Endgame Discovery?

After looking at 18th century games by the likes of Philidor and Bowdler yesterday, today I thought I'd get more up to date. I've been looking at games of Chigorin today. Yes, I know, I'm still over 100 years behind the times, but I enjoy looking at the history of chess, and an interesting position is exactly that, whenever or wherever it was played.

Chigorin is a well known historical chess figure playing 2 World Championship matches in the late 1800's against Steinitz. He lost both matches, but in them he proved himself a worthy competitor. He had a tactical flair and a great imagination, which I'd never really understood because I hadn't studied many of his games, and certainly not in any depth.

Here he is black against Isidor Gunsberg in a match they played in 1890. Chigorin came up with the magnificent line opening sacrifice 35..Rxf3!!. While the majority of white's pieces sit idly on the queen side, black's will penetrate the white position on the weakened dark squares around white's king. The rest of the game sees more imaginative moves bring black's pieces into the attack.

Of course by this stage in the development of chess, a player had to able to play in a rounded style, combining opening knowledge, endgame ability, tactical flair and defensive skills. Steinitz' new positional approach was taking hold of the game, and more comprehensive study was finding defensive resources against the old school of gambiteers.

The fighting qualities of all players is shown through their desire to win, and to play on in even positions. This is seen no more clearly in the games of the current World Champion, Magnus Carlsen. Chigorin had this tenacity too. I looked at an even endgame that he kept fighting on to eventually beat another heavyweight of that era, Tarrasch. The game has been analysed by many, including Kasparov et al. in "My Great Predecessors Volume 1" (MGP). Now I'm hardly one to criticise the great man, who is in my opinion the greatest player to have ever lived, but I think there might be an error in the analysis of this endgame by Kasparov and his team.

Here's the critical position from this endgame. The build up to this had been fascinating, as white worked hard to get blood from a stone. Here Tarrasch played 54..Rc1? "the decisive mistake" according to MGP. Instead black had to play 54..Rc2 winning a tempo by hitting the h2 pawn. The point in its effort to help promote the pawn, white's king will either have to go to c8, or c6 giving the black rook time to take on h2 and then bounce back to c2 to sacrifice itself for white's remaining pawn, giving a drawn rook versus pawn endgame.

After 54..Rc1 55.Ke5 Tarrasch played 55..hxg3 56.hxg3 Rc3 and he is indeed losing this position.

With black to move here, he would have no useful moves, so Chigorin simply played 57.Ra7! (after a couple of repetitions) leaving black in zugzwang.

My question is why did black have to capture on g3 on move 55? In my opinion, 54..Rc1 isn't a decisive mistake, but 55..hxg3 most certainly is. Instead of 55..hxg3, black has 2 defences which should draw.

Black can play 55..Rc6 cutting off black's king, or even 55..Rc2 returning to the position from before but a tempo down. I don't think that tempo makes a difference. After 55..Rc2 if white's king approaches the c-pawn then we go with Kasparov's plan of checking it until it goes to the c-file. The only other plan seems to be 56.gxh4 Kxh4 57.Kxf5

Now if black plays 57..Kh3, I can't see how white can win. Black's plan is simply to check the white king from the side until it isn't attacking g4, then take on h2. White can sacrifice the c-pawn and then win black's g-pawn with 58.c8=Q Rxc8 59.Rh7+ Kg2 60.Kg4, but according to Nalimov tablebases this is a draw.

Perhaps someone can refute my analysis, or perhaps I can be added to the list of annotators who have contributed something to endgame analysis?

The Longest Win of the Week

It's time to get back into looking at some endgames, and the best way to start is to download The Week in Chess  (TWIC) and sort the games according to how many moves were played in descending order. The latest TWIC is number 1038 and Mark Crowther has been running the site for over 20 years now, an amazing achievement and a great service to chess.

Anyway, once downloaded I like to look through some of the longest games, and see if there are any endgames which interest me. In the latest edition, I saw a game between A. Bergougnoux(1895)-J. Hebert (IM 2378) which reached the following position:

Like most club players, I'm guessing my knowledge of rook endings is pretty patchy. This game ended in a win for black, and my first thought was why isn't this is a draw? So I went to Averbakh's "Comprehensive Rook Endings" and looked at the section on where a rook fights against rook and doubled pawns. Here's what the Russian Grand Master and endgame expert has to say about these types of positions:

"Compared with the other forms of pawn structure, doubled pawns are less dangerous. We will first consider examples where the defenders king stands in the way of the pawns. In this case the result is normally a draw"

Ok, that is pretty much the same for rook and pawn versus rook endings, and it describes the position above. Averbakh then goes on to say that a passive rook, or when the defending king isn't in front of the pawn can affect the result. The examples he uses are excellent!

In this position, the defender has to use the same procedure as if the d4 pawn wasn't there. That is, wait till the pawn reaches the 6th rank, and then move behind the enemy king to start checking. 1.Rb7 Rg6 [Cutting off the white king] 2.Rb6

 2..Rg4!! [This is important. Heading for the back rank now is premature: 2..Rg1 3.Kc6! when either check fails] 3.d6 [3.Kc6 Rxd4 doesn't help white 4.Rb8+ Ke7 is a theoretical draw as the defending rook is behind the pawn and the king isn't cut off] 3..Rg1! [Now the rook heads for the back rank when there is no useful shelter for white's king]

White can make no progress. 4.Kc6 Rc1+ forces the king to retreat, while 4.Kd5 doesn't require any special treatment, so black could play 4..Rh1 gaining checking distance and waiting for white's king to try to advance. Now, if you look at the position in the first diagram, you'll see a position not unlike this one, a cast iron draw!

Sometimes, the draw is not so easy:

Here, for example, white has advanced the pawn to the brink of promotion, and the threat is Re8+, so black must seek drastic measures. 1.Rh2+ Kg6, and now that the black king is stalemated, 2.Re2!! and black's rook will keep diving in front of its white counterpart!

If the defensive rook is passive, things aren't easy, and maybe even impossible.

Black's rook is passive and white's king has penetrated the 6th rank. 1.Rd6 [Taking control of the 6th rank] 1..Rf8!? [A last attempt]

2.g5! [2.g7? Rf6+!! another stalemate possibility] 2..Ra8 3.g7 Rb8

White has a very simple plan. Rf6-f8, leading to a won pawn ending. 4.Rf6 Ra8 5.Rf8+ Rxf8 6.gxf8=Q+ Kxf8 7.Kh7 and white will promote on 3 moves.

Finally, take a look at this amazing technique!

Black's king is cut off, but the win isn't as straightforward as you'd think. Without the b6 pawn, white would build a bridge on the 5th rank, but that is now not possible. 1.Rd2+ [Driving white's king further from the action] 1..Ke7

[2.Rd5 fails to work after 2..Ra1 3.Kc7 Rc1 and white's king must go back to b8!] 2.Rd6!! [An unbelievable technique!] 2..Rc3 [Taking the rook doesn't help 2..Kxd6 3.Kc8 Rc2 4.Kd8 Rh2 threatening mate, but white promotes with check! 5.b8=Q+]

So what now? 3.Rc6!! [Building a bridge! If the rook isn't taken, then white's king will escape to c7] 3..Rxc6 4.Ka7, and black has no checks and cannot stop promotion!

So that's the theory, what about the example we started with?

I guess we've all been in this sort of position where we're struggling to draw against a much higher rated opponent, who just keeps playing and playing. Hebert changes the structure to try to upset his opponent. 1..f2. White still manages to keep playing solid moves. 2.Ra7 Kg5 3.Rg7+ Kf4 [A repetition is a good sign for the defender] 4.Ra7 Kg4

[My first reaction when I saw this position was to play 5.Ra3 cutting off black's king. 5..f4 and now throw the rook up the board 6.Ra8 when I don't see how black will progress. White played differently, but still good enough to draw] 5.Ra8 [According to Nalimov Tablebase, this position is drawn] 5..f4 6.Ra7 [Again, I like 6.Ra3 cutting off the black king. If 6..f3, white has the stalemate try 7.Rxf3!] 6..Kg3

In this position, after an heroic defence, the game ended. I'm not sure if white ran out of time, but I hope white didn't resign. According to Tablebases there is a move to draw, but only one. 6..Ra3+! [6..Rg7+ 7.Kf3 is hopeless for white] 7.f3 [Retreating the king back to g4 is no winning attempt] 

7..Rxf3+ with the same stalemate  theme! 8.Kxf3 stalemate!

Learning Endgames

Why is it that some players can just pick up an endgame book and methodically work through it, while some of us can't get to grips with them? I remember being a young player who wasn't converting good positions. As a result I purchased an endgame book. That book was called 'Practical Chess Endings' by one of my favourite players, Paul Keres. However, when I started to go through it, I found it not as practical as I was expecting, and in fact a lot of the positions that were covered didn't mean very much to me having never reached them before.

So I think for many players, myself included, study of the endgame has to evolve at a pace that reflects our practical application of that phase of the game. Nowadays, I am interested in any endgame, but I still get most interested in positions that I have experienced, wither through my own play, or through that of my students. I was recently looking at some games of one of my students when the following position was reached.

My student was white in this position, and he was very happy that the game ended in a draw (and perhaps a little lucky too). I asked him what he would have done if his opponent had played 49..g4? We played the moves 50.hxg4 Kg5 51.Bd6 Kxg4 52.c7 Nxc7 53.Bxc7 when the following position appeared.

I asked him if he'd ever looked at this ending before, and he replied he hadn't, so we played it out and I won the game easily with the pawns. However, from playing this position he learned a lot about this type of ending. First, white has a thankless task because the best he can hope for is a draw. So black can play on for free in this position. Actually there are a lot of positions like this, and it is good to get to know them and resist the temptation to offer draws. Thankfully, we have a World Champion who plays to the bitter end, thus encouraging us all to test our opponent's endgame knowledge. Second, without a plan, or some working knowledge of this endgame, it is almost impossible to know how to save it. Third, and as a consequence of the last point, it makes us think of all the other types of endgames that we need to learn, giving us that much needed incentive to get down and learn some technique.

So then, what about the ending Bishop vs 3 connected pawns? First, here are some general considerations:

- the worst pawns for trying to win include a rook's pawn
- if the pawns can all reach the 5th rank, they win.
- with a rook's pawn, it is better for the defender of the bishop controls the promotion square of that rook's pawn.
- king position is also a big factor with the defending king wanting to get in between or in front of the pawns.

A good way to learn these endgames is to have some basic positions to head for, so here are some typical drawing positions:

In both cases, the pawns can make no progress as they have been blockaded by the joint efforts of king and bishop. In the top diagram, if it is black's move and he plays 1..Ke5, white should prevent black's d-pawn advance by 2.Kc3.

It is worth noting that to draw, white wants to get his king in front of the pawns, and his bishop to a position where it is preventing the pawns' advance.

So with this knowledge, it should be able to create a plan if you ever get into this sort of position with specific moves being guided by general principles. There are even some amazing ideas like this one:

The general considerations first: white's king and bishop are in front of black's pawns which include a rook's pawn, and the bishop controls h1. The pawns have all reached the 5th rank, however, and black's king is very active. It's a close call. 1.Bb5 f3 2.Bd7 Kf4 3.Be6 g3 4.Bd7 Ke3 [Black plans to bring his king to e2 or e1 to help his pawn promote] 5.Be6 Ke2 6.Bh3 [guarding the promotion square of the most advanced pawn] 6..f2+

This seemingly hopeless position for white has one last twist. 7.Kh1 Of course if black now promotes white will sacrifice his bishop for stalemate, while playing 7..g2+ [to give white's king a flight square fails to] 8.Bxg2 f1=Q+ 9.Bxf1+ Kxf1 10.Kh2 =

So going back to the original position, what should white play in order to draw?

1..Kf5 [1..f5 2.Kd4 f4 3.Ke4 and the pawns will make no more progress] It certainly makes sense for white to bring his king to the defence] 2Kd4 f6 3.Ke3 [manouvering his king in front of the pawns advance] 3..e5 4.Bb8 [white can afford to play a waiting game allowing the pawns to advance which they surely will if black has any designs on winning] 4..g5 5.Kf3

Black can't advance any of the pawns without compromising his position and advancing the king doesn't help either. 5..Kd5 6.Bc7 e4+ 7.Ke2 f4 8.Bd8 g4 9.Bc7 f3+ 10.Ke3 with a dark squared blockade.

Saying that, it can be seen just how difficult it is to play these type of positions. I seriously recommend setting up some positions and playing them out, with an opponent if you can find one. There is also the Nalimov Tablebases which work with 6 man endgames, and thus can definitively tell us the result of all endgames with king and bishop versus king and 3 pawns. Interestingly, I originally set the wrong position up in the Tablebase and was surprised to see that white was losing.

Even though this position sees black with a rook's pawn, and it is further back than in the main example, this position is winning for black according to the Tablebase. I suppose white's king is further from the action and his bishop doesn't control h1. It would be an interesting practical position to play from, maybe changing things a little by placing the bishop on b7 as well.

* I used Averbakh's volume on minor piece endings to help me write this: