Thursday, May 3, 2007

Instructive Opposite-Coloured Bishop Endgame

I'm showing this endgame because it demonstrates an important endgame principle everyone should know about, and also to help me digest the lessons from it. I'll also include a position from earlier in the game to demonstrate the kinds of thinking errors I (and I suspect many others) need to work on.

The game was another ICC blitz at 2+12 time control, but it produced a very interesting endgame:

The first point to note is that "Bs of opps" endgames offer excellent drawing chances for the weaker side, even when several pawns down. We'll see that that's what happened to me in this endgame.

The second point is the "principle of two weaknesses": if your opponent has one weakness to cover, they can often defend, but if they have two weaknesses to cover they may be unable to defend against both threats at the same time (someone somewhere described this as "you can't attend two weddings at once"). If White can either take the h- pawn or advance the a- and b- pawns, he may queen a pawn and win.

The third point is the concept of a "mismatch". Once again, I have to STRONGLY recommend Soltis' book Grandmaster Secrets: Endings. Seriously, this is one of I'd say three chess books that had a revolutionary impact on me. A mismatch is where one side has a localized superiority of force, one which may defy a "point-count" assessment. In this endgame, the mismatch would be K+a+b pawns vs. B . In the absence of Black's king, Black's B would have to sacrifice itself for one of White's queenside pawns to prevent it from queening, allowing the other to queen and win.

White has two choices here: support the queenside pawns with his bishop and try to take the h-pawn with his king, or support the kingside with his bishop and charge the queenside with his king. The first plan was what I tried, but the second plan is necessary. To understand why, let's introduce the fourth point: schematic thinking.

What position does Black seek to get a draw? If Black can park his king on a dark square in front of the a- and b-pawns, he will be immune to attack from White's bishop, and can just shuffle his bishop around to defend the kingside pawn and prevent White from getting a passer there. In other words, Black wants this sort of setup:

This position is very similar to, and could have occurred in, the actual game continuation that ended in a draw.

What does White need to aim for to win? If White tries to go after the h-pawn with his king, Black can guard it with his bishop on the c1-h6 diagonal. However, the bishop may also have to work on the a7-g1 diagonal to hold back the queenside pawns. White was thinking that he could overload the bishop by using a threat on one side of the board to divert it from a threat on the other. Unfortunately, what's critical here is the activity of Black's king. In the time that it would take White's king to make good on this threat, Black's king would be on the queenside picking up the slack, and we would have a position like the above.

In this sort of position, it's critical for White to get his king in front of the passed pawns and not Black. How critical? Watch how much material White jettisons in the winning line. From the first diagram:

57. Ke4! Kf6 (57... Kxg4 58. Kd5 will win similar to the main line here) 58. Kd5!! (see diagram on the left) The Bishop can be left to its fate because White gets a winning mismatch on the queenside 58...Kxf7 59.Kc6 Be3 60.b5 and White will queen a pawn.

By analyzing this position, I determined for myself that in these endgames the attacker's king must get in front of the passers. While re-reading parts of Soltis' book as I prepared this article, I saw that he stated this principle explicitly himself. By working out this endgame myself and by re-reading some endgame instruction, I feel I've gotten a firmer grasp on this sort of endgame. Another example of mining a blitz game for valuable lessons.

Ok, that was the important part. What follows are errors from earlier in the game that give insight into the flawed workings of my brain.

First, I was completely crushing my opponent (up a rook) up until this point:

Black just played 33...Rf6xf3. I succumbed to the zwichenzug
34. Qxe5? rather than just recapture directly. I had analyzed out to around move 36, and got a spidey-sense that ...Bxf2+ was potentially going to spoil things, but everything else looked too "pretty". This is the story of my life. When you have an advantage, and you have the choice of a clear, good continuation and a tactical, more complex and unclear one, you should take the simpler path. Nunn's Secrets of Practical Chess points out that calculating tactics is an inherently risky endeavour, so if you're not 100% sure of the outcome you shouldn't allow yourself to be seduced. 34... f6 35. Qxc7 threatening mate ...Bxf2+ 36. Kh1 Qg7 37. Qd8+ Qg8 At this point, both 38.Rd1 and 38.Qd2 are clearly winning still (thanks, Fritz). However: 38. Bxf3?? Even under severe time pressure, how can you hang your queen with a 12 second time increment? Bxe1?? Or miss that my queen is hanging? 39.Qxf6+ Qg7 40. Qd8+ Qg8 41. Qf6+ Qg7 42. Qxa6 Qg5 43. Qa8+ Qg8 44. Qxg8+? (simplifying to the dreaded "Bs of opps") ... Kxg8 45.Bd5+ Kg7 46. c4 bxc4 47. Bxc4 Bd2 48. a4 Ba5 49. g4 Kf6 50. Kg2 Kg5 51. Kg3 Bc7+ 52. Kf3 Kh4 53. b4 Kxh3 54. a5 Kh4 55. Bf7 Kg5 56. a6 Bb6 gives us the endgame position I analyzed above.

Here's the entire game, for the curious:


Grandpatzer said...

Once again, I wanted to edit for readability, but the contents disappear and I can't click on the "compose" or "edit html" tabs in the edit screen.

Ah well, hope it makes sense as it stands.

Joe Erjavec said...

After 61...Kc5, it looks like 62. a7 would win the game, as the Black King is blocking the Bishop.

Grandpatzer said...

Thanks for catching that missed opportunity, Joe!