Before we find out what that Bähr is up to, I must address one note from my PREVIOUS TRUE COMBAT ARTICLE, regarding the game Taylor-Kallio, specifically the note to White’s 49th move. There I gave two exclams to my actual choice, 49.Re6, while I gave some analysis that showed how I didn’t trust the alternative 49.Rb6, which appeared to lose for White.

However, I am aware of the new “tablebase” computer programs that can exactly analyze 5 man endings like this, and asked for assistance from readers. I received a couple of letters; the following was particularly helpful. I quote, in part:

“Dear Mr. Silman, I only today read Tim Taylor's last "True Combat" article. He asks for comments from someone with access to Nalimov table bases on his endgame against Finnish GM Kallio. Maybe you can relay the following information to him: Everybody can access Nalimov tablebases on the Internet on the following URL: http://www.lokasoft.nl/tbweb.htm

It has all 5-piece positions and a couple of 6-piece ones! Very convenient, quick response, and no need to load 20 GBytes on your hard disk. I took a brief look at his ending and in fact 49.Rxb6 does draw, but White has to play a couple of only moves in succession. Following IM Taylor's analysis (an exclamation mark indicates "only move"): 49.Rxb6 Rxe4+ 50.Kd3! Re1 51.Kd2! Re5 52.Rb1! Re6 53.Kd3! (instead of 53.Rg1+) Kf4 54.Rf1+ Kg3 55.Kd4!, but play remains extremely intricate both for White to draw and for Black to win if White errs.

Best regards from the Netherlands, Jan Hondebrink”

I checked Mr. Hondebrink’s analysis by setting up his final position, and taking the White pieces, playing it against Fritz: I drew, with difficulty, on the second try!

So I conclude two things: scientifically speaking, 49.Rb6 and 49.Re6 are equivalent: they both draw.

But from a practical perspective, the latter is much easier to play (I only had to find one “star move” after that, 58.Rb8!!) while the R vs. R and g-pawn ending reached after 49.Rb6 requires endless precision on every move! Even when I knew the position was drawn, and knew how to draw it, I still lost to Fritz (due to good old human error!) the first time I played it out.

On the other hand, even under the pressure of my opponent’s great desire to win, I was able to draw the position after 49.Re6 fairly easily.

And now, back to Bähr! This creature made a noteworthy appearance in my first win from my second tournament in Hungary, an IM double round robin in Kecskemet. I was so encouraged by this endgame victory that I went on to tie for first (with the Russian IM Sutorikhin)!

The game that follows is with another Russian IM, Pavel Bogumil. Before we get to the actual ending, I present the following chess problem: consider the two diagrams below, both of which could have occurred in the game.

Taylor-Bogumil variation, with White pawn at g3

Taylor-Bogumil variation, with White pawn at g4

These two diagrams are identical in every respect, White to move in both, except for the fact that in one the White passed pawn is on g3, and in the other, the White passed pawn is on g4. And yet, amazingly enough, one of the endings is drawn, and one is won for White!

So I have two questions:

1.Which position wins for White?

2.Can you determine which one wins without calculating?

I’ll tell you now I can answer the second question with a quick affirmative, thanks to another excellent ending book, “Secrets of Pawn Endings,” by Karsten Müller and Frank Lamprecht. So during the game I knew what to aim for, even in time pressure, without having to resort to lengthy calculations.

But we will get to that in good time. First the game:

Timothy Taylor (IM USA) - Pavel Bogumil (IM RUS)
Kecskemet, 2003
Old Indian Defense [A53]
1.d4 Nf6 2.c4 d6 3.Nc3 Nbd7 4.e4 e5 5.Nge2 Be7 6.g3 0-0 7.Bg2 Re8 8.0-0 Bf8 9.h3 c6 10.Be3 Qc711.g4 g6 12.Ng3 Nb6 13.b3 Bg7? 14.c5 dxc5 15.dxc5 Nbd7 16.g5 Nh5 17.Nxh5 gxh5 18.Qxh5 Nf819.Bf3 Be6 20.Bg4 Qc8 21.Rad1 Bxg4 22.hxg4 Re6 23.Ne2 Qc7 24.Ng3 Rd8 25.Nf5 Rd7 26.Kg2 Qd8 27.Rd6 Rdxd6 28.cxd6 Rxd6 29.Nxd6 Qxd6 30.Qh1 Ne6 31.Rd1 Qe7 32.Qh5 b6 33.Rd3 c5 34.Bd2 b5 35.Rh3Nf8 36.Be3 c4 37.bxc4 bxc4 38.Qh4! c3 39.g6! Qb740.gxh7+ Kh8 41.Bh6 Qxe4+ 42.Kh2 Nxh7 43.Bxg7+ Kxg7 44.Qh6+ Kg8 45.Rxc3 Qb7

As usual in this ending series, I’m not paying too much attention to the early stages of the game: suffice it to say White won a pawn early, and after a certain amount of messiness, emerged from the tactical melee a clear Exchange up. And this is where our ending struggle begins, for to repeat the ancient cliché—which still carries a load of wisdom with it—there is nothing harder than winning a “won” game.

What are White’s advantages?  There are the same number of pieces on the board, but the White Rook is obviously (especially on this open board) much superior to the Black Knight. For example, right now the Rook attacks 14 squares, the Knight, just 3. This means that a Queen exchange hugely favors White: without the balancing effect of the Black Queen, the White Rook will quickly overwhelm the short stepping Knight.

A second advantage is that White has the relatively safer King; the Black King is under dire threats of Rook attacks on the 8th rank, or down the h-file. Essentially, this means that White has two ways to win.

During the game I chose option one: I aimed relentlessly for a Queen exchange, and even further simplification, finally forcing a winning basic ending.

However, my post-game analysis shows that White could also win by direct attack, taking advantage of Black’s open King, as follows: 46.Rh3 (This develops into a double switchback theme, based on the fact that the board is clear enough for the White Queen + Rook, which are now a formidable attacking team—Black’s defensive, short-stepping Knight can hardly defend threats on both wings, which means his Queen will be driven into a hopelessly passive position) So, 46.Rh3 Qe4 (forced) 47.Rb3 (Switchback! I missed this idea during the game) 47...Qa8 (Black’s Queen is forced to this miserable square, as the exchange of Queen’s is obviously fatal: 47… Qf4+ 48.Qxf4 exf4 49.Ra3 etc.) 48.Qe3! Double switchback! Now White threatens the entire board, and Black can’t keep up, as can be seen:

a) 48...Qd5 49.Rb8+ Kg7 50.Re8 f6 51.Re7+ Kg6 52.Qh3;

b) 48...f6 49.Qd3 Qe8 (or 49...Kg7 50.Qd7+ Kg6 51.Rb7 Ng5 52.Qg7 mate) 50.Rb7 Nf8 51.Qc4+ Ne6 52.Rc7 Kf8 53.Rc8 Nd8 54.Qc7;

c) 48…e4 49.Qd4 Nf8 (49...a5 50.Qe5 Nf8 51.Rb8 Qc6 52.Qe7 Qh6+ 53.Kg2 Qg7 54.Qxe4 [54.Qxf8+ Qxf8 55.Rxf8+ Kxf8 56.Kg3 Ke7 57.Kf4 a4 58.a3 Ke6 59.Kxe4 Kf6 60.f4 Ke6 61.g5 Kd6 62.f5 Ke7 63.Ke5 Kf8 64.Kd5 Ke7 65.Kc5 Kd7 66.Kb5 Kd6 67.Kxa4 Ke5 68.g6 fxg6 69.fxg6 Kf6 70.Kb5 Kxg6 71.a4 Kf6 72.a5 Ke7 73.a6 Kd7 74.a7] 54...Qg5 55.a4 Kg7 56.Qd4+ Kg8 57.Rb5) 50.Qd6 and, as in all the other lines, White wins.

You could say this is prettier than the game, but my line is just as effective, if a bit longer, and also gives me a chance to bring out the Bähr!

I played:

46.g5

Which has the extremely simple threat of 47.g6 fxg6 48.Qxg6+ with either a Queen exchange or a winning attack. In general, the idea behind 46.g5 is to exchange Black’s last King protecting pawn, and once that is accomplished, Black will be unable to avoid the Queen exchange on the wide-open board.

White’s point! Black has to give up his f7-pawn (and so leave his King wide open to checks) since 48...fxg6? (48…Qxg6 49.Rg3 is also instantly fatal) 49.Rf3 Nh7 50.Qd8+ Kg7 51.Qe7+ Kg8 52.Rf7.

48…Nxg6 49.Rc8+ Kh7

49… Nf8 doesn’t help: 50.Qh6 Qb4 (50…Qf4+ 51.Qxf4 exf4 52.Ra8 is too easy) 51.Qg5+ Kh8 (51…Kh7 52.Rc7) 52.Qxe5+ Kg8 53.Qg3+ Kh8 54.Rc7 and White wins the f-pawn anyway, while maintaining a fierce attack—in short, White has a winning advantage.

Decisive! Due to Black’s lack of king protecting pawns, White can force a winning pawn ending. But how did I know the pawn ending would be winning? It’s time to bring out the Bähr!

Let’s go back to the two diagrams that started this article. If you guessed diagram one is winning, and diagram two is drawing, either you are a good counter, or you know Bähr’s rule (“Secrets of Pawn Endings” doesn’t give any biographical info on Bähr, but it seems he was a problem composer who did remarkable work on pawn endings in the 1930s).

The simplest way to explain the rule is this: With a passed pawn on the other wing, and blocked R-pawns, draw a diagonal backward from the defender’s RP to the c(f) file, then draw the diagonal the other way to the attacker’s passed pawn. If the passed pawn is on or below the border diagonal, the attacker wins, if the passed pawn has moved up past the diagonal (other things being equal, like King position) it is a draw.

Note that if the attacker’s RP is on the fifth or higher, the attacker wins any normal position.

In diagram one, the backward diagonal goes to c7; then switch the slant toward the passed pawn, and you see the pawn at g3 is ON the border diagonal, and so White wins.

In diagram two, the pawn is ABOVE the border diagonal, which leads to a draw.

Variations bear (so to speak!) this out, e.g., Diagram One could continue 1.Kf2 Kf5 2.Ke3 Kg4 3.Kd4 Kxg3 4.Kc5 Kf4 5.Kb5 Ke5 6.Kxa5 Kd6 7.Kb6! and White cuts him off at the pass and wins.

Instead, Diagram two could continue: 1.Kf3 Kf6 2.Ke4 Kg5 3.Kd4 Kxg4 4.Kc5 Kf5 5.Kb5 Ke6 6.Ka5 Kd7 and Black slides safely into c8 and draws!

This would be a good time to mention that “Secrets of Pawn Endings” also lists a few exceptions to Bähr’s rule, so if you have time, be sure to calculate!!

Now let’s get back to the game.

The reason I knew the coming pawn ending was won was this: I saw I could eliminate Black’s e-pawn, and exchange all the pieces. My a-pawn could always get to a4 at least. Therefore the “border diagonal” would be b8-h2; and my pawn on f2 would be under that diagonal, and a capture on g3 would still leave my pawn on the diagonal, winning in both cases.

And since this a typical Bähr, no exception would apply (the exceptions relate to excellent defending King position, a less than distant passed pawn, or a weak blocked rook pawn, none of which apply here).

So with Rg8 I calmly prepared to clear off most of the board!

52...a5

Not advancing this pawn makes White’s win easier: 52...a6 53.Rxg6 Qxg6 54.Qxe5+ Kh6 55.Qe3+ Kg7 56.Qg3 a5 57.a4, or 52...Qd3 53.Rxg6 Qxg6 54.Qxe5 when Black should resign in either case.

53.a4!

All according to Bähr! The further up my rook-pawn is, the more leeway I have with my passed pawn. Right now it can win on any of the possible squares f2, f3, f4 or g3.

53…Qg4

Staying the Exchange down loses as well: 53...Qh4+ 54.Qxh4+ Nxh4 55.Ra8 +-, e.g. 55… Kg4 56.Rxa5 Kf3 57.Rc5 Kxf2 58.a5 Nf3+ 59.Kh3 Ng5+ 60.Kg4 Ne6 61.Rc2+ Ke3 62.a6 Nd4 63.Rc5 e4 64.a7 Ne6 65.Rc4 Kd3 66.Rc8 e3 67.a8=Q e2 68.Qd5+ Nd4 69.Rc4 e1=Q 70.Qxd4+ Ke2 71.Rc2+ Kf1 72.Qf4+ Kg1 73.Qh2+ Kf1 74.Qh1, mate.

54.Rxg6!

54…Qxg6 55.Qxe5+ Kh6

The exchange of Queens is forced no matter where he goes: note that even advancing the White passed pawn diagonally still wins according to Bähr, e.g., 55… Kh4 56.Qg3+ Qxg3 57.fxg3+ .

56.Qf4+ Kg7 57.Qg3 Kf6

As above, 57… Qxg3+ loses to 58.fxg3 Kg6 59.Kg2 (but not 59.g4??, =) 59…Kf5 60.Kf3 Kg5 61.Ke4 .

58.Qxg6+ Kxg6 59.Kg3 Kf5

The alternative 59...Kg5 can lose in two ways:

A. 60.f4+ Kf5 61.Kf3 Kf6 62.Ke4 Ke6 63.Kd4 Kf5 (63...Kd6 64.Kc4 Kc6 65.f5 Kd6 66.Kb5 Ke5 67.Kxa5 Kxf5 68.Kb6) 64.Kc5 Kxf4 65.Kb5 Ke5 66.Kxa5 Kd6 67.Kb6 Kd7 68.Kb7!.

B. 60.Kf3 Kf5 61.Ke3 Ke5 62.Kd3 Kd5 63.f3! Kc5 64.Ke4 and now:

B1. 64…Kb4 65.f4 Kxa4 66.f5 Kb3 (66…Kb5 67.f6) 67.f6 a4 68.f7 a3 69.f8=Q a2 70.Qh8.

B2. 64...Kd6 65.Kf5 Kc5 (65...Ke7 66.Kg6 Kf8 67.Kf6 Kg8 68.f4 Kf8 69.f5) 66.Ke6 Kb4 67.f4 Kxa4 68.f5 Kb3 69.f6 a4 70.f7 a3 71.f8=Q Kb2 72.Qb4+ Ka2 73.Kd5.

Now back to the game, which only lasts one more move!

60.Kf3, 1-0.

A possible finish is 60...Ke5 61.Kg4 Kf6 (61...Kd4 62.f4 Kc4 63.f5 Kb4 64.f6 Kxa4 65.f7 Kb3 66.f8=Q a4 67.Qh8 Ka2 68.Qg8+ Kb2 69.Qg7+ Ka2 70.Qf7+ Kb2 71.Qf6+ Ka2 72.Qe6+ Kb2 73.Qe5+ Ka2 74.Qd5+ Kb2 75.Qd4+ Kb3 76.Qa1) 62.Kf4 Kg6 63.Ke5 Kf7 64.Kf5 Ke7 65.Kg6 Ke6 66.f4 Ke7 67.f5 Kf8 68.Kf6 Kg8 69.Ke7 Kg7 70.f6+ and mates shortly.

Conclusion:

What does that Bähr do in the woods? Here it is again: in a 2 pawn vs. 1 pawn ending, with blocked rook pawns and a passed pawn on the other wing, draw a diagonal line backward (make sure you draw it in your mind, don’t take a crayon to the chessboard in the middle of the game!) from the defender’s rook pawn to the c(f) file, then slant the diagonal the other way toward the attacker’s passed pawn, creating a critical “border diagonal.” If the attacker’s passed pawn is on or below the border diagonal, the position is a win. If the pawn is too far up the board, past the border diagonal, the position is a draw, barring exceptional circumstances.

In other words, even though you always hear, “passed pawns must be pushed,” this is precisely wrong in a Bähr situation: the only way you can win is if your passed pawn is back far enough!

Does that make sense? Don’t ask me, I didn’t make the rule!