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An endgame clinic – Bishop vs. Knight

In my last blog post we looked at a really interesting endgame involving a pair of Bishops vs. a pair of Knights with pawns on both sides of the board. This time around we’re going to examine the same idea, but we’ll simplify it a bit: we’ll look at a single Bishop against a single Knight.

In both cases, though, the underlying principle remains the same: in endgames in which both players have pawns on both sides of the board, Bishops tend to be better than Knights. It’s simply a mobility issue: Bishops move farther than Knights. A Bishop can not only zip quickly back and forth across the board in a single move (shuttling from the Kingside to the Queenside and back whenever necessary) but also just plain controls more turf than a Knight. On an open board, a Bishop controls seven squares at its worst, while at its best a Knight controls only eight squares:

Even a cornered Bishop can control seven squares

A centralized Knight controls just eight squares - and that's the best it can do

A Bishop can easily pick off opposing pawns and/or support and defend friendly ones on both sides of the board. But Knights are slow and often have to struggle just to defend friendly pawns on one side of the board — never mind trying to reach the opposite side in time to be effective.

Using a program like ChessBase 10, you can finds literally thousands of Bishop vs. Knight endgames. Here’s just one that I discovered, a game from 2009 played between grandmasters at the chess World Cup (and, by the way, the Black player isn’t the former World Champion of the same name):

Meier,Georg (2653) – Petrosian,Tigran L (2615) [D81]

World Cup Khanty Mansiysk (1.2), 22.11.2009

Position after White's 27th move

White is winning as he’s a pawn ahead, but Black can still make a fight of it as long as he tries to keep material on the board. White can’t advance the e-pawn to create a passed pawn (e5 is controlled by both of Black’s pieces) and his Rook is tied to the e4-pawn’s defense. Black’s best strategy is to try to keep White’s pieces tied up and play for the “frustration draw”.

27…g5 28.Be3

The Bishop retreats, but now Black decides to do something ill-advised: he’s going to trade Rooks. He’d have been far better off playing 28…f5-f4.

28…Rxe4 29.Rxe4 fxe4

Position after 29...fxe4

The material is now equal and neither player has a passed pawn. White, though, still has the advantage because (you guessed it!) his Bishop is better than a Knight with pawns on both sides of the board. And Black’s a-pawn is hanging…

30.Bxa7 Kg7 31.Bd4+

The Bishop hustles back and checks the King, picking up a tempo.

31…Kg6 32.Ke2 Kf5 33.Ke3 Nh6 34.h3 g4 35.a4

Here’s a fundamental reason why the Bishop is better than the Knight. White’s Queenside pawns, supported by the Bishop, can advance and create a passed pawn. Meanwhile the Bishop (if necessary) can still help out on the Kingside. Black’s Knight, less mobile, can only be active on the Kingside.

35…gxh3 36.gxh3 Ng8

Black loses more time as he tries to reposition his slow Knight to a more active spot.

37.b4 Ne7 38.Bc5 Nd5+

This just drives the White King to a better square. Black is really scrambling here: he can’t let White create a Queenside passed pawn, he needs to try to create his own passed pawn, and he really can’t afford to lose any more material. It’s just plain impossible for the Knight to be everywhere at once.

39.Kd4 Nf4 40.b5 Ke6

Position after 40...Ke6

Black is hopeful that his King can dash White’s plan to gain a passed pawn. But now the e4-pawn is dangling, and White’s in a happy place: he has a choice of winning moves.

41.a5

[41.Kxe4 would also win. 41…Nxh3 42.f4, then Black really has nothing better than 42…Nxf4 43.Kxf4 Kd5 44.Be7 and, to use that really annoying phrase, “the rest is a matter of technique”. But, honestly, White’s game pretty much plays itself from here.]

41…Kd7 42.Kxe4 Nxh3 43.f4 h5 44.Kf3

Black is just plain sunk. Sooner or later he’s going to have to trade his Knight for White’s f-pawn, the White King will then snap up the h-pawn, and a White Queenside pawn (aided by the Bishop) will promote. In fact, Rybka4 (with the help of the Nalimov tablebases) finds a forced mate in fourteen here. Fire up your tablebases and see for yourself!

Black resigns. 1-0

So what does all of this mean to you? When you’re in a late middlegame or early endgame, knowing that Bishops tend to be better than Knights with pawns on both sides of the board will help you determine whether or not a particular minor-piece trade is a good idea. If you have Knights, try to trade them for your opponent’s Bishops if possible, but also try to keep your Rooks (or Queen) on the board (as seen in the game above). If you have the Bishops, try to hang onto them instead of trading them for an opponent’s Knights.

On the other hand, if you have two Bishops and your opponent has a Bishop and Knight, try to swap off the same-colored Bishops so you’ll have a straight one Bishop vs. one Knight endgame.

Want to learn more about minor-piece endings? ChessCentral carries Karsten Mueller’s FritzTrainer Endgame DVDs. ChessCentral also offers an extensive line of chess pieces, boards, software, and gift items (Christmas is coming soon!)

Have fun! — Steve

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“Tricky” chess positions

I’ve recently been reminded of an old chess lesson I learned many years ago. An acquaintance was asking me about the relative values of the pieces, information which I was happy to provide:

Pawn = 1
Knight = 3
Bishop = 3.5 (roughly)
Rook = 5
Queen = 9
King = Infinite (but about 3 as an attacker or defender in an endgame)

I was quick to point out the caveat that a Knight is actually worth more than a Bishop in a closed game, and that a “good” Bishop was worth more than a “bad” one. But I also threw out another warning which seemed to baffle my acquaintance: “Don’t put that much stock in ‘counting points’ because the specific material imbalance is far more important, plus other factors such as space advantages come into play as well.”

Did I say “baffle”? The guy was totally confused. He’d been learning chess from some antiquated beginner book which seemed to indicate that being ahead on “points” is all that matters, and that any trade is a good trade as long as you come out ahead on “points”.

I’m sorry to say that I once experienced the same deficiency in my own chess education; back in high school I had a teacher who was big on the idea of “grabbing material”. It required many years (and more than one poisoned pawn) for me to unlearn that lesson.

Properly evaluating a position requires much more from a chessplayer than the ability to “count points”. Here’s an example. Take a look at this position for a second, count to three, and then quickly say aloud who you think is ahead in the following position:


OK, now — quick! What’s your answer?

If you did this exercise according to my instructions, allowing yourself no more than three or four seconds to examine the board, I’ll bet dollars to donuts you said “Black”; after all, Black’s ahead by a Queen, Rook, and Knight for two pawns (or Queen, Rook, and one pawn if you’re playing “count the points”). I won’t say you’re necessarily wrong here, but there are a pile of problems with that answer, not the least of which is the fact that I didn’t tell you whose turn it is to move. Ooooops…

Look again. This is a great position; in fact, it’s a classic from an actual game. If it’s Black’s turn to move he mates instantly with …Qxg2#, so in this regard the “point count” doesn’t matter anyway. But I’ve tricked you a little: it’s not Black’s turn to move in this position — it’s White’s move. And in this case the point count definitely doesn’t matter because White mates with Bxe7#.

This is arguably one of the most famous positions in chess history, the next-to-last position from the “Evergreen Game”, played in 1852 between the great Adolf Anderssen and Jean Dufresne. The game has nothing to do with Christmas trees either; it’s called “evergreen” becauseĀ  no matter how many times you replay it, the game still blows your mind each and every time:

Anderssen,Adolf – Dufresne,Jean [C52]
Berlin, 1852

1.e4 e5 2.Nf3 Nc6 3.Bc4 Bc5 4.b4 Bxb4 5.c3 Ba5 6.d4 exd4 7.0-0 d3 8.Qb3 Qf6 9.e5 Qg6 10.Re1 Nge7 11.Ba3 b5 12.Qxb5 Rb8 13.Qa4 Bb6 14.Nbd2 Bb7 15.Ne4 Qf5 16.Bxd3 Qh5 17.Nf6+ gxf6 18.exf6 Rg8 19.Rad1 Qxf3

At this point Dufresne threatens 20…Qxg2#, but he never gets the chance to play it. Anderssen launches a series of sacrificial checks which end in mate.

20.Rxe7+ Nxe7

To modern eyes, there is a flaw in Anderssen’s analysis. Dufresne didn’t have to capture on e7: he could instead have played 20…Kd8 21.Rxd7+ Kc8 22.Rd8+ Kxd8 23.Bf5+ (discovered check) Qxd1+ 24.Qxd1 and Black’s still in the game. But we need to bear in mind that this was the “Romantic Era”, in which it was considered unmanly to refuse to accept an offered sacrifice. Anderssen counted on this, which is why his sacrificial combination works. After 20…Nxe7, mate is forced:

21.Qxd7+ Kxd7 22.Bf5+ Ke8 23.Bd7+ Kf8 24.Bxe7# 1-0

Dufresne’s reaction to the move 20.Rxe7+ is a wonderful illustration of why “bean counting” doesn’t always work and why we shouldn’t ourselves fall prey to the blind temptation to just grab material for its own sake. Dufresne not only lost the game, but probably also spent the rest of his life hearing, “Oh! You’re the guy who lost that game!” from chessplayers he’d meet.

If you got hoodwinked by this little position, you shouldn’t feel badly about it — even chess computers sometimes get suckered by big material advantages. Here’s a famous example:


Sure, White’s a Rook up, but the position’s dead drawn — the pawns are locked and neither player can make any progress, so the extra Rook doesn’t mean doodly-squat. Unlike the first position with which I tricked you this one’s easy to figure out, and the side to move doesn’t matter — it’s drawn either way.

But almost all chess computers mess this position up. I checked this position using more than a dozen chess engines and all but one of them showed White to be ahead by more than a Rook (because of the space advantage provided by the White pawns). The only chess engine to come close to getting it right was Shredder 12 which evaluated the position as “=” (but still showed White with a 0.13 pawn advantage for some odd reason, even after a 33-ply search).

The moral of the story is that “bean counting” (that is, just counting up the captured material) can sometimes be a useful start toward arriving at a valid positional analysis, but it’s not the only available tool and is seldom the best one.

Shredder12 is available right now from ChessCentral and, if you buy it from us, you’ll get free technical support provided by yours truly should the need arise.

Have fun! — Steve

Free beginner chess videos from ChessCentral

I frequently encounter people who would love to learn to play chess, but who don’t know how to get started.

“I don’t want to buy a book and then find out I can’t understand how to play.”

“I bought a book and read the first chapter but I still just can’t understand how the pieces move.”

“I wish somebody could just show me how the pieces move, but nobody I know plays or wants to teach me!”

Ah! That last one — I’ve seen that one before, more than once, usually online.

So we’ve decided to take that particular bull by the horns. I’ve created a series of videos designed to take an absolute chess beginner step-by-step through the process of learning how the pieces move. I’ve also included castling, pawn promotion, and en passant captures for good measure, as well as checkmate and the various ways a game can be drawn.

Best of all, these videos are available online and are absolutely free. All you have to do is go to the host page at ChessCentral and start watching. Each video is very short (less than three minutes each); if you’re quick on the uptake and can remember the moves, you could start playing chess less than an hour after you start watching the first video!

Each of the video pages at ChessCentral contains three videos, except for the last one which has two. There are fourteen Flash videos in all, each viewable right there on the page.

If you’re well past the beginner stage but know some folks who’d like to learn to play, please send them the link to the videos. To make that easy, here’s a “cut and paste” version of the link to the start page:

https://www.chesscentral.com/Articles.asp?ID=326

And don’t forget to visit the other pages at ChessCentral, the leader in cutting-edge chess!

Have fun — Steve

Steve’s Chess Tips: Pigs on the Seventh Pt. 3

When GM Yasser Seirawan hung the tag “pigs on the seventh” on the seventh rank Rook pair, he was referring to the fact that they could gobble up opposing pawns just as greedy hogs devour slop. Even a single Rook on the seventh rank can mop up the opponent’s undeveloped pawns with relative ease, as we will see in today’s post.

This position is from the 1988 chess Olympiad. G. Martineau, a member of the Hatian team, is in position to invade the seventh rank with one of his Rooks. His opponent, San Marino’s Andrea Magalotti, appears to have been asleep through part of the game; his Bishop is trapped, his pawns are undeveloped, and his Rook and King are on the back rank. Black is way behind positionally, but White is about to put him behind materially as well:

Position after 24...Bh7

25.Re7

White’s Rook comes screaming into the seventh rank like a dive bomber.

25…hxg4

Black’s intent is clear: he seems to have a single-minded fixation on freeing the trapped Bishop. He intends to play …Bxf5. Black’s real problem here is that there’s not much he can do; White’s Rook and Bishop are gunning for the f7-pawn. 25…Rc8 loses to 26.Rxf7, while 25…Rf8 gives White time for 26.h3 and the Black Bishop stays trapped. Black has actually played the best move, which gives us an idea of just how horrible his position remains.

26.Rxf7

And one pawn falls.

26…Kh8 27.Rxc7

A second pawn drops.

27…Bxf5 28.Rxb7

Followed by a third…

28…Re8 29.Rxa7

…and then a fourth. So we can see that a single Rook on the seventh (typically teamed with a second threat or magnifying an existing positional advantage) can easily devastate an opponent’s forces by snapping up unguarded pawns.

Position after 29...Rxa7

White is winning here, but give Black credit: he valiantly struggles on by trying to create counterplay as compensation for his lost material:

29…Re3+ 30.Kd4 Rh3 31.Ke5 g6 32.Kf6 Rxh2 33.Ra8+ Kh7 34.Bg8+ Kh8 35.Be6+ Kh7 36.Ra7+ Kh8 37.Bxf5 Rxb2 38.Ra8+ 1-0

With a forced mate on the board, Black throws in the towel.

ChessCentral carries the book and disk widely regarded as THE definitive work on the endgame: Dvoretsky’s Endgame Manual. If you buy the disk version, ChessCentral will ship it free (no shipping charge!) through July 11, 2010.

Have fun! — Steve

Steve’s Chess Tips: Pigs on the Seventh Pt. 2

In our last chess tip we saw how effective the Rook pair on the seventh rank can be. But in that game the Black King was actually trapped by its own Rook; White’s mating combination was actually helped by Black’s piece placement. Occasionally the mate by Rook pair requires some help by another friendly piece to keep the opposing King cornered, as we see in the following example (from Nikontovic-Bekker Jensen, Danish Team Championship 1999):

Position after 24.c4

White’s pawns are really making things miserable for Black. The move 24…dxc4 would be wrong because of 25.Bxc4+, so Black chooses to further overprotect his d-pawn:

24…e6

Probably not the way to go, as the White Bishop and pawn make an effective “battery” of sorts. Black’s in trouble here no matter what he does, but 24…Kh8 was arguably better.

25.cxd5 exd5 26.Rc1

Position after 26.Rc1

White starts getting ideas about a “horizontal Rook battery” (e.g. pigs) on the seventh rank. The next stop for the c1-Rook will be c7.

26…Qb5

I’ve won a game or two in my time by “bluffing” my opponent with a faux counterattack. But this isn’t the time for it, I’m afraid. This move pretty much loses instantly. Black would have been better off circling the wagons with 26…Bf8.

27.Rcxc7 Qxe2

This is actually a slick little Queen sacrifice by White, who doesn’t care a bit about his Queen — checkmate is now forced.

Position after 27...Qxe2

Note that the White Bishop on b4 helps keep the Black King trapped in the corner. It doesn’t matter whether a Black piece sits on f8 or (as happens here) a White piece controls that square; the important point is that f8 is denied to the Black King’s use.

28.Rxg7+ Kh8 29.Rxh7+ Kg8 30.Rag7# 1-0

And the greedy pigs emerge triumphant. This was a really sweet ending; I’ll bet it took the White player a day or two to come back down after this one.

Learn more about Rook endings in this eBook from ChessCentral.

Have fun! — Steve

Steve’s Chess Tips: Pigs on the Seventh Pt.1

In our chess studies we hear the term “Rook battery” quite often. A Rook battery is a pair of Rooks on an open or half-open file; the Rooks support each other and are poised to batter the enemy position (hence the term “battery”). But a pair of Rooks on an open rank can also be an effective and deadly combination, especially when they’re positioned on the seventh rank (with the opposing King trapped on its own back rank). GM Yasser Seirawan often refers to such a Rook pair as “pigs on the seventh” because, like greedy hogs, they can gobble up pawns (and everything else in sight).

Even titled players sometimes forget the power of pigs on the seventh. In this game from the 1982 Danish Championship, Jesper Norgaard (playing Black) is in some serious trouble; his position is pretty near lost, but he can still make a fight of it:

White to move

His opponent, Curt Hansen, increases the pressure by playing 43.e6. Here’s where Norgaard slips and forgets the power of the paired Rooks on the seventh rank. Instead of moving his Bishop to a better spot, or maybe even trying a desperate escape with …Kg7, Norgaard reflexively takes the offered pawn by 43…fxe6:

Position after 43...fxe6

Norgaard has completely opened up the seventh rank, and now the pigs can run wild. As much as I despise the phrase “the rest is a matter of technique”, it definitely applies here: this position is quite literally the textbook example of how to mate with a pair of Rooks on the seventh rank. It’s a forced mate-in-three. Do you see it? Take a minute to try to find it before looking at the answer below.

Sometimes a little help is required in order for the Rooks to achieve a back-rank mate. We’ll look at an example of that in an upcoming post.

Do you want more info on Rook endgames? ChessCentral has Karsten Mueller’s DVD Chess Endgames 2: Rook Endgames in stock and ready to ship!

Answer: The forced mate-in-three revolves around driving the King into the corner with one Rook, then letting it come back and be mated by the second Rook. It goes like this — 44.Rg7+ Kh8 45.Rh7+ Kg8 46.Rbg7#.

Have fun! — Steve

Steve’s Chess Tips – Trading down

When is it a good idea to swap material in chess? I’m not talking about the times (both rare and fun) when an opponent lets us capture his Queen at the cost of a pawn or minor piece; I mean straight even trades. When is trading a good idea?

Back when I was starting out, I’d trade like a Moroccan rug merchant just to get as many pieces off the board as I could. I figured that the fewer pieces on the board, the less trouble I could get into, so I’d hoover off as many as I possibly could. Wellllllll, sometimes this was good thinking and sometimes this was very bad thinking.

There are exceptions to every rule, but in general it’s a good idea to trade down when you have a material advantage. Let’s consider a straight King-and-pawn ending in which you’re ahead seven pawns to your opponent’s six. You launch a series of trades and captures in which you end up with a two pawn to one pawn advantage. This is good — do the math. A 2-1 advantage is far better than 7-6.

Conversely you generally don’t want to trade pieces when you’re behind in material. The same math applies here. Being on the short end of a 7-6 pawn differential isn’t pleasant, but being on the downside of a 2-1 deficit is even worse.

So trade when you’re ahead and keep material on the board when you’re behind. By the way, you’ll also want to trade down when you can obtain a clear advantage by doing so.

Here’s an example of bad trading, by a guy who should have known better. Check out this position from Frank Marshall – Akiba Rubinstein, Vienna 1908. White has just played his Rook from f7 to g7:

Position after 51.Rg7

Marshall is ahead material and decides to sucker Rubinstein into a disadvantageous trade. Akiba takes the bait and obliges — in spades. After 51…Rxg7
52. Bxg7 hxg4 53. Kxg4 Nxc3, we get this:

Position after 53...Nxc3

Now here’s the question: should Marshall trade one more time by playing 54.Bxc3 here? Why or why not?

ChessCentral is taking pre-orders for Rybka4. Order yours now and get a free copy of my Guide to Computer Chess CD!

Have fun! — Steve