White to move and win. How should White proceed?
Daily Chess Improvement: Tricky Chess Tactic!
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White to move and win. How should White proceed?
An interesting ending and tricky, but the first move plays itself, and a little thought shows a way to keep black from ever bringing that rook to h4 protected by the pawn on g5 after black’s first move. White will end up with a queen and pawn vs a rook and four pawns, but the weak and unprotectable a7 pawn will kill black’s chances to draw.
1. h7 g5 2. Nd4 Rxd4 3. c3+ Kxc3 4. h8Q with a pin
after 1. h7 g5 2. Nd4 Rxd4 3. c3+ Kxc3 4. h8=Q Kc4 5. Qb8 Kb5 6. Qxa7 Ra4 7. Qxc7 g4+ 8. Kg3 Kxa6
I can’t find a winning line for white. I only see a black fortess, also without the g4-pawn.
An excellent point! I had underestimated black’s drawing chances. Yes, that line is drawn with best play, as I verified with a Nalimov Tablebase at Link. Using that same site, however, revealed a possible path to win, albeit it would be immensely difficult for anyone to find over the board.
White must gain a tempo to prevent black from capturing at a6 with the king, and he must do that by making use of the weakness in the connections between the rook and king after black has Kb5. From the top:
1. h7 g5
2. Nd4 Rd4
3. c3 Kc3
4. h8Q Kc4
And now, as Urso ably pointed out, if white goes to a8/b8 to capture at a7, black puts the king on b5, puts the rook on a4 and captures at a6 with the king:
5. Qa8 Kb5
6. Qa7 Ra4
7. Qc7 g4 (or Ka6 draws, too)
8. Kg3 Ka6!
When I checked Urso’s position in the Tablebase, it did indeed confirm this as a drawn position. In my haste last night, I didn’t bother counting moves and just assumed white would be able to queen the a-pawn, but there is no way I can find to save that pawn- black always has just enough time to win the pawn and to set up a fortress where the rook on the a or c file is protected by the b-pawn. In such a set up, the white king is always cut off from putting a double attack on the black pawn. However, I decided to dig a little with the tablebase, and it turns out that black’s 8th move above must be Kxa6– if he takes with the rook white has a forced win in no more than 46 moves with 9.Qd7+ (white also wins in 50 moves with 9.Kxg4 and 60 moves with 9.Qe5). Now, at first, I thought white might be able to win by forcing black to take with the rook by playing 7.Qb7 rather than the greedy 7.Qxc7, but it also fails. From the beginning:
1. h7 g5
2. Nd4 Rd4
3. c3 Kc3
4. h8Q Kc4
5. Qa8 Kb5
6. Qa7 Ra4
7. Qb7
And now white is threatening to march the pawn, so black must either take the a-pawn immediately with the rook, or do so after checking with g4 first, but the order doesn’t matter:
7. ………..Ra6 (or g4 8.Kg3 Ra6=)
8. Qc7
And the Nalimov Tablebase again confirms this position is also drawn with either Ra4 or Ra5. White can only win with the setup if it is reached with White to move. In my next comment, I am going to show a possible method for reaching the following positions that the Nalimov Tablebase shows as won: 8/2Q5/rp6/1k6/6p1/6K1/8/8 w – – 0 1 and 8/2Q5/rp6/1k4p1/8/7K/8/8 w – – 0 1
So, in my previous comment, I verified Urso’s analysis of the following line:
1. h7 g5
2. Nd4 Rd4
3. c3 Kc3
4. h8Q Kc4
5. Qa8 Kb5
6. Qa7 Ra4
7. Qc7 g4
8. Kg3 Ka6=
The question for the day is this- can white win at a7 and c7 while forcing black to capture at a6 with the rook when the white queen is sitting on c7 and the black king is sitting on b5? These are the following two FENs for the targeted positions: 8/2Q5/rp6/1k6/6p1/6K1/8/8 w – – 0 1 and 8/2Q5/rp6/1k4p1/8/7K/8/8 w – – 0 1
With that in mind, we have what I think is the critical variation point at white’s 5th move (though I will look at the earlier moves later as wrap up- see the note about black’s first move below):
1. h7 g5
2. Nd4 Rd4
3. c3 Kc3
4. h8Q Kc4
For the moment, we will just assume this line is the optimal for both players, though I do need to tie up one loose end at black’s very first move where he could have played 1. …Rxc2. So, now white actually has a choice about what to do- go immediately for the a7 pawn, which Urso has shown is drawn, or try an indirect approach making use of the fact that black must separate the king and rook for a move in order to put an attack on the remaining white pawn- this suggested to me an attack on the c7 pawn which also kept an eye on the rook at d4:
5. Qg7!?
White is threatening 6.Qc7 with check, and is preventing an immediate 5. …Kb5 by keeping an eye on the rook. If black plays 5. …c5, white then takes at a7 and black must lose the rook just to prevent white from gaining a second queen. The only plausibly different path for black here is to gain the tempo needed by checking from d3:
5. …………..Rd3
6. Kg4 Kb5
Again, black cannot play c5- white takes at a7 and the white a-pawn will win black’s rook. Additionally, black could try 6. ….Ra3 7.Qc7+ Kb5 8.Qa7 Ra6, but this is much like the two losing positions I identified earlier where black has captured at a6 with the rook, but it is white’s turn to move- indeed, I verified that this position is also lost, and I can’t find any other move for black other than 8. …Rxa6 that doesn’t lose as well, so black appears to have to play 6. ….Kb5. Continuing from 6. …Kb5 above where we now come to what I hope is the winning play for white:
7. Qb2+
This takes advantage of the lose connection between black’s rook and king- black cannot take at a6 without allowing white to pin and win the rook at d3 with Qe2. So, what can black do now- I see exactly three moves for black that don’t lose the rook to a double attack- Ka5, Kc4, and Ka4. I will try to dispense with each, but I in no way imply these are the most efficient methods for white to win- my only intention right now is to reach the positions I identified above with the tablebase as won- white may have even quicker wins in some of these variations, and I can’t even be certain I am not overlooking yet more ways for black to draw, but at the moment, I don’t see such saves for black
Variation A
7. ………….Ka4
8. Qc2 Rb3 (forced)
9. Qc7 Ra3 (or Ka5 10.Qa7+-; or Kb5 10.Qd7+ Ka6 11.Qa4+-)
10. Qa7 Kb5
11. Kg5 Ra6 (black loses this position according to Nalimov: 8/Q7/rp6/1k4K1/8/8/8/8 w – – 0 1)
Also, at move black’s seventh move:
Variation B
7. ………….Kc4
8. Qe2
The pin restricts black’s moves to the following list: c6, c5, b5, Kd4, and Kc3:
Variation B1
8. …………..Kc3
9. Qe5 Kb4
Or, according to Nalimov, (9. …Kc4 10.Qc7 Kb4 11.Qa7 Ra3 12.Qb7 Ra6 13.Kg5 is won for white); or (9. …Rd4+ 10.Kg5 c5 11.Qg7 Kc4 12.Qa7 is definitely won for white). Additionally, it should be clear that Kd2 or Kc2 at move 9 also lose to 10.Qxc7. Continuing with Variation B1:
10. Qe4 Kc3
11. Qb7 Rd4 (what else?)
12. Kg5 Kc4
13. Qa7 and this is easily won by white now.
Variation B2
8. ……………Kd4
9. Qe7 Rc3 (or Kc4 10.Qc7 Kb5 11.Qa7 Ra3 12.Qb7 is lost according to Nalimov)
10. Qd8! Kc4 (or Ke3 11.Qb8 wins for white)
11. Qc7 Kb4
12. Qa7 wins easily for white.
Variation B3
8. ……………b5
9. Qe7 Rd4 (only plausible defense given all the above)
10. Kg5 Rd5
11. Kf4 Rc5
12. Qe4 Kb3
13. Qb7 and this also wins easily for white.
Variation B4
8. ……………c5
9. Kf5
The threat is 10.Ke4:
9. ……………Kc3 (Kd4 10.Qe4)
10. Qe7 again wins easily with the white a-pawn.
Variation B5
8. ……………c6
9. Kf5 with the same threats as in Variation B4.
Now, let’s turn to Variation C from black’s 7th move, and the most difficult for me, and probably anyone:
Variation C
7. ……………Ka5
8. Qa2 Kb4 (Kb5 9.Qe2 Kc4 10.Kf5 is analogous won white position from Variation B4 and 5)
9. Qb1 Rb3 (or Kc4 10.Qf1 should also be analogous to the Variation B lines)
10. Qe4 Kb5
11. Qd5 Kb4
12. Qb7 Kb5
13. Qa7 Ra3
14. Qb7 Ra6 (forced)
15. Qc7
And, Nalimov tells me this is won for white in 82 moves. How does white win it? I have no clue right now. I will study have to study the tablebase, and maybe I can at least construct an understandable procedure for the why and how.
And now for the loose end at move 1 for black where he could just concede the new queen for white immediately by taking at c2. Last night, I summarily dispensed with that option, but in light of Urso’s discovery, I have to deal with it:
1. h7! Rc2
2. h8Q
Look at this for a while last night, and I don’t see any way to save the knight by moving it on the 2nd move- the problem is black can play 2. ….Rc5 with the threat of 3. …Rh5+. Even this morning, I don’t see any way to save the knight, but maybe I am missing something- I have a particular difficulty with knights in any position. So, my default is that 2. h8Q must be white’s optimal move here:
2. …………..Rc3
Pretty sure this is required. If black takes the knight with the king, white wins easily with 3.Qa8. Continuing:
3. Kg4 Rb3 (again, 3. …Kxb3 costs too much time)
4. Qb8 Kb5 (or Ra3 first)
5. Qa7 Ra3 (can Rb4 be any better?)
And, I have verified with the tablebase that black draws with the following:
6. Qc7 Ka6!
And black also draws with….
6. Qb7 Ra6
7. Qc7
Now, the question is, can white improve on his 7th move, or any other move. Honestly, it is almost enough interest for me to buy access to the 7-man Lomonosov Tablebase. In addition, I could envision lines where white forgoes winning at c7, and instead wins the g6 pawn with the queen, but the following position, 8/8/rp4Q1/1kp5/6K1/8/8/8 b – – 0 1 is also drawn, so no juice in that line for white.
In all honesty, right now I would have to recommend 1. …Rxc2 for black- it looks like a draw to me, but I need to think about some of white’s alternatives to just to be sure.
In the 1. ….Rxc2 line, maybe white does better with…
1. h7 Rc2
2. h8Q Rc3
3. Kg4 Rb3
4. Qd4+
Need to think about it.
Of the winning positions I could find for white in this ending, this one was the longest according to Nalimov Tablebase:
8/1Qp5/rp4K1/1k6/8/8/8/8 b – – 0 1
It is a position I think white can reach even in the 1. h7 Rc2 line I discuss above. White has forced the capture at a6 with the rook, and white has then taken the pawn on g6 in reply (I will discuss how to get there tomorrow once I have cleaned up my notes on the line. I spent a while this evening playing through the main variation in the tablebase, and I think I understand in general sense how white wins it- the queen variously checks the king and attacks the rook disrupting all attempts at setting up the fortress where the the rook is on the c-file and protected by the pawn, and where the king isn’t blocking the rook’s coverage of the c-file once the white king is set to cross it and get in behind the pawn. That seems to be the critical plan- get the white king to the d-file behind the pawn, and then cross the c-file once the black king is forced behind the rook on the c-file, or the rook has been driven from the c-file. Eventually, after many moves, white drives the the king and rook away from the pawn (else black loses the pawn and the resulting Q vs R ending is shorter than normal because the king and rook are already near a corner of the board), and black tries to hold the pawn on the 2nd rank with the rook protecting from the flank. However, white then eventually drives the rook away from the second rank with threatened pins and double attacks and captures the pawn on move 50, with one of the longer Q vs R endings still to come.
I am still trying to fully understand the maneuvers- unfortunately, it is only possible to understand by looking at the shorter, alternate lines which I haven’t had the time to do.