Wednesday, June 17, 2015

Calculating Forcing Moves: Defensive Idea 1, Part 4 (Restrict the Attacker, Prepare to Capture)

In earlier posts we examined different ways of implementing defensive Idea 1 (do something to the attacker), including capturing, pinning, and deflecting your opponent’s attacking pieces.  Here we’ll look at another very cool way of doing something to the attacking pieces – restriction, and “prepare to” capture.

In a recent blog post on, National Master Jeremy Kane posted a position from an online blitz game where his opponent resigned following a tricky move by NM Kane, and only later did Kane see that his opponent had a winning defensive move (the ultimate blunder, Kane says in the post, is resigning a won position!).

In the following position NM Kane had white and just played 1. Rh1.  Black to move.

1r6/6p1/2pR2Bk/2n1pPp1/p1P1P3/1qQ4K/r7/7R b - - 0 1

Let's evaluate the position, and then find and prioritize all of white’s threats.

Evaluation:  Black is up two pawns and has a powerful outside passed pawn supported by all of his pieces, but his king is incredibly weak and has zero defenders.  Black should win the endgame if he can survive the next few moves.  White’s pieces are very active but his king is also exposed.  White is fighting to draw, and his basic plan is to capture black’s pawns (if he can’t checkmate black that is!).

Threats:  White’s threat is the discovered checkmate 2. Kg4+ or 2. Kg3+ followed by 2…Rh2 (only) 3. Rxg2#.  White’s other discovered check (on the 6th rank) could be useful in gaining tempo if we can find a useful square for the bishop, but is not our priority for calculations.  

Let's look at the five defensive ideas to see what options black has to defend against the checkmate.

Idea 1 – do something to the attacking pieces (the g6 bishop, h1 rook, and h3 king).  We cannot capture, pin or deflect the bishop.  We cannot directly capture the rook, however, we can “prepare to” capture the rook by attacking it (with 1…Ra1 and 1…Qb1; if 1…Qd1 2. Rdxd1 and now black cannot stop the discovered checkmate).  We cannot pin or deflect the rook.  We can restrict the king from moving to g3 (with 1…Nxe4, but that fails to 2. Kg4+), and we can restrict both g3 and g4 at the same time (with 1...Rg2, but that fails to 2. Kxg2#).

Idea 1 has generated two candidate moves.

Idea 2 – block the attacking pieces (the h1 rook from h6).  Black can prepare to block on h2 by adding a second blocking piece (1…Qb2/1…Qc2) but white can easily refute both of those (with the simple 2. Kg3+, then capturing twice on h2 after which white is again threatening checkmate with …Qh3#).  Black can prepare to block with the queen on h5 (with 1…Qd1, but per the above variation that fails).

Idea 2 has generated zero candidate moves.

Idea 3 – move the piece being attacked (the white king).  The black king has zero moves.  We can create one escape square (1…g4+, which just encourages the checkmate 2. Kxg4+ Rh2 (only) 3. Rxh2#).  

Idea 3 has generated zero candidate moves.

Idea 4 – reinforce/defend the mating square (the h1 square).  Since the threat is not to move the rook to h1, but to discover the rook’s attack by moving the white king, there are no moves that defend h1 that we did not already consider above using Idea 1, and we already considered moves that restrict the black king under Idea 1.

Idea 4 has generated zero candidate moves.

Idea 5 – counterattack with an Equal or Greater Threat (of checkmate).  Looking at the EGT chart from earlier we can see that against a checkmate threat, you can only counterattack with a check.  Black has three checks in this position (1...Qxc3+, 1…g4+, are both refuted by 2. Kg4+; and 1…Rh2+ is refuted by 2. Rxh2 and now black cannot stop the discovered checkmate).

Idea 5 has generated zero candidate moves.

This process has generated two specific candidate moves:

The next step is to calculate both candidates.  Since neither move is particularly forcing, let’s try to first refute the apparently bad queen move 1…Qb1:

Black is now threatening checkmate himself (with 2…Qxh1+ 3. Kg3/Kg4 Qh4+ 4. Kf3 (only) Qf4#), and is also prepared to pin the queen (with …Rb3).  Black’s rooks and knight are well-placed (although seemingly uncoordinated) to support his passed pawn too, so I’d evaluate that black is winning here, and that white should be fighting for a draw.  Let’s see if white can prevent the checkmate.

White can capture the queen (2. Rxb1), he has four blocks (2. Qc1, 2. Qe1, 2. Rdd1, and 2. Bh5+/3. Bd1), he can move the rook (2. Rh2, 2. Re1, 2. Rd1, 2. Rc1), he can defend the rook (2. Qf3, 2. Bh5+/3. Bf3), and he can counterattack with a greater threat (check) using the two discoveries, but Kg3/Kg4 fails to the queen capture, and it is not clear where the g6 bishop might go (he only has four squares) that we haven’t already considered.

That gives us 11 candidates to consider.

Let’s start with the most active move (and seemingly obvious refutation of black’s play), the capture 2. Rxb1:

2…Rxb1 (threatening 3…Rb3) and now I like 3. Bh5+ Kh7 (forced; 3…Kxh5? 4. Qf3+, and both blocks seem pointless) 4. Bd1 (defending b3) 4…Nxe4!? 5. Qxe5 (where else?) Nf2+ 6. Kg3 (forced) Nxd1 and even though material is exactly equal (rook, knight and two pawns vs queen) black is again threatening checkmate with 7…Rb3+ 8. Kg4 (forced, both blocks are pointless) Rg2+ 9. Kh5 (only) Rh3#.  That means moves like 7. Qe8 that threaten mate in 2 are too slow, and white now must defend against the checkmate.

White can’t capture, pin, or deflect the rooks or the g5 pawn.  White can prepare to block (with 7. Rd3, or 7. Qe4 to play 8. Rd3 while also attacking the b1 rook, and setting up a discovered check).  White can move his king (7. Kf3, 7. Kg4, 7. Kh3), and he can create an escape square on f5 (7. f6).  White can defend the b3 square (but we already looked at Rd3), and can defend g2 (we already looked at 7. Qe4) but cannot defend h3.  White’s counterattacks must begin with a check because of the checkmate threat, and we have two (7. Qxg7+, 7. Rh6+).

This has generated eight candidate moves for white.  

Let’s start by looking at the most forcing moves first, the two checks.  I don’t see any clear follow up after 7. Qxg7+ Kxg7, so let’s calculate the rook check and see if white can at least pull out a draw, so now 7. Rh6+:

7…gxh6 of black’s three options, the pawn capture avoids the checkmate and the forced draw (if 7…Kg8? 8. Qe8#; if 7…Kxh6 8. Qe6+ forces draw by repetition) but it is not clear where this leads after the obvious follow-up 8. Qe7+ Kg8 (or 8…Kh8).  White has been able to force the black king away from the white king so black’s mate threat is no longer looming, but black has a five point material lead following the rook sac while white’s only plus is the position of his queen unopposed against the black king.

Thinking back to the goals of counterattacking (win, draw, defend), white can threaten mate in one (9.f6), but he can’t capture either of black’s rooks (even though they are both loose) since both light diagonals are blocked by his own pawns. I can see that stalemate is not an option for white because of the mobility of his pawns and king, but he can force a repetition (9. Qe8+).

That gives us two candidate moves for white.

Before bailing out into the draw or looking for more defensive moves, let’s see where the most forcing move leads us after the mate in one threat, 9. f6:

Black cannot capture, pin, deflect, block the queen or pawn, and he can’t move his king to escape.  He can defend g7 (9…Rb7, but that just loses the rook), and black’s counterattacks must begin with a check because of the checkmate threat, and we have three (9…Ra3+, 9…Rb3+, 9…Rg2+).  Of black’s three checks, the most promising seems to be 9…Rb3+:

10. Kg4 (forced) and now it is not at all clear that black can do anything useful with his last few checks.  He could try to defend the g7 mate square with 10…Ne3+ 11. Kh5 (forced) Nf5, but that fails to the simple 12. Qe6+, picking up the knight.

I don’t see a clear defense for black, so we can reject black’s move seven (7…gxh6).  His only alternatives at move seven allowed checkmate or draw by repetition (7…Kxh6 8. Qe6+), which so far appears to be black’s KOTH.

While most of the play in that line was forced for white, white does have another 10 candidate moves to consider at move two.  Do any of them lead to a position that is better than a draw?  We have only considered 2. Rxb1, but we still have four blocks (2. Qc1, 2. Qe1, 2. Rdd1, and 2. Bh5+/3. Bd1), four rook moves (2. Rh2, 2. Re1, 2. Rhd1, 2. Rc1), and two moves that defend the rook (2. Qf3, 2. Bh5+/3. Bf3).

So where do we start with those 10 remaining moves?  Are any of them particularly forcing, or can any of them be quickly rejected as bad.  Scanning quickly – and not really calculating – most of them look bad for white.  The four blocks and the four rook moves all seem to allow black to play 2…Rb3 (with or without check), which does not look good for white’s health…although some appear less bad than the others.  But the two moves that defend the rook are in fact extremely forcing!  Rerouting the bishop to f3 to defend the rook comes with check and relieves white of black’s …Rb3 threat.  However, the more interesting move both defends the white rook AND threatens checkmate in one move!  If there is a refutation of black’s 1…Qb1, this is probably going to be it!  Let’s see if white can get better than a draw by playing 2. Qf3:

The only thing better than a mate-in-1 threat is TWO checkmate threats!  This candidate move does just that with the new mate-in-1 threat of 3. Qh5#, and the mate-in-3 threat of 3. Kg4+/Kg3+ Qxh1 4. Qxh1+ Rh2 5. Qxh2#

It is very difficult to see an obvious defense for black, because what defends against one checkmate seems to encourage the other!  Let’s see what we can find.

We can capture the rook on h1 (2…Qxh1+), and pinning the queen is something that would normally be very powerful but here it fails completely (2…Rb3? 3. Kg4+ Qxh1 4. Qxh1+ Rh2 5. Rxh2+ Rh3 6. Rxh3#).   We can block the queen from getting to h5 (2…g4+) but that just encourages the other mate (3. Kxg4+), and we can prepare to block the mate-in-3 (2…Rbb2) but that does nothing to prevent the mate-in-1.  We cannot move the king, and creating an escape square just encouraged the mate-in-3 (2…g4+ 3. Kxg4+).  We can defend h5 (with 2…Qd1) but that does nothing to stop the other (3. Kg4+).  Our counterattacks must start with a check, and of black’s four checks there are only two we have not yet considered but they both appear to be easily refuted (2…Rh2+ 3. Rxh2; and, 2…Qf1+ 3. Kg4+).  That gives us only one candidate move to consider for black, so let’s see if black can get at least a draw with 2…Qxh1+:

3. Qxh1 looks like the best of white’s three possible replies, and again white is threatening checkmate.  The only move I can find from the five Ideas that addresses the checkmate is the move that prepares to block the check with 3…Rbb2. Now white might have better but he can at least force simplification to a won endgame with 4. Kg3+ Rh2 (only) 5. Qxh2+ Rxh2 (only) 6. Kxh2.

This line after 2. Qf3 is clearly much better for white than the more obvious original move capturing the queen (2. Rxb1), and is a very clear refutation of black’s first candidate move (1…Qb1).

What about white’s other nine candidate moves?  Well, since we already found one reply (of the 11) for white that is clearly winning, black can reject his initial candidate move without further calculation.  Sure, white might have an even stronger reply, but this one refutation is all black needs to see in order to reject his candidate move.  If black were to actually play that move, white could consider using some additional time to look for something even stronger than Qf3, which would be a great situation for white!

So having found white’s refutation, black can reject his candidate move 1…Qb1, and we can update our chart with what we have learned so far.

Let’s see if black can hold on to the position and avoid the loss with his only other candidate move 1…Ra1:  
Black’s threats are now to win white’s pinned queen and h1 rook (both are capture-checks), and checkmate is very likely to follow.  White can capture the queen and the rook, but both moves appear to fail.  For example if:

2. Qxb3 Rxh1+ 3. Kg2 axb3 and now it looks impossible to stop black’s a-pawn from promoting.  Or if instead 2. Rxa1 Qxc3+ 3. Kg4 Qxa1, and black is clearly winning.

White can’t pin either piece.  He can’t block the queen, but he can block the rook (2. Rdd1) but that fails (2…Rxd1 3. Rxd1 Qxc3).  Queen moves along the 3rd rank (due to the pin) all fail.  There are no safe squares for the rook along the first rank, and only one square along the h-file that appears safe (2. Rh2).  He can defend the queen (2. Rd3) but that fails as well (2…Rxh1+ 3. Kg2 Nxd3).  We have already looked at one move that defends the rook (2. Rdd1) which we determined was not good.  That only leaves counterattacks.  We already have one equal threat (against the queen) that we determined is not actually a threat at all, and a greater threat would consist of mate threats or checks.  We have already considered moving the rook to a square that maintains the mate threat (2. Rh2), and it does not look like any of our eight checks get us anywhere.

So that really only leaves one candidate move for white, 2. Rh2:

White is again threatening checkmate in one move (3. Kg3#/3. Kg4#), so let’s again consider the five defensive ideas and see if black can hold on:

Black cannot capture the h2 rook, but he can prepare to capture (2…Rb2, and 2…Rh1 but the latter obviously fails).  Pinning the rook wouldn’t help here, but he can prevent the king from moving to both g3 and g4 (2…Rg1).  He can prepare to block on h5 (2…Qd1, but that fails to stop the checkmate 3. Kg3+ Qh5 4. Rxh5#).  He cannot move his king and creating an escape square (2…g4+) just encourages the checkmate (3. Kxg4#)!  That only leaves counterattacks, which must begin with a check, and there is only one check we have not yet considered (2…Qxc3+) but that also just allows white to checkmate.

That gives black two candidate moves.

Preparing to capture the rook (2…Rb2) just allows the position to repeat and doesn’t seem to make much progress, but we might come back to it if black’s other candidate move fails to impress, after 2…Rg1:

Black’s threat is to checkmate starting with the capture-check (3…Qxc3+ 4. Rd3 (only) Qxd3#).  White can capture the queen, but that just forces checkmate.  He cannot block the queen, and the queen has no safe squares on the 3rd rank.  He can defend the queen (3. Rd3, and 3. Rc2), and can counterattack with a greater threat using the discovered check but where to put the bishop?  Now if Bh5+ black can take the bishop since the white queen can no longer swoop in to deliver checkmate due to the pin (like the earlier lines with Qf3+) and white does not have the discovery on the h-file.  That only leaves three squares (Bh7, Bf7, and Be8) none of which allow the bishop to reposition to a more useful square.

That gives white two candidate moves.

Both look really bad for white.  Let’s start with 3. Rd3:

The natural 3…Nxd3 now threatens checkmate (4…Nf4#).  White can’t capture or pin the knight or the queen.  He can’t block the knight from getting to f4.  He cannot move the king but he can create an escape square by moving his rook on h2, however that fails to Qxc3 (perhaps following a check or capture-check, in case of 4. Rg2 Rh1+ first).  He can defend f4 four ways but the all fail (4. Rf2 Qxc3; 4. Qc1/Qd1/Qxe5 Nf4# (double checkmate)).  Counterattacks must begin with a check, and white has none.

With zero viable candidate replies for white we can conclude that black's 3…Nxd3 refutes white's 3.Rd3, so let’s look at white’s only other candidate move 3. Rc2:

And now simplifying to an endgame looks good enough for black to declare victory after 3…Qxc3+ 4. Rxc3 Nxe4

Let’s see what our final chart looks like:

Conclusion.  So this process has shown us that black has one and only one defense to white’s checkmate threat using two new variations on the first defensive idea of “doing something to the attacker”:  prepare to capture, and restrict.  These two ideas themselves are rather sophisticated and we had to go many ply deep to prove that the first candidate was bad for black.  What I found interesting about the calculation process here was in the refutation of black's candidate move 1...Qb1.  The obvious-looking capture (2. Rxb1) only allowed a draw, but the move that both defended and counter-attacked (2. Qf3) which was not totally obvious to find is what wins for white.  I'm not sure of any other calculation process that would have lead to finding that move!

This is the process you should be able to do mentally:  prioritize the threats, use all five defensive ideas to search for specific candidate moves, calculate each one completely, and then pick the best variation based on the final evaluation.  And now you have two new tools in your defensive calculation toolkit -- preparing to capture the attacker, and restricting the attacker.  It is possible that these ideas only come into play for certain discovered checks (obviously this wouldn't work for discovered checks that are double checks!).


  1. I am not sure, but this post is quite hard to read. Sorry, but I think you should seriously consider making so called "numbers" (pointers) to the specific idea and its parts. For example something like this:

    Idea 1 has generated two candidate moves.
    a) 2. Rd5 Nxd5 and 3.Qh7#
    b) 2. Rxd8+ Bxd8 3. Re8#
    (these above are fictious - just to show what I mean)

    What elements help to clear the explanation? This one for sure: "That gives black two candidate moves". It is a way to a good direction.

    The tables (pictures/charts) are quite useful and I really like these. Maybe you should think about the method HOW to "zip" (pack) the variations into the simple and easy to understand form. At present your GREAT text and ideas.... is extremally hard to break through :(.

    It is an advantage that your explanation is very extensive, but with hundreds of variations most (if not any?!) people just run away... and miss such a great ideas you wanted to share. I hope you understand what I mean. Your work is VERY valuable, but the way you present the material... is quite far from perfect (to say it lightly)

    1. Tomasz - thanks for the reply. I do understand what you mean...I know these posts are very dense and I have tried to make the ideas more accessible with charts and formatting, but the process of calculation itself is not something that has ever been easy to present. Most authors just give lines of variations with no explanation at all. Even if the variations are hard for readers to visualize, I hope at least that the logic of how to choose moves and how to trim branches comes through.

      Ive almost finished this series (just a few more ideas to demonstrate in counterattacking to defend) and I'll see if I can make the next ones more accessible somehow. I do understand your point. Thanks as always for the feedback.

  2. Your ideas are quite well explained. However some of the points of your conclusions are quite hard to comprehend (even if correct).

    Probably it will be a good idea to "cut off" some variations as you can make statements like: "now white draws due to perpetual check, going with the Queen at the squares c6-d6-e6-f6".

    And yes, I got it! You can "cut of the variation" with the astericks behind it * (* - as see the variation in the table). This way your presentation will look much clearer (better).

    BTW. I know how hard is to present the ideas with (many) variations included. I have tried to do that a long time ago, but I quit due to "too messy presentation". I was not able to present is clear enough without bombarding the text with hundreds of variations.