## Tuesday, December 16, 2008

### Xmas is a time for sharing...

...so I'll share with you this ending that appeared in Chess Today last Sunday.

Rowe v Roussel-Roozmon, Jamaica v Canada, Dresden Olympiad 2008: position after 63...Ka4-b3.

White now has a choice of four legal moves. Should he play:

a. 64. Kd1 ?
b. 64. Kd2 ?
c. 64. Bb2 ?
d. 64. h5 ?
e. doesn't matter, they all lead to the same result?

Explain your answer.

#### 30 comments:

Tom Chivers said...

I'd play 64. Kd2. It's closer to the kingside than 64. Kd1, whilst 64. Bb2 loses to 64...a1=Q+ etc and 64. h5 looks like it just drops the pawn.

ejh said...

Could you expand on...

(a) "etc"?
(b) the specific differences between the king moves, if any?

Tom Chivers said...

I can try :)

(a) 64.Bb2 a1=Q+ 65.Bxa1 Ka2 66.Bb2 and then black just passes with his bishop until white has to surrender his.

(b) I'm not sure there are any objective differences, but 64.Kd2 is closer to the kingside by a move than 64.Kd1 (ie to defend the kingside after 64.Kd1, you have to play Kd2 later to get there anyway.) This might be a useful tempo if black tries to route his own king over to the h-pawn to try to win it; with 64.Kd2 white is one move closer to defending it . . . I think :)

an ordinary chessplayer said...

I agree with everything Mr. Chivers said. But I can see why it's interesting. ... Looks like it might be a coordinated squares position. If the black king reaches f5 then it can also get to either e4 or g4, winning, so white has to stop ...Kf5. Maybe ...Ke5 also wins? Maybe even further back? Wish I had time to analyze it out, but I haven't slept in a week and I need to be functional at work tomorrow.

If I had this position with either color then I would want at least 1/2-hour on my clock, plus a delay. Otherwise with white I would just play Kd2 and let my opponent try to figure it out.

david said...

If White oscillates between c1 & d2, and if Black does nothing much, I can't see how either side makes progress. So it looks as if Kd2 or Kd1 are equivalents.

But there is one vaguely teasing idea arising from this line, within which other stuff may occur, I suppose.

1 Kd1 Be2+ (trying to lure K from c2) 2 Kxe2 Kc2; 3 h5! is drawn, because 3...Kb1; 4 Kd1 Kxa1; 5. Kc1 wins for White. So 3...Kc1 keeps the draw.

But I can't see a B win if W just oscillates while the BK remains on b3. And I can't see a B win if B embarks on a journey to the K-side.

And if there's a forced W win, I might just give up the game!

Tom Chivers said...

The plot thickens . . . and I think it thickens even further.

I too saw 64.Kd1 Be2+ 65.Kxe2 Kc2 and thought it won for black, not realising the king can be stalemated. However, I think if we look a bit further it's actually a draw still: 66.h5 Kb1 67.Kd1 Kxa1 68.Kc1 g5 69.h6 g4 70.h7 g3 71.h8=Q g2, and the pawn promotes with stalemate!

Tom Chivers said...

Ah, but 68.Kc2 does win. Just not 68.Kc1.

david said...

Anyhoo (as you say in here), 1...Be2+ is a load of artificial clobbers because it's not forced. I too looked at tricks arisng from 1..g5, including temporising with the Black bishop. But W need not be deflected from c1/d2...

...except of course by a BK tour to the K-side, whereafter I've assumed that a WK on f4 with WB oscillation a1/b2 keeps the draw.

Tom Chivers said...

Quite . . . the Be2+ idea might be worth in try in blitz --- if it actually worked, that is.

Anonymous said...

Right, after 20 minutes ruminating on the bus (the London Paper only lasts so long) here are my thoughts:

1. h5 loses trivially to 1...Be2 and 1. Bb2 loses as already mentioned.

I can see no obvious difference between Kd1 and Kd2 - if there were a difference i'm pretty sure black can easily gain a move.

Black's plan is now to move his King to the Kingside.

The obvious first "defensive position" for white is white K on f4, Black K on d5.

1...Ke6 with idea of Kf6. If White parries with 2. Kg5 then i think 2... Ke5 probably wins.

So white ignores by shuffling his bishop.

Black now moves his K to h5 and white must defend with Kg3. Then Black moves his bishop to g4 and plays ...g5! After the pawn exchange I don't see how white can prevent black's King marching into b1. He puts his bishop on h5 and the K moves in via f5,e4,d3 etc.

The alternative defensive plan for white is to keep his King on the Queenside. As black moves his K to take the h-pawn, white will win one of the c or a pawns by alternating his K between a3 and b4. I suspect however that the g-pawn will be too fast.

So conclusion...

All first white moves lose!

Richard

Tom Chivers said...

Superb! It's always good to be reminded why stronger players are indeed stronger.

an ordinary chessplayer said...

Work is over-rated.

Richard proved to my satisfaction that white cannot defend the kingside. Here is my demonstration on the queenside.

Say 64. Kd2 (b) Ka4 65. Kc1 Kb5 66. Kb2 Bb1 67. Ka3 Kc5 68. Bb2 g6!? 69. Ba1 Kd5 70. Kb4.

Now, giving up the c-pawn only draws: 70... Ke4 71. Kxc4 Kf4 72. Kb4 Kg4 73. c4 Kxh4 74. Bh8 g5 75. Ka3 g4 76. Kb2 g3
77. Bd4 with the wrong color queening square on a1.

Surprisingly, so does giving up the a-pawn: 70... Bd3 71. Ka3 Ke4 72. Kxa2 Kf4 73. Kb2 Kg4 74. Kc1 Kxh4 75. Kd2
Kg3 76. Ke1 g5 77. Bb2 g4 78. Ba3 Kg2 79. Bc5 g3 80. Bd6! Kf3 81.
Bc5 g2 82. Kd2 Kg3 83. Bg1 with a blockade.

But 70... Bc2! keeps both pawns and wins easily: 71. Ka3 Bb3 72. Kb4 Ke4. Munch.

david said...

Richard may still be right, but first answer this: how does the BK in practice both transfer to the K-side and defend a + c pawns?

For example: 1. Kd2 Ka4; 2. Kc1 Kb5; 3. Kb2 Bb1; 4. Ka3 Kc5; 5. Bb2 Kd5; 6.Ba1 Ke4; 7. Kb4 is level, I think.

BUT a nice try coming up. In the line above, try 5...Kd6; 6.Kb4 Kd5 triangulating.

Alas, so what! 7. Ka3 Ke4; 8. Kb4 Kd3; 9. Ka3 Kc2; 10. Ba1 Kc1 and while amusingly the two Ks have swapped positions moreorless, B is no nearer a win, I think.

Of course, if W allows B to dump a bishop on b3 via c2 defending both pawns, B wins. But despite the analysis in the post above, W is not forced to concede this

So finally, can B let the a-pawn go and round up the h-pawn? I think not. Once the WB is released, it looks to have time to get to g5

David
Atticus CC

david said...

A few further comments and corrections arising from my latest analysis in the previous post, and from the lines in the post before that.

First, in the latter: 70. Kb4 isn't forced. Keep the WK on a3; shuffle the WB instead. If/when the BK vacates defence of c4, then Kb4, forcing Bd3 (or a BK reversal to defend); then Ka3 forcing Bb1 with repetition. The point is: W can shuffle Ka3/b4 and Bb2/a1 while keeping Bc2/b3 off the agenda.

Second, if B heads for the h-pawn regardless, so what? Once W wins either a- or c-pawn, the WB is released. Getting the WB to g5 is not relevant of course; any square targeting g1 will do.

So third, maybe the final piece in the puzzle. Let's say W wins the c-pawn, and B wins the h-pawn. In due course, B will win the WB after g1(Q) and then round up the c-pawn. Meanwhile, the WK sits on a1/b2 twiddling his thumbs in the certain knowledge that the game is drawn - because the bishop is the wrong colour for the queening square!

Draw!

David
Atticus CC

an ordinary chessplayer said...

My mistake was in thinking that white could not allow ...Kd3 (say Kb4-a3 Kd5-e4 Ka3-b4 Ke4-d3) but as David says, so what! I can no longer find a win for black.

Curious: will we get to see the analysis from Chess Today?

ejh said...

Of course not, this is much more fun.

Anonymous said...

After having read Munch's post this morning I was all ready to point out that white didn't have to allow ...Bc2, but alas i was beaten to it. The way that black cannot manage to get his bishop out of the way to get the King to b1 has a nice symmetry with the way that white cannot get his K to a1 to free the white bishop.

Anyway, the analysis continues...

In the position with the white K on a3, black K on d3 (black to move) we can continue...

1... Ke4 2.Kb4 Bd3 3.Ka3 Kf4 4. Kxa2 Kg4 5. Kb2 Kxh4 6. Kc1 Kg3 7. Kd2 Kf2 which is winning is it not? The key difference being that Black has an extra tempo on the line given by Munch this morning.

I'm not sure what the relevance is of white's bishop being released to cover g1, as in David's post.

Richard

david said...

Hhmm.....Bc5 or similar is relevant if the c-pawn drops, but clearly not if the a-pawn drops. I overlooked that.

That'll do. Black wins. I can't stare at this position any more anyway. It's fried my synapses.

Anonymous said...

Astonishingly it may still be a draw. If white moves his bishop to e7 before bringing his king over it appears that Black loses back that crucial tempo!

Richard

Anonymous said...

BTW the ending does take on a slightly different complexion when you discover that Black had the winning position on the K-side some 15 moves earlier!

Richard

Anonymous said...

Indeed he did! We'll never know if Black had something brilliant in mind, or just played for the trap-ette involved with 1. Bb2.

I've also been trying to force through the g-pawn in lines similar to the one Richard last mentioned. Continuing his line from 7. Kd2 Kf2 ...

8. Bb2 g5 9. Ba3 g4 10. Bc5+ and now what? 10. ... Kf1 is met by Bd6 halting the pawn. 10. ... Kf3 allows 11. Ke1 and a fortress. If Black tries ... g3, ... Kg2, ... Kh2, then Bd6 still halts the pawn permanently.

One other idea I've spotted but can't quite make work: Black could give up the c-pawn at the right time to force his king through to b1, viz (from Ka3/Kd3, Ba1): 1. ... Ke2 2. Kb4 Bc2 3. Kxc4 Kd2 4. Bb2 Bd1 5. Kb4 Kc2 6. Ka3 Kb1 0-1. But that trick doesn't work with the bishop already on b2.

So I'm inclined towards DRAW, but think there's a subtle Black improvement somewhere.

an ordinary chessplayer said...

Re giving up the c-pawn, if the bishop is on b2 just start with ...Kd2 instead of ...Ke2. (In general black can have the bishop on either square in whatever line he chooses.) But I rejected giving up the c-pawn for a different reason, e.g. in your line 3 Kxc4 Kd2 4 Kd5 Kc1 5 c4 -- Move the bishop, sac for the a-pawn, run for the g-pawn, and deflect with the c-pawn.

Black has *yet another* try: giving up the a-pawn. Say 1 Kb4 Kd3 2 Ka3 Kd2 3 Kb4 Bd3 4 Ka3 Kc2 5 Kxa2 g6. Eventually ...Ba4 (idea ...Bb3) In order to save his bishop white has to play Ba3 allowing ...Kxc3. Doesn't work. After the sequence Ba3 Kxc3, white gets his bishop to g5, and answers ...c3-c2 with Kb2, draw.

You can call me "Munch" if you want, but that wasn't my handle, it was black's next action. That'll teach me.

ejh said...

I assumed you took the name off the detective in Homicide.

Anonymous said...

OK, for those still watching my final thoughts - the Conclusion is DRAW, but not without another couple of glorious twists.

Firstly consider position:

W:Ka3,Ba1,Pc3,Ph4
B:Kd3,Bb1,Pa2,Pc4,Pg6

1...Ke2 is only a draw as previously demonstrated because white wins the a-pawn and brings his bishop to e7 before bringing the K over.

However Black has another try:

1...Kd2!

Now 2.Kb4 loses to 2...Bc2! 3.Kxc4 Kc1! so white has to go 2.Bb2!

Now black can win the c-pawn for the a pawn as follows:

2...Bf5! 3.Kxa2 Kc2!

Now 3.Ka3 loses to 3...Kb1 and 3.Ba1 allows Black to bring his bishop around to a4 and b3 forcing the K to a3.

However if white goes 3.Ba3! Kxc3 I think the position is never the less a draw because white can set up a blockade in a similar manner to the variations earlier with black trying to push his g-pawn.

There is however one final twist in this glorious ending. In the initial position (W: Kc1,Ba1,Pc3,Ph4 B:Ka4,Bd3,Pa2,Pc4,Pg7) the position is winning if Black's bishop is on b3. He can take his K to the Kingside and white is denied the defensive option of keeping his K on the Queenside. But the problem is how to get the Bishop to b3??? With the white king on d2/c1 it has to go via a4 but this is easier said than done without dropping the a-pawn.

Black must aim for the following position on the queenside with white to move:

W: Kc1,Ba1,Pc3
B: Kb3,Ba4,Pa2,Pc4

1.Ba1 loses to 1...a1=Q! and 1.Kd2/d1 allows 1...Ka3 and 2.Bb3

However white can avoid this position by keeping his K away from c1 until AFTER Black has moved his bishop to a4 (by alternating his K between d1 and d2). So we have the following position (black to move):

W: Kc1,Ba1,Pc3,Ph4
B: Kb3,Ba4,Pa2,Pc4,Pg7

1...Ka3 allows simply 2.Bb2+!

However we now have the final cruel twist. Black can gain the crucial tempo with 1...g6! 2.Kd2 Ka3 and 3...Bb3.

The cruel twist is that with the black pawn on g6 rather than g7, white can revert to the original defensive plan of following defending the K-side with his K. Because there is now no way for Black to get his K to h5! White can keep his K on f4/g5 (to prevent Black moving his K to h5 via g7 and h6) as appropriate and alternate his bishop on a1/b2.

Did Chess Today consider any of this? ;)

Richard

Anonymous said...

OK so most people have long abandoned this thread for those still tracking there is a new 'definitive' final answer. The original diagram should be entitled 'White to play, black to win'.

1. kd2 Bf5 2. kc1 Bd7 3. Kd2 ka3! 4. Kc1 Bc6! 5.Bb2+ kb3 6. Ba1 Ba4 and wins...

Richard

an ordinary chessplayer said...

How about this: 64 Kd2 Bg6 65 Kd1 Be8 66 Kd2 Ka3 67 Kc1 Bd7 68 Bb2+ Kb3 69 Ba1 Ba4.

Anonymous said...

So what's the final answer (before this disappears off the main page!)

ejh said...

There is no final answer, for no work of art is ever completed, but only abandoned.

an ordinary chessplayer said...

Black wins, as Richard said.

Appropriate to let him have the final word, as he did the most work on this. For the record, I was not trying to "amend" his comment #25. I must have been looking at a cached version of the page, so I was still working on comment #24.

ejh:
I have never seen Homicide, because I don't own a TV. But I am old enough to remember "the Belz" as a standup. I vividly remember him doing a bit about falling down and knocking himself unconscious, and later in the hospital every channel he flipped to had the same video clip of the deed, so he had to watch himself over and over.

I also read something very recently (Entertainment Weekly probably) where he made an "accidental" arrest while doing a street scene for a show. The guy came around the corner, surrendered, then recognized Belzer and said "Munch".

Anonymous said...

Quoting Leonardo da Vinci as you don't know the answer lol.