Friday, January 31, 2014

The Vancura Position

So if you've remembered, I issued the following challenge for everyone yesterday:

White to move, can he win?

The answer to this question is: White cannot win, regardless of whose turn to move. The bad position of his rook coupled with Black's active counterpart will guarantee that Black will save half a point with correct play. And yes, this is one of the many examples illustrating the power of active rooks over passive ones.

In fact, this rook endgame position is known as the Vancura Position. It is a draw for Black thanks to the following:

  1. Black's rook attacks the h6 pawn, thus tying White's rook down to its defense.
  2. White's king has no shelter from Black's barrage of rook checks. If the pawn were on g6 instead of h6, then it would be a different story altogether because White can hide his king on h6.
  3. If White tries to push the h-pawn, then Black's rook will just leap to the h-file and continue to tie down White's rook. Then White cannot make any progress as long as Black keeps his rook on the h-file.


If it were Black to move he could just play 1... Rd6, shuffling along the 6th rank and keeping an eye on the h6 pawn. So let's give White the move here:

1. Kg5

Threatening to release the rook from its guard duty with 2. Rb8. Other variations such as 1. Rh7+ Kb6 give White no progress, while 1. h7 Rh6 2. Kg5 Rh1 leads to the draw which we discussed in Point 3.

1... Rc5+

The first of many checks to be unleashed upon the White king

2. Kf6 Rc6+
3. Ke5 

Since 3. Kg7 Rc7+ doesn't achieve anything, White tries to walk closer to Black's rook in order to pick it off...

3... Rg6

... but Black's rook can simply leap along the 6th rank and get out of harm's way

4. Kd5 Rf6 (D)

You can't catch me!

Notice that when Black is not checking White's king, he makes sure that his rook stays on the 6th rank, thus tying down White's rook to defending the h6 pawn. If he feels that shuffling the rook is too boring, he could throw in some variety with 4... Ka7 which would not make much of a difference.

However, Black must be careful not to throw away the game with 4... Rc6?? 5. Rb8+! Kxb8 6. Kxc6 with immediate defeat.

5. Rh7+

Since moving the king or pawn makes no progress, how about checking the king?

5... Kb6

Still no chance! White's rook is still forced to look after the h6 pawn.

6. Ke5 Rc6
7. Kf5 Rc5+
8. Kg6 Rc6+
9. Kg7 Rc7+
10. Kh8 Rc8+ (D)
1/2-1/2

Time to shake hands

White's king cannot escape from the volley of checks, and the pawn can never hope to advance.

The Vancura Position will prove to be a useful building block as we move up the ladder in our investigation of rook endgames.

Sources:
"Silman's Complete Endgame Course" by Jeremy Silman

Thursday, January 30, 2014

Lunar New Year Challenge

Now before any of us gets a hangover from our LNY drinking spree, I am going to issue a new challenge for the upcoming holidays. Look at the following position:

White to move, can he win?

White is a pawn up, and it is only two files away from promotion. However, his rook is in a bad position: According to the Tarrasch rule, having your rook in front of a passed pawn is usually not a good thing. On the other hand, Black's rook is more active (remember the concept of active vs passive rooks!) and hovers around the White pawn like a hawk watching its prey.

All these make it sound like Black has serious drawing chances... or can White save the full point? I'll leave this as a challenge for y'all to try through the LNY break. As usual, if you think you have the answer feel free to comment below.

And also, does the outcome (win or draw) change if it were Black to move instead?

Have fun!

Rook vs Rook + Connected Passed Pawns

Apologies for the long stretch of silence these few weeks, I was weighed down under external commitments so could not find the time to post here. But now since all the rush is over for me, let us continue with what I have promised to show everyone: How to win with a rook + two connected passed pawns.

White to play and win

Now once again, the win is not very difficult once you've got the general idea, but precise play is needed if you're to avoid the many drawing traps which Black can throw at you! Also, do note that knight and rook connected pawns are often the hardest case (which is what we are going to look at now); once you've mastered that, then you will not have too much difficulty with connected central pawns.

The trick to winning this easily is to make sure you keep your pawns advancing together so that they can protect each other; don't let one pawn charge forward on its own only to get mowed down by machine-gun fire! The king must also stay close to the pawns, both to escort them and to use them as protective cover against enemy rook checks. Who says teamwork isn't necessary when playing chess?



1. Kh3

Stepping up to support the pawns

1... Kf6
2. g3

Of course 2. g4 is possible but it is always good to keep the g4 square open for the king, in case he needs some shelter from enemy rook checks.

2... Rf1

Similar to the Philidor Position (I hope that rings a bell!), Black threatens to lay down a barrage of checks from the back rank, and this is one of the many drawing threats which White must prevent. Another variation is 2... Ra4 3. g4 Ra1 4. Rf5+ Kg7 5. Kh4 Rh1+ 6. Kg5 leading to similar gameplay which we will encounter later on in the main line.

3. Kg4

This move serves two purposes: White uses the g3 pawn as protective cover against Black's checking threats, and also prepares to push back the Black king.

3... Rf2

Also possible would be 3... Ra1 4. Rd6+ Kg7 (4... Ke7 5. Rb6 Ra4+ 6. Kg5 Ra5+ 7. Kg6 and the White king can safely escort the h-pawn up to promotion) 5. Kg5 Ra5+ 6. Kh4 Ra4+ 7. g4 going back to our main line analysis

4. Rd6+ Ke7
5. Ra6 Rc2
6. Kh4 (D)


A shelter for the White king

Once again notice that White can use his g-pawn to shield his king from checks: 6... Rc4+ 7. g4 or 6... Rh3+ Kg4

6... Kf7
7. g4 Kg7
8. h6+

After 8. g5? White will have no cover for his king, and for Black that means... UNLEASH THE BARRAGE!!!! (8... Rc4+)

Another possibility for White will be 8. Ra7+ Kh8 (8... Kh6?? leads to 9. g5#, while after 8... Kf6? 9. g5+ Kf5 10. Rf7+ Ke6 11. Rf6+ Ke7 12. h6 Rh2+ 13. Kg4 Rg2+ 14. Kh5 Rh2+ 15. Kg6 White has sought shelter from the enemy rook, and Black's king is powerless to stop either pawn from promoting) which will return to our main line.

8... Kh7
9. Kh5 Rc5+

By now, the practice of using the pawn to shield your king from enemy checks should be familiar to y'all.

10. g5 Rb5

Keeping the pawn pinned; 10... Rc7? loses faster with 11. g6+ Kg8 12. Ra8+

11. Ra7+ Kh8

The other variation is 11... Kg8, where playing 12. h7+?? will be a mistake because of 12... Kh8 13. Kh6

Black to move, draw!

13... Rb6+ 14. g6 Rxg6+! 15. Kxg6 with a stalemate. This stalemate threat must be avoided at all costs!

The correct response to 11... Kg8 should be 12. Rg7+  12... Kh8 13. Re7 (and NOT 13. Kg6?? Rxg5! 14. Kxg5 with a draw) which returns to our main line.

Let us now return to our main line:

A critical moment

12. Re7!

Looks weird? But if you have been following me through the past few articles this should be familiar: It is similar to the "building a bridge" maneuver in the Lucena Position!

To elaborate further, the reasons behind this move are as follows:

  1. White wants to bring his king to f7, where the rook on e7 shields him from any 7th rank checks.
  2. If White's king is forced to f6, then 6th rank checks can be blocked with Re6 (building the bridge!).
  3. Once White can get his pawn to g6, the threat of back-rank mate will force Black's rook to fall back onto the back rank. Once that happens, White's king can march to f7/d7 and force a trade of rooks. The resulting king + connected passed pawns vs king should be an easy win thereafter.
Any other move does not fulfill these 3 purposes; for example after 12. Rd7 Rb8 13. g6 (13. Kg6 Rb6+ 14. Kf5 Rb5+ 15. Kf6 Rb6+ and White cannot hope to reach the 7th rank without hanging his g pawn) 13... Rb5+ 14. Kg4 Rb4+ 15. Kg5 Rb5+ 16. Kf6 Rb6+ 17. Kf7 Rb8 White will still have to play 18. Re7 anyway (and NOT 18. g7? Kh7 with a hanging h-pawn, or 18. h7?? Rf8+ 19. Ke6 Rf6+ with an inevitable draw) in order to save the game.

12... Rb8

The other variation will be 12... Kg8 13. Kg6 Rb6+ 14. Kf5 Rb5+ 15. Kf6 Rb6+ 16. Re6 (building the bridge!) 16... Rb8 17. g6 Ra8 18. h7+ Kh8 19. Kg5 transposing back to our main line.

13. g6

And once again not 13. h7?? where after 13... Rb7, 14. Rxb7 leads to stalemate while moving the rook away allows 14... Kxh7 with an upcoming Philidor Position and a subsequent draw. By now, we should all be aware about the dangers of pushing h7 too hastily, due to the many stalemate tricks that the Black can throw at us. The lesson learnt from here is this: Only push the pawn to h7 once you're absolutely sure the other side cannot use any sacrificial stalemate traps!

13... Rb5+
14. Kg4 Rb4+
15. Kf5 Rb8

If Black insists upon more checks with 15... Rb5+ then White simply marches his king to the sheltered 7th rank: 16. Kf6 Rb6+ 17. Kf7

16. Ke6 (D)

Patience is a virtue!

The threat of back rank mate has forced Black's rook to retreat to the back rank. Now, White's plan will be to force a trade of rooks and simplify the position into a winning pawn endgame. In this case, the threat is Kd7 followed by Re8+.

16... Ra8
17. Rd7

Black's last move unveiled the possibility of 17... Ra7+ which would follow should White play 17. Kd7. Thus White's rook gives extra space for the threat of Ke7 followed by Rd8+ forcing the exchange of rooks.

Now, the tempting 17. Kf7 gives Black the stalemate trick of  17... Rf8+, which will manifest after the bullheaded 18. Kxf8??. Fortunately, after 17... Rf8+ White can still save his point with 18. Ke6. 

17... Re8+
18. Kf7 Rg8

This time Black will not want to play 18... Rf8+ because of 19. Ke7 followed by 20. Rd8 (and another forced rook trade!)

19. g7+ Kh7
20. Re7 Ra8

Of course 20... Kxh6 falls prey to 21. Kxg8

21. Re8 Ra7+
22. Kf8 (D)
1-0

Time for Black to resign

There is no way to stop the promotion of the g-pawn, so the game is as good as won for White.

...

Looks too long and drawn-out? Let's sum up the general ideas behind winning this endgame:

  •  As the stronger side, make sure that both your pawns advance together; don't allow one pawn to perform a one-man show and botch up the entire operation.
  • Use the king to support the pawns, and use the pawns to shelter the king from enemy rook checks. Teamwork is necessary!
  • Use your rook and king to slowly push back the enemy king (by cutting off files with the rook) so that the pawns can advance safely.

When the pawns have advanced to the 6th rank or so, and the enemy king is stuck in a corner, keep in mind the following tips:

  • Using your rook to "build a bridge" on both the 7th and 6th ranks is essential to shelter your king from those pesky rook checks
  • When your king has safely made it to the 7th rank, the threat of back-rank mate will force the enemy rook to retreat to the back rank. When that happens, the most straightforward plan will be to force a rook exchange and simplify the endgame to an easily winnable position
  • Watch out for the sacrificial stalemate tricks! In this case, only push your pawns to the 7th rank once you're absolutely sure you have avoided these traps!

And thus the ways for you to mess up this endgame will be if: (1) You blunder your pawns/rook (2) You destroy your king's shelter by letting your pawns advance too far, thus exposing your king to an endless barrage of checks, and (3) If you have advanced far down the board and hastily push your pawns to the 7th rank without taking into consideration any possible stalemate tricks that the enemy can throw at you.

To fully familiarize yourself with this position, it is good to read through the summary and go through the variations again; and keep in mind that like all other endgames, patience is always a virtue!

And if you crave more challenge, you can try to apply this new-found knowledge to the position below. But since connected-knight+rook pawns are often more difficult than connected central pawns, you shouldn't find it too much of a problem!

Connected central pawns: White to play and win

Sources:
"Silman's Complete Endgame Course" by Jeremy Silman

Monday, January 13, 2014

Challenge yourselves: Rook vs Rook + Connected Passed Pawns!

So we shall return to our journey into the mysteries of Rook Endgames... and now let's see the following position:

White to play and win

White is two pawns up, and they're connected passed pawns! This is an obvious win for White; but as I said, all rook endgames can be tricky. In this case, White can win but he must watch out for the many stalemate tricks that Black can throw at him.

Once again I'll leave this as a challenge for y'all to try out. Once you've figured out the general winning strategy (and how to avoid those pesky stalemate traps), feel free to comment below. We'll go through the method sometime later in the year.

Oh and by the way... I deliberately used knight and rook connected pawns because they're the hardest example. If you're able to master the winning strategy behind this, then winning with central connected pawns should not be much of a problem.

Have fun!

Friday, January 10, 2014

CCA fair presents!

Having been giving out so many presents to the new Year 1s it doesn't feel right to leave y'all out. So here's the 4 best puzzles from the 20 that I have chosen to display during the CCA fair. Have fun!

White to move and mate in 2

White to move and mate in 2

White to move and mate in 2

Finally, if you thought mate-in-ones were child's play, then try your skills at the following puzzle by Leonid Kubbel, where you have to find... a mate in one!

White to move and mate in 1

Monday, January 6, 2014

Queen vs 7th rank pawn

So as promised earlier I'll go through the answer to the following position. In fact, from today's discussion I'm glad to see that many of you have found the solution on your own; nevertheless, for the benefit for those who were not around, I'll show everyone the winning strategy again.

White to play and win

White can win over here (cos he's a Queen up!), and in fact the concept behind the winning strategy is in fact very easy. But be prepared: The process will be long and tedious!

What do I mean? Let's take a look: Black's pawn is on the verge of promotion, so White's immediate task will be to find a way to stop and capture the pawn. To do this he must get both his king and queen close to the enemy pawn; the problem is that as long as White's Queen is not checking Black's king, Black will get the opportunity to queen his pawn and turn the game into a draw. UNLESS.

Unless White can force Black's king to step in front of his pawn, in which the pawn cannot queen even if White does not perform a Queen check! And this is the basic concept behind winning this position: White must keep checking Black and force his king to step in front of his own pawn. When that happens, the White king can then move one step closer to the pawn; after Black's king steps out, the entire process repeats itself until the White king is close enough to capture the pawn.

So that was what I meant when I said the method is easy but tedious! Let's see an example of how the game can proceed:

1. Qd6+ Ke3

2. Qg3+ Kd2

Any other move (e.g. 2.. Kd4??) and White plays 3. Qe1, forever stopping the pawn.

3. Qf2 Kd1
4. Qd4+ Kc1
5. Qe3+ Kd1
6. Qd3+ Ke1

7. Kb7

With Black's king in front of the pawn, White can now move his king one step closer; after the Black king steps out again, White simply repeats the process. You can see the entire variation in the KnightVision viewer:



Now what if I shifted the coordinates of Black, and placed the pawn on the f-file instead? Once again it's great that many of you pointed out that it was a draw; for those who are still not sure, here's why!

White to move, draw!

Suppose White tries to win with the same method as explained earlier:

1. Qe5+ Kf3
2. Qf5+ Kg2
3. Qg4+ Kh2
4. Qf3 Kg1
5. Qg3+ Kh1!


And now you see why: If 6. Qxf2 the game ends in stalemate, while 6. Qf2+ Kg1 simply repeats the position. White can now no longer get Black to block his own pawn because of the stalemate threat!

In fact, shifting the pawn to the side of the board (ah, rook pawns!) also create a drawn position, but I guess I'll leave the proof to those of you who want to challenge yourselves.

White to move also draws

And a final note: While the two positions which I have shown above are draws, there are in fact a few exceptions where the stronger side can force a win; but I'll not show them here right now!

Source:
"Silman's Complete Endgame Course" by Jeremy Silman

Friday, January 3, 2014

Can you win this?

While y'all are still drunk from yesterday's orientation, let's sober up again with a short diversion from our discussion on rook endgames. Take a look at the following position below:

White to move

White is a Queen up, so he should win easily, right? And yes-- White can win in this position, but the method is not as straightforward as that of a conventional queen mate. Black's pawn is on the verge of promotion, so be careful!

Here's the twist: We're NOT going to learn the winning method for White right now. I'm going to let y'all try to find the winning strategy by yourselves-- once you've figured it out, feel free to comment below! I'll go through the position sometime later in the school year, and how to win it.

And if you've found out the winning method, then congratulations-- your reward for all the hard work you've put in is... more work. Look at the position below:

What happened!?

Nothing happened; I just displaced the Black king and pawn by one square, that's all! Can White still win here? (Assume it's still White to move)

Once again, if you've figured out the answer, feel free to comment below. I'll go through both positions later on when we've time.

Have fun!