Aronian – Dubov after 47…Kf6. This position is a technical win for white. However, white MUST understand the winning motif. Pushing the g pawn too early would result in a draw.
For example, in this similar position, it would be a draw if white plays either g3 or g4. Therefore, white MUST push the pawn ONLY at the right time.
On the other hand, in this position, g4 is the right winning move. Do you understand why?
In the Aronian. the ending plan isn’t immediately obvious to me, but I think the first part of the plan literally has to be to bring the white king up the board and then down behind the black pawn, also the case in the second position I would think.
However, in the last position, the white has already advanced the king to the same level as the black pawn and the black king is already separated from the pawn itself, so that the black bishop must remain on that b1/h7 diagonal just to keep the white king out of f5- in that case, g4 freezes the black pawn on a black square and keeps the black king out of h5- this allows white to use both the rook and king on the fourth rank to drive the bishop off of that diagonal. In the third position (8/5k2/2R5/4K1p1/8/3b4/6P1/8 w), I would do as follows:
1. g4
I think the position is such that white has a lot of “winning” moves here, but they almost surely all travel through the same path at some point, so it is likely 1.g4 is the shortest route. Continuing:
1. …………Bb1 (the bishop must control f5 here at all times to prevent white from playing Kf5)
2. Rb6
Starting the process of forcing the black bishop off of the b1/h7 diagonal. This will require both white pieces. Continuing:
2. ………..Bd3 (I will discuss the alternatives in a moment)
3. Rb3 Bc2
4. Rb7
It will be clear in just a moment why this is the most accurate move here even though it seemingly allows the black king back to defend his pawn and to guard the f5 square:
4. ………..Kg6 (K 8th rank moves allows an immediate Kf6 winning the pawn)
5. Rb2 Bd3 (Bd1 6.Rb6 Kf7 7.Kf5+-)
6. Kd4
The white king now participates and the bishop now has no place to go on that diagonal:
6. ………..Bf1 (by far the most resistant defense now)
7. Rb6 Kf7 (or Kg7)
8. Ke4
More accurate than Ke5 which allows black to put the bishop on d3 again forcing white to repeat moves:
8. ………..Bg2 (nothing better)
9. Kf5 and the black pawn falls.
So, back at move 2, black had other squares on that diagonal to put the bishop other than d3- c2, g6 and h6. Those are no better:
2. ………….Bc2
3. Rb7 Kg6 (again, K8th rank moves allow Kf6)
4. Rb2 Bd1 (we have already seen Bd3 here)
5. Rb6 Kf7
6. Kf5+-
Or:
2. …………..Bg6
3. Rb7 and white gets Kf6 almost immediately to win.
Or:
2. …………..Bh7
3. Rb7 Kg6
4. Ra7
A waiting move given black’s constricted position……
4. ………….Bg8 (Kh6 5.Kf6 Be4 6.Rg7+-)
5. Ra6 Kf7
6. Kf5+-
So, I think this clearly demonstrates the power of 1.g4 in the last of the three positions, so I think one should consider how white creates such a position out of the first two, and I have to think about this a bit more since those positions aren’t immediately obvious to me, as I wrote right at the start of this comment.
I’m trying to understand why Danill Dubov didn’t claim a draw due to the threefold repetition rule (Fide 9.2) as Levon Aronian had moved Rd2 six times during the match from moves 60 to 91 and Daniil was in trouble? If someone could help me out on this one I would be very appreciative.
Let’s now discuss the 2nd position (8/8/4bk2/1R4p1/8/5K2/6P1/8 w)
Here, an immediate g4 is plausible as it isn’t in the 1st position since the king is on f3 instead of f2, so let’s see how the positions of the kings changes things (I am simply accepting the blogstress’ assertion for the moment that 1.g4 is a draw, but I think I now see why it is:
1. g4 Bd7
Not really sure yet, but I think several moves here draw for black- but I also think all the king moves lose- I will come back to this in a few moments if what I think is actually true about this position. With Bd7, black harasses the rook and keeps the white king tied down to f3/g3/h3 to guard the pawn:
2. Rb6 Be6 (Kf7 should be ok, too)
And now think about what white needs to do here- he would like to get the king to e5 or f5, but the king can only play away from f3 or g3 if the bishop is pinned to the black king, or if the bishop isn’t attacking the pawn at all- or, of course, he could use the rook guard the pawn from the fourth rank. Let’s see how the pin works after black’s 2nd move:
3. Ke4 Kf7
Unpinning the bishop. Here, 4.Ra7 will just repeat after the black king returns to f6. After 3. ….Kf7, the white king must return to f3 since he has the fourth rank blocked up. So, at move 3, white must try to bring the king around the other side of the rook as the rook protects g4:
3. Rb4
With the idea of Rd4 and then Ke3-Kd3-Kc3-Kb4-Kc5 etc:
3. ……………Bd7 (lots of draws, I would think)
4. Rd4 Be6
5. Ke3 Bc8
6. Kd3 Be6 (preventing Kc4)
7. Kc3 Bc8
8. Kc4 Be6
9. Kc5
And, so, white has accomplished the task of getting the king to the fifth rank after 1.g4, but I think most of you can now see the problem, right? How do you drive the black king back now? As long as the black bishop rests on the c8/e6 diagonal, the rook can’t leave the fourth rank without dropping the pawn unless the rook goes to d6 and pins the bishop first, but then black unpins it with Kf7/e7. In addition, unless the black king relents to the 7th rank, the white king can’t get to e5. I think black can just wait after white’s 9th move;
9. ………….Bc8 (probably lots of draws now)
10. Kd6 Be6
11. Re4
What else is better here? Nothing that I see:
11. …………Bc8
12. Kc7 Be6
13. Kd8 Bg4
Lots of draws, but this one liquidates the position immediately to a draw that I know well- the white king has strayed far enough away on d8 to allow black to sacrifice the bishop for the white pawn, and will obtain a draw by forcing white to sacrifice the rook just to prevent black from queening the g-pawn.
I think the point is this- white must advance the king before the pawn is put on g4 or even g3, which I now deal with to show that is also a draw.
1. g3
You might think this will be different from the 1.g4 line, but I can already see that it isn’t. Yes, the white pawn doesn’t need to be guarded on g3 from the bishop and white has full use of both pieces, but now black has more options for his king and bishop….
1. …………Bf5 (or Bd7/c8, or even Kg6)
2. Ke3
With the same plan as before get the king to the 5th or 6th rank:
2. …………Bd7
I think 2. …Be6 will now lose: [2. ….Be6?? 3.Ke4! Bg4 4.Rb6 Kg7 5.Ke5 and this should be won now based on the analysis I did for the 3rd of the three positions Susan gave us]. With Bd7, black attacks the rook…..
3. Rb6 Kf5 (or Ke5 here)
4. Rb7 Ke6 (for purposes of illustration)
5. Kd4 Ba4 (or Be8, left as an exercise for why all other moves lose for black)
6. Rb6 Kf5! (only move now)
And, I think it should be obvious what the problem continues to be- driving the black king back who now has a hole at f5 and g4 to get at the white pawn. At move 7, white must try…
7. Rb4 Bd1
8. Kd5
So, white has closed off the 4th rank, gotten the king to the fifth rank, and is no closer to winning……..
8. …………..Be2
And now what for white? He can’t play g4 without losing the pawn. If the rook leaves the 4th rank, black plays Kg4 forcing the rook to the 3rd rank guarding the pawn. There is simply no way to make progress after 1.g3 either.
In my next comment I will show why leaving the pawn on g2 works. I do now understand it.
So, dealing with the 2nd position, let’s see how advancing the king first before moving the pawn at all is better:
Starting position: 8/8/4bk2/1R4p1/8/5K2/6P1/8 w
1. Ke4
I think of all the winning moves here, this one has to be shortest since it double controls f5 preventing Bf5. It also puts the white king one square away from e5 forcing black to keep the king on f6 for the moment. This leaves bishop moves, or even black’s own g4. I will deal with them in order:
1. …………Bc4 (alternatives later)
2. Rb6 Be6 (of course, Kf7 allows Kf5 winning immediately)
3. Rc6
Simply waiting for black to move…..
3. …………Kf7 (alternatives in a moment)
4. Ke5 Bg4 (nothing better now)
5. Rc4
Harassing the bishop to drive it away from the f5 square….
5. …………Be2 (nothing better)
6. Rd4
Covers the d3 square and g4 square. White is now threatening Kf5. Black can prevent this with Kg6, can play g4 immediately, or attack the white pawn with Bf1. We will look at all three briefly:
6. ………….Kg6
7. g4
Quickest win. We have already seen similar position in my first comment on the 3rd position, and this is easily won now since black can’t prevent a check from the 6th rank followed by Kf5 and the loss of the black pawn. Or at move 6:
6. ………….g4
7. Kf5
Double attacks the pawn. With the white pawn on g2, white is a a position to actually sacrifice the rook for the bishop and the pawn since the resulting K+P vs K ending is a win for white. There is nothing black can do now, but try to muck things up by attacking the pawn…
7. ………….Bf1
8. Rg4+-.
Or, at move 6:
6. …………Bf1
7. g4 Kg6 (else 8.Kf5)
8. Rd6 Kg7
9. Kf5+-
So, at move 3, black had some alternatives, but they are no better than Kf7:
3. ………….g4
4. Kf4
Threatening Rxe6 followed by the winning Kxg4 for a winning K+P vs K ending:
4. ………….g3 (Kf7/e7 5.Rxe6 Ke6 6.Kxg4)
5. Re6 Ke6
6. Kg3 and this is also a won K+P vs K ending for white.
Or, at move 3:
3. …………..Ke7
4. Ke5 Bd7 (keeping an eye on f5)
5. Rc7
Threatening Rxd6 for another winning K+P vs K ending.
So, I now need to think a bit more about the very first position Susan gave us. The second position was easy because the white king was one move away from e5 after the first move. The 1st position looks a bit trickier to me, and I have give it a bit of thought.
My first attempts to find a win for the 1st position are coming up empty. That extra move white has to make to reach the fifth rank is causing me a lot of pain at the moment. After the 2nd position, I thought I had it all in hand, but I can’t recreate that same motif for some reason. I am obviously overlooking something right now and have to take a much deeper thought.
My first instincts about the first position might have been right all along- the king has to go much further up the board than was needed in the 2nd position- I just can’t quite nail down why that is- why that one extra move makes that much a difference.
So, here is what I have so far:
1. Kf3 Bf5 (covering the e4 square to prevent Ke4)
2. Rc5
A waiting move that keeps the black king out of e5. White would welcome 2. …g4+ since then Kf4 is winning. This leaves 2. …Kg6 and bishop moves. Continuing:
2. …………Kg6 (alternatives later)
3. Ke3
Another waiting move….
3. ………..Kf6
4. Kd4
Readying a move to e5 if the black king again moves to g6, so black must move the bishop…..
4. …………Be6 (nothing better now)
5. Ke4
Double controlling the f5 square. Now black must prevent an immediate g4 that wins as we saw earlier, so……
5. ………..Bd7 (threatens Bc6+ if the rook leaves the c-file)
So, this is where I have gotten stuck. I can’t leave the king on the fourth rank while advancing the g-pawn, and the black king can’t be driven away from the sixth rank opening the e5 square for the white king, and the rook can’t check from c6 and can’t leave the c-file at the moment without allowing Bc6+ followed by Bxg2. And I already know I can’t advance g3 either. This leaves only Kd5 as a move that makes progress….
6. Kd5
Right now, Kf5 is no threat from black since it drops the bishop at d7 to Kd6 discovered check, so white can play this move. Hard now is finding the best plan for black, but I would just play Be6 here…
6. ………….Be6
7. Kd6
What else can change the dynamic? What I can’t quite wrap my mind around is this- why this position is so different from the 2nd one? It makes me think my analysis of the second position has big hole in it somewhere, but I just looked it over again and it seems rock solid to me. So, after 7.Kd6, what should black do? I would just keep the bishop on the a2/g8 diagonal in the most flexible spot….
7. …………Bb3
This puts the onus back on white- what to do? I want to drive the king back, but can’t figure out how to do this without allowing the black king access to f5/g4. For example:
8. Rc1
With the plan of Rf1+:
8. …………..Kf5 (with the idea of Kg4 after 9.Rf1+)
9. Rf1 Kg4
And now white has a problem- the pawn is in danger. For example:
10. Rb1 Bc2
11. Rb2 Bf5
12. Ke5 Bg6
13. Kf6 Be8!
Which prevents Rb5 double attacking the black pawn before the black king can reach g3- i.e., white will capture with the rook which then guards g2. However, with 13. …..Be8, how do you make progress? For example:
14. Ra2 Kg3
15. Kg5 Bc6 and white loses the pawn.
Right now, I feel pretty good about the line up until white’s 9th move- all of that before that point looks solid to me, but I can’t quite figure out what to do after that point- 9.Rf1 just looks terrible to me.
What I would like to create here is the white king on f6 (like after move 13 above), the black king on g4, and the rook with a clear square to go to the fifth rank before black can play Kg3. That way white can win at g5 with the rook and protect the pawn from black king long enough to get g3 in as a move.
Aronian moved Rd2 six times between moves 60-91 , why didn’t Dubov take a draw ( threefold repetition) ?
Because the rule requires threefold repetition of the POSITION, not just of a single move. Although the R kept going to d2, the other pieces were on different squares.
Thanks Craig B.for your response ,sorry I wasn’t specific enough but Rd2 Bb1 occurred three times on moves 71, 82 and 88. All of the pieces on the board were in the identical position after moves 82 and 88 but upon further review the positions of the other pieces on the board were not in the same position as after move 71 so no threefold repetition there . After move 88 Levon moved his rook away from d2 and the position didn’t repeat. Looks like I will be wearing a dunce cap for the rest of the day.
Ok, I think maybe I have it now- what about:
1. Kf3 Bf5 (covering the e4 square to prevent Ke4)
2. Rc5
A waiting move that keeps the black king out of e5. White would welcome 2. …g4+ since then Kf4 is winning. This leaves 2. …Kg6 and bishop moves. Continuing:
2. …………Kg6 (alternatives later)
3. Ke3
Another waiting move….
3. ………..Kf6
4. Kd4
Readying a move to e5 if the black king again moves to g6, so black must move the bishop…..
4. …………Be6 (nothing better now)
5. Ke4
Double controlling the f5 square. Now black must prevent an immediate g4 that wins as we saw earlier, so……
5. ………..Bd7 (threatens Bc6+ if the rook leaves the c-file)
So, this is where I have gotten stuck. I can’t leave the king on the fourth rank while advancing the g-pawn, and the black king can’t be driven away from the sixth rank opening the e5 square for the white king, and the rook can’t check from c6 and can’t leave the c-file at the moment without allowing Bc6+ followed by Bxg2. And I already know I can’t advance g3 either. This leaves only Kd5 as a move that makes progress….
6. Kd5
Right now, Kf5 is no threat from black since it drops the bishop at d7 to Kd6 discovered check, so white can play this move. Hard now is finding the best plan for black, but I would just play Be6 here…
6. ………….Be6
7. Kd6
What else can change the dynamic? What I can’t quite wrap my mind around is this- why this position is so different from the 2nd one? It makes me think my analysis of the second position has big hole in it somewhere, but I just looked it over again and it seems rock solid to me. So, after 7.Kd6, what should black do? I would just keep the bishop on the a2/g8 diagonal in the most flexible spot….
7. …………Bb3
This puts the onus back on white- what to do? I want to drive the king back, but can’t figure out how to do this without allowing the black king access to f5/g4. For example:
8. Rc1
Now, here, my plan was 9.Rf1 check, but I don’t think that was appropriate- my plan is a bit too hasty after…..
8. …………..Kf5
9. Ke7!
The idea is the one I outlined just above- get the white king to f6 in time to double attack the g-pawn and capture with the rook protecting g2 at the same time. 9.Rf1 just loses time white doesn’t have to set up this plan. Now black has a problem if he advances on the g-pawn…..
9. ………….Kg4 (alternatives in a moment)
10. Rc5!
It would be an error to play 10.Kf6 immediately: [10.Kf6? Bd5! 11.Rc2 Kg3=]. 10.Rc5 both attacks the g-pawn and prevents Bd5:
10. …………Kf4 (what else?)
11. Kf6 g4 (else Rxg5 wins)
12. Rc3!
Cuts off the third rank to the black king thereby protecting the pawn from the king……
12. ………….Bd5 (anything better?)
13. g3! Ke4
14. Kg5 Kd4
15. Ra3 Be6 (Bf3 16.Ra4 Ke5 17.Rg4 Bg4 18.Kg4 with a winning K+P vs K ending for white).
I think this is the plan you have to follow in the first position. There are some holes in this analysis, and I will fill them in later, but I have things to do right now that I have put off as long as I can.
I compared my line for all three positions to those in the Nalimov Tablebase, and they are mostly correct, though my work in the Aronian game missed a couple of more tenacious defenses for black, though they eventually ended up in the same basic place- white attacks the black pawn from behind with the pawn left on g2 just to keep it out of reach of the black king. I will fully outline this tomorrow. I still don’t quite understand why the first and second position are so different tactically, but they are.
The Aronian game position- 8/8/4bk2/1R4p1/8/8/5KP1/8 w – – 0 1- is a six-man problem whose solution can be found in a Nalimov Tablebase. Below is the most tenacious defense against best play by white:
1. Kf3
White has 11 winning moves here, but this one is the shortest win at 47 moves total to mate. 1.Ke3 is almost as good at 48 moves. White draws with the following moves Ke1, Kg1, g3, g4, and the trivial Rxg5. The really interesting thing to me are the draws after Ke1 and Kg1- I don’t really understand that very well yet.
1. …………..Bf5
As I suspected yesterday, this is the most tenacious defense by one move over Bd7- it controls e4 and g4 for a move.
2. Rc5
A waiting move to get black to move the bishop or the king- for example a move like 2. ….Bb1allows Kg4 or Rc6 which shortens things considerably. A move like 2. ….Bd3 keeps the option open for a check from e2 to foil Kg4. Black’s longest defenses here are 2. …Bd3 and 2. ……Kg6 (which I covered yesterday). Let’s follow Bd3:
2. ……………Bd3
3. Ke3
This move basically plays itself- especially after I had thought about this problem all day yesterday- the goal is to get up through d4 using other threats to do so.
3. ……………Bf5 (keeping e4 closed to the king)
4. Kd4 Be6 (or Bg4)
5. Ke4
Double controlling f5 for the moment.
5. ……………Bd7
Easy defense to find in retrospect. Prevents Rc6 for a move.
6. Kd5
I don’t yet fully understand why white has to pursue this line further up the board compared to the 2nd position Susan gave- I have tried to reduce it down to something understandable, but have failed so far. In other words, I can’t figure out exactly where the extra move white has to make played its role in the solution to the second position.
6. ……………Be6 (or Ba4)
7. Kd6 Bb3
And we have arrived at a position I found yesterday, but with a different move order. Not so bad on my part, though I better understand the other moves possible now having looked through some of them in detail in the tablebase. In any case, my thinking yesterday was a check on the f-file, but I figured out that was worthless, but I think the threat is necessary, and Nalimov tells me that Rc1 and Rc8 are the moves here for white. Since I had already looked at Rc1 yesterday, let’s follow Rc8:
8. Rc8 Kf5
It is this or white plays Rf8+ followed by Ke6 after black retreats to g6 (which is better than Kg7). In other words, white still gets to where he is going, but it takes longer if black keeps the option open to getting at the g-pawn.
9. Ke7
White basically loses a move or two with the safe rook moves on the c-file, draws with every other king move except for the one move that gets the king closer to the black g-pawn. All rook moves along the 8th rank also draw because black basically gets to the white g-pawn before white can win the black g-pawn with the rook and get the pawn to g3 so black can’t double attack it.
9. ……………Kf4
Yesterday, I could only see Kg4 in the analogous line where the white rook is on c1, but I can now see that was making white’s life much easier because it block the black g-pawn which black can threaten move in some variations. In any case, we have now reached the critical juncture of the ending since white has a single winning move….
10. Rc5!
Like in yesterday’s line, 10.Kf6 is too hasty because black is threatening to double attack the white g-pawn before white is ready to guard it effectively- Rc5 prevents an immediate Kg3 by threatening Rxg5 and it prevents Bd5. We now diverge significantly from the line I found yesterday.
10. …………Bd1 (the alternatives will make sense if you follow this main line)
11. Rc3!
The only move to win. It is the only move that prevents black from playing g4 followed by Kg3.
11. …………Kf5 (other moves are as long or nearly as long, but this line is the most different yesterday’s line)
12. Rc4
Foreclosing a return to the fourth rank for the moment. Now, if the bishop leaves the d1/h5 diagonal, white can play a move like g4+.
12. …………Be2 (here g4 is like yesterday’s line and then below)
13. Rd4 g4
14. g3
And we have reached a very similar position from yesterday, but where black has his pawn better guarded at the moment, but white now has a clear path to winning……
14. ………….Kg6 (keeping the white king away from the pawn the longest)
15. Kf8
Flanking the black king- the threat, of course, are checks on the 6th rank driving the black king towards and then away from the pawn…..
15. …………Kh7
16. Kf7 Bf3
17. Rd2
A waiting move with a mate threat- black is in zugzwang
17. ………..Kh6 (only move to not lose almost instantly)
18. Rh2 Kg5
19. Kg7 Kf5
There really isn’t anything better- if black doesn’t try to get around through e4 and e3, white will just transfer the rook to to the queenside for a check or mate from c5/a5.
20. Rb2 Ke4
21. Kg6
Closing in on the pawn.
21. …………Bd1 (hoping for a mistake)
22. Kg5
The white pawn is safe from Kf3, but that is still the best defense for black….
22. …………Kf3
23. Rd2 Ba4 (by far the stingiest defense since Be2 is met by RxB followed by Kxg4)
24. Rd4 Bc2
25. Rg4
And the rest isn’t so hard- white will guard the pawn from h4 with the king and then run the pawn protecting it initially with the rook and then the king up the h-file.