the idea. :)

  4. edwin: thanks! I've added you to my blogroll as well.

    likesforests: I am still fairly weak in endgames unfortunately, so for me this takes some time to go over. I only discovered the win after the game when i went back and retrace it. good that you've spotted the win :)

    your advice on counting definitely would have make things easier. i'll definitely try to remember it. thanks.