Calculating Forcing Moves: Defensive Idea 2, Part 1 (Block)

When your opponent creates a (real) threat, or you are considering creating one against your opponent, there are five defensive ideas to consider.  We have already looked at three different ways to implement the first defensive idea of going after the attacking piece:  capture the attacking piece, pin the attacking piece, or deflect the attacking piece.  This post will explore the second basic defensive idea of blocking the attack.

The idea here is pretty straight forward -- you put something less valuable on one of the squares between the attacking piece and the piece being attacked -- but there are some interesting subtleties to keep in mind.  When there is an immediate threat on the board, it is often very easy to find specific moves that satisfy this idea.  The search method is simply to look at the squares between the two pieces, and see what pieces/pawns you can place on any of those squares.  Those moves go onto your candidate list to calculate further.

Blocking with similar pieces is more forcing than blocking with pieces that don't attack back, and sometimes you can gain a tempo by blocking this way.  We'll look at an excellent example of this below.

Also, when the threat is not immediately on the board but is on the next move (like a mate-in-1 threat), you can "prepare" to block by rearranging your pieces.  We'll look at an example of that in another post.

The general process is to evaluate the position, identify all threats, and then to use the five defensive ideas to identify specific candidate moves.  Next, calculate each candidate move to the end and evaluate the final positions (material and activity).  As you progress through the candidates, keep in mind the "king of the hill" (KOTH) candidate move to help you pick the best at the end.

Let's start with a simple position to demonstrate the basic concept in the second defensive idea.  White just played Bd2 attacking Black's knight.  Black to move.

3N4/4p3/8/npp2k2/3b4/3P2P1/P2B4/7K b - - 0 1

Let's evaluate the position and then find all of white's threats.  Material is equal, bishops are on the same color, but black's pawn structure is better and his king is more active than white's.  Black has an advantage and should be playing for a win, while white is currently playing for a draw.  White's immediate threat is to capture black's knight with Bxa5.  Let's look at the five defensive ideas to see what candidate moves we find, and then pick the best move.

Idea 1 (capture, pin, deflect):  none.
Idea 2 (block):  searching square by square between the bishop and the knight, we see black can put his bishop on c3, or his pawn on b4.  1...Bc3 counterattacks white's bishop, but it is unsafe and appears to simply lose the bishop, so we'll only consider 1...b4
Idea 3 (move):  the knight has four moves, none of which appear safe.
Idea 4 (defend):  black cannot add a defender to the knight (aside from Bc3, which we already considered).
Idea 5 (counterattack with an equal or greater threat to WIN, DRAW, DEFEND):  an equal threat would be to attack white's bishop or knight, which isn't an option here.  A greater threat would be to attack a rook, queen, give check, or threaten promotion.  1...c4 looks like it might threaten promotion.

The easiest move to calculate is 1...b4, after which neither side has any immediate threats.  Black might try to trap white's knight, or try to promote a pawn, but the immediate threat has been addressed and black has an edge due to his pawn structure and more active king.  This is our KOTH.

Let's see if 1...c4 leads can force anything better for black than our KOTH.  After 1...c4 2. Bxa5 (most forcing reply) black now has 2...cxd3 and 2...c3 but after both moves white can force a blockade and remain up a piece with no chance of black promoting, so then 1...c4 2. Bxa5:

If 2...cxd3 3. Bd2 and white is winning.  Not better than our KOTH.

If 2...c3 3. Nc6 and now the bishop must retreat while also defending the c-pawn, so 3...Bf6 4. Nb4 followed by 5. Nc2, and white is winning.  Not better than our KOTH.

So 1...b4 blocks the attack, and allows black to keep his edge.

Calculating Forcing Moves: Defensive Idea 1, Part 3 (Deflect the Attacker)

When your opponent creates a (real) threat, or you are considering creating one against your opponent, there are five defensive ideas to consider.  We have already looked at two different ways to implement the first defensive idea:  capture the attacking piece, and pinning the attacking piece.  This post will explore the third and final way to implement the first idea (of doing something to the attacking piece) by looking at deflection.

The basic idea here is to get the attacking piece to go do something more important than what it is currently threatening.  I think this idea might be more of a counterattack and could be better placed in Idea 5 than Idea 1.  The two questions that come to mind are: (1) are there any positions where deflection can be achieved without creating a greater threat (counterattacking)?; and, (2) how are the counterattacking goals in Idea 5 different?  Perhaps deflection is a sort of a hybrid of 1 and 5.  I'm not quite sure yet.

The general process is to evaluate the position, identify all threats, and then to use the five defensive ideas to identify specific candidate moves.  Next, calculate each candidate move to the end and evaluate the final positions (material and activity).  As you progress through the candidates, keep in mind the "king of the hill" (KOTH) candidate move to help you pick the best at the end.

Black just played Na7 discovering an attack against the White queen.  White to move.

2rr3k/n2p1R2/1pb5/p5pN/Q1Pp3p/PP6/6PK/8 w - - 0 1

Let's first evaluate the position, and then identify black's threats.  Each side has a rook and a knight, white has four pawns to black's six, so the material balance is a queen vs rook, bishop and two pawns.  Black is up one point, but the black king is weak and white's rook and knight are active.  Black has a passed pawn but that seems irrelevant at the moment (the white king can step into its square with Kg1 if needed).  Black's threat is to capture the queen on a4 and then the c4 pawn (1. (skip) Bxa4 2. bxa4 Rxc4), which would leave black ahead a rook a three pawns which is winning .  Let's see if any of the five defensive ideas allow white to keep his queen.

Idea 1 (capture, pin, deflect):  white can capture the bishop (Qxc6).  White cannot pin the bishop to something of equal or greater value.  To find the deflection in this particular position (and perhaps in all cases?) we need to look at counterattacking options, which we'll do below in Idea 5.
Idea 2 (block):  none
Idea 3 (move):  The queen has three moves (Qxa6, Qb5, Qb4) all of which appear to fail, but we might return to these moves out of desperation if other candidates don't save the queen.
Idea 4 (defend):  White cannot add another defender to the queen.
Idea 5 (counterattack with an equal or greater threat to WIN, DRAW, DEFEND):  an equal threat would be to attack black's queen which isn't an option here.  A greater threat would be to attack the king, gaining a tempo to either with the game, force a draw, or use one of the other defensive ideas.  White has two checks (Rh7+ and Rf8+) both of which seem to fail. White can create a mate in 1 threat with 1. Nf6 (an Arabian Mate pattern).

That gives us seven candidate moves to calculate (Qxc6, Qxa6, Qb5, Qb4, Rh7+, Rf8+, and Nf6).  Where to start?  With the most forcing, of course.  The most forcing replies are the mate threat and capturing the bishop (in that order), so let's start with 1. Nf6:

What is white's threat?  After 1. Nf6 (skip) 2. Rh7#  I do not see any other threats for white.  So now black needs to find a defense to white's mate in 1 threat.  Let's look at the five ideas now for black:

Idea 1: Black cannot capture the rook or knight, and cannot pin the rook to the white king.  No deflections.
Idea 2: No blocks.
Idea 3: The black king is stalemated, and cannot move or create an escape square.
Idea 4: Black can defend the mating square on h7 by playing 1...Be4.
Idea 5: Black has no checks, so no counterattacking possibilities.

Black has ONLY one defensive candidate move, so after 1. Nf6 Be4:

Black now has zero threats that I can see.  Therefore white is free to play any move he wants, keeping in mind he is down one point.  Now 2. Rh7+ fails because h7 is defended twice, so let's look at the obvious capture and see if black has any refutations, so after 1. Nf6 Be4 2. Nxe4:

White is now up two points, and has the threat to return his knight to f6 again threatening mate on h7, which gives black two tempos to defend.  Black has zero checks, and zero captures (Rxc4 looks pretty bad).  He could simply attack the rook with 2...Kg8 which also addresses the mate threat, but white simply has too many options, and at this point I would be comfortable as white saying 1. Nf6 is safe.  It saves the queen AND puts white ahead materially (by two points).  This is our KOTH candidate move.

The only other move worth considering is simply capturing the bishop so that white can try the Arabian mate again.  So let's see if black can stop the mate after at 1. Qxc6:

White is now ahead materially, and has three threats: capture a pawn (2. Qxb6), a mate in 2 by force (2. Qh6+/Qh7#), and Arabian mate in 2 (2. Nf6/Rh7#).  Black can restore his material lead and address all three threats with 1...Rxc6, defending the f6 square, and leaving black ahead an entire rook.  If white continues with 2. Nf6, black can simply capture with 2...Rxf6 3. Rxf6 Nc6 (blocking to protect the b6 pawn), after which white has no threats and black is now ahead a knight and two pawns, which is winning.  That means our KOTH is still 1. Nf6 Be4 2. Nxe4.

The search strategy of looking for counterattacks (from the Idea 5 basket) is what allowed us to find the mate-in-1 threat which forced white to divert the attacking piece (bishop) away from the queen.  However, since the end-result was in the Idea 1 basket of "somehow dealing with the attacking piece", I'm going to leave this idea in Idea 1 for now.  After looking more deeply at counterattacking positions I might come back to this, but for now my sense is that while the search strategy is from Idea 5, the end-state is Idea 1.

But what is more important, categorizing by search strategy or end-states?  Hmm...

Calculating Forcing Moves: Defensive Idea 1, Part 2 (Pin the Attacker)

When your opponent creates a (real) threat, or you are considering creating one against your opponent, there are five defensive ideas to consider.  We looked at the first defensive idea a little bit here (capture the attacking piece).  This post will explore the first idea a bit more by looking at pinning the attacking piece to something of greater value.  I'll start out with a simple position, and will add more complex positions over time.

The general process is to use the defensive ideas to identify specific candidate moves.  Next, calculate each candidate move to the end and evaluate the final positions (material and activity).  As you progress through the candidates, keep in mind your "king of the hill" (KOTH) candidate move to help you pick the best at the end.

The first defensive idea is to do something to the piece creating the threat: capture, pin, or deflect it.  Of course when you are in check you have no time to pin or deflect the piece.  But any other kind of threat gives you more time and therefore more options.

White just played Ne5 attacking the pinned black bishop.  Black to move.

Let's first evaluate the position, and then identify white's threats.  Each side has four pawns, one rook, but black has two bishops vs a knight.  Black is currently winning, and white is playing to draw (equalize).  White's threat is to capture the bishop on c4 (the count is 2-1:  2 attackers, 1 defender), which would make the material balance equal again.  Let's see if any of the five defensive ideas allow black to keep his material advantage.

Idea 1 (capture, pin, deflect):  black cannot capture the rook or the knight.  He can't deflect the rook or knight.  The knight and king are in alignment on the dark diagonal, which could mean there is a pin, so we'll look at Bd6.
Idea 2 (block):  none
Idea 3 (move):  The bishop cannot move and defend the rook at the same time, nor can it move and create an equal/greater threat (losing the rook).
Idea 4 (defend):  Black cannot add a defender to the bishop.
Idea 5 (counterattack with an equal or greater threat to WIN, DRAW, DEFEND):  an equal threat would be to attack black's rook, which the bishop can do with Ba3 or Bh6.  A greater threat would be against the king, but black has no checks.

That gives us only three candidate moves to calculate (1...Bd6, 1...Ba3, 1...Bh6).  1....Bh6 seems to be the most forcing because of the capture-check, forking all three of white's pieces:  the king, rook, and knight.  Then 1...Ba3 is next because it is attacking the rook, and we'll look at 1...Bd6 last.  Let's look for white's possible refutations after: 1...Bh6:

Let's see if black's move created any threats by skipping white's move, so 1...Bh6 2. (skip) Bxf4+

White cannot capture the bishop, he has one block (g3), and can move to h3, h1, and g1.  Let's look at the more forcing 3. g3 first, so 1...Bh6 2. (skip) Bxf4+ 3. g3, and now black can simply capture the rook on c1 with 3...Bxc1 (as he could also do after any move by the white king on move 3).  White can now trade bishop for knight on c4 with 4. Nxc4 Rxc4.  So does black's move 1...Bh6 contain a threat?  Yes, the capture-check on f4 winning the rook and a pawn.  Therefore, white should defend against black's threat.

White cannot capture, pin, or deflect the h6 bishop.  He cannot block it.  He could move the f4-pawn out of the way of the attack, but it is pinned to the c1 rook.  He can defend the pawn with g3, Rxc4, and with two knight moves (both of the knight moves clearly fail).  He can counterattack with Nxc4 possibly winning the bishop, per the original threat.  That gives white three defensive candidate moves.  Let's start with the most forcing (Rxc4) since it does three things:  captures a piece, threatens the rook, AND defends the f4 pawn.  Let's see that is enough to refute black's move, so if 1...Bh6 2. Rxc4:

Now 2...Bxf4+ fails to 3. Rxf4 because now White is the one up an entire piece!  Black could exchange rooks with 2...Rxc4 3. Nxc4 and after Bxf4+ black is now up one pawn which is worse than when he started the variation (being up an entire piece).  That means 2. Rxc4 refutes black's first move (1...Bh6).

Black's second most forcing idea was to counterattack with a greater threat (attacking white's rook), and the candidate was 1...Ba3:

Black's threat is to capture the rook, which (per the five defensive ideas) white can easily refute by moving the rook (idea 3) and capturing the bishop at the same time with 2. Rxc4.  Material is now equal, which is not good for black.  Black can only make more equal trades now.  That means 2. Rxc4 refutes black's 1...Ba3.

That just leaves black's last candidate move from idea 1 (pin the attacker), which is also black's last hope to hang on to his material edge and avoid equality.  After 1...Bd6:

Does black now have a threat?  None that I see.  White's knight on e5 is attacked once, and defended once.  Since black is up an entire piece, his most simple plan is to make equal trades of pieces.  White wants to avoid piece trades, and instead trade pawns.  That's a slightly more advanced topic, and I would not categorize black's Bxe5 as a "threat", just more of a plan.  Since there is no threat, the question then is whether 1...Bd6 actually defends the c4 bishop?  Let's look for a refutation by white, looking at his most forcing moves first (the two captures on c4: Rxc4 and Nxc4), so after 1...Bd6 2. Rxc4:

Black now has the simple remove the defender tactic 2...Bxe5 and now if 3. Rxc7 Bxc7 and black stays a piece ahead.  If 3. fxe5 Rxc4 and now black is a rook ahead.  Neither of which are any good for white, but of the two Rxc7 is less bad.  Let's see if white's other move 2 choice is any better, so after 1...Bd6 2. Nxc4:

Material is now equal, however, it is black's move and he has the capture-check 2...Bxf4+ forking the king and c1 rook.  This was the key behind the black's defensive idea -- the white knight is in fact pinned to the f4 pawn.  After any move by white, black will capture the rook.  In this forced line black is an entire rook ahead instead of just a piece ahead.  That means this variation is worse for white than the earlier line:  1...Bd6 2. Rxc4 Bxe5 3. Rxc7 Bxc7.

In this case our KOTH came at the very end, and neither of black's first two candidate moves were good enough to qualify at his KOTH.  For black, his first two candidate moves allowed white to gain material back, thus refuting both candidates.  In his third and final candidate, black does not win any material but is able to keep his piece, and thus his winning material edge.

For white after 1...Bd6, he is left having to pick from several bad forced variations, all of which still leave black ahead an entire piece.

The key idea for black in this position was to deal with white's threat to equalize (by capturing the pinned bishop), and here black's ability pin one of the attackers is what allowed black to hold his edge.

Next we'll look at the idea of diverting the attacker (the other part of defensive idea 1), which crosses into the counterattacking theme.

Calculating Forcing Moves: Defensive Idea 1, Part 1 (Capture the Attacker)

When your opponent creates a (real) threat, or you are considering creating one against your opponent, there are five defensive ideas to consider.  This post will explore the first idea starting out with a simple position, and I'll add more complex positions over time.

The general process is to use the ideas to identify specific candidate moves.  Next, calculate each move to the end and evaluate the final positions (material and activity).  As you progress through the candidates, keep in mind your "king of the hill" (KOTH) candidate move to help you pick the best at the end.

The first defensive idea is to do something to the piece creating the threat: capture, pin, or deflect it.  Of course when you are in check you have no time to pin or deflect the piece, but any other kind of threat gives you more time and therefore more options.

Black just played Bd8 to block white's d-pawn and attack the queen.  White to move.

In this postion white is up one pawn (a passed pawn), but black is threatening to capture white's queen, giving check and attacking white's h4 bishop.  Let's review the five ideas to identify actual candidate moves, and then calculate each candidate and pick the best one.

Idea 1 (capture, pin, deflect):  Qxd8; can't deflect or pin the bishop to anything of equal/greater value (the queen or king).
Idea 2 (block):  none
Idea 3 (move):  Qf5, Qe5, Qd5, Qf4, Qe3, Qd2
Idea 4 (defend):  Does not make sense to defend the queen here.
Idea 5 (counterattack with an equal or greater threat to WIN, DRAW, DEFEND): an equal threat would be to attack black's queen; a greater threat would be to attack black's king.  Rd6 attacks the queen; h6 might be interesting since it threatens a capture-check.

That gives us nine candidate moves to calculate.  Let's start with white's most forcing move first, and look for black's possible refutations: 1. Qxd8:

White is now up a bishop and a pawn, and is threatening to win black's rook with 2. Qxg8+ Kxg8 (only) 3. d8=Q+.

1...Rxd8 2. Bxd8.  Material is now equal (R/B/PvsQ), however, white's threat is to promote his pawn to a queen in two moves, leaving white up an entire R/B.  Black has no way of stopping the pawn from promoting without giving up his own queen.  Black should reject 1...Rxd8.

A quick search for other candidate moves for black yields nothing:  1...Qh6+ allows the simple block 2. Qg5.  1...Qa8 (defending the rook) allows the simple 2. Qxa8 (any) 3. d8=Q.  1...Qe6 (again defending the rook) still allows 2. Qxf8+ (any) 3. d8=Q.

This makes 1. Qxd8 our KOTH.  Now, in an actual game with time controls white can stop calculating at this point because our KOTH forced the win of a lot of material:  capturing the attacker with 1. Qxd8 simply wins a bishop (at least) by complete force.  Black has no moves to refute it.

However, for the sake of this exercise let's look at white's other defensive candidate moves.

There are six square the queen can move to in order to escape the attack.  However, the bishop on h4 is hanging so any move must either defend the bishop or create a greater threat.  The only move that comes close to that is 1. Qd5 (we can reject the other "move" candidates):

White's threat is to capture black's queen.  In a more complicated position, we could also apply the same five defensive ideas here to consider how black can best respond to white's threat.  But here black's best defensive idea is also to capture the piece, which refutes white's move:

1...Qxd5 2. Rxd5 Bxh4.  Now black has two defenders on d8, and can rather simply move his king over, capture the passed pawn, and comfortably be a full bishop ahead.  Since this evaluation is much worse than our KOTH, we can reject 1. Qd5.

There are two counterattacking moves that appear to create an equal or greater threat.  Let's start with 1. Rd6:

1...Bxg5+ 2. Bxg5 Qxd6.  Completely refutes 1. Rd6, so no need to look any further.  Since this evaluation is much worse than our current KOTH, we can reject 1. Rd6.

The second counterattacking idea 1. h6:

Is an interesting idea but the "threat" to play the capture-check on g7 is too slow.  White's biggest threat is still to capture on d8.  So 1. h6 simply allows black to avoid losing his bishop with the defensive idea of pinning the attacker (white's queen) to something of greater value (the king) with:

1...Qxh6 2. Qxh6 gxh6 and now white has lost a pawn (so equal material), and can only initiate equal trades.  Now white's d6 pawn will likely be captured.  So black need not look any further at defensive replies to h6 since he is now at least equal.  Since this evaluation is much worse than white's current KOTH, we can reject 1. h6.

That's it.  The goal is to do this calculation in your head in seconds.  Many of you probably found Qxd8 in a couple seconds, and did not even consider other replies for white.  Or maybe you considered other replies for white first, and then looked at Qxd8 out of desperation.  Future positions will be more challenging, I promise!

Assessing the Threat

In previous posts I discussed the process of calculating forced variations, which begins by first finding all threats.  After every move your opponent makes, stop and look for ALL threats your opponent has created.  If you find one, keep looking for more.  For example in the below position, how many threats did white's move Qe4 create?

White has two threats:  the mate threat (Qxh7) and the capture on d4 (Qxd4).  The mate threat takes priority, but ideally black would like to find a move that prevents mate while also defending his bishop.  In subsequent posts we'll go through the calculation process to find black's best response.  For now though let's just focus on identifying and prioritizing the threats.

Some positions are more complicated, such as the following:

White has two threats --  to mate on f8 (Rxf8), and to play Qe5 creating two new threats for a total of three:  to capture the queen (Qxc5), to mate on g7 (Qxg7#), and to mate on f8 (Rxf8) if the queen moves.  The mate threats are greater than the threat to the queen.  Here it does not matter whose turn it is to move and we're not calculating defenses yet.  We're just looking for all the threats we can find.

It is also very important when you are assessing the threats that you take time to make sure it is a real threat.  To do that you need to calculate a bit.  The trick I recommend is to skip your turn, and allow the "threat" to play out in your mind.  At the end of the line you can ask yourself what you could do with an extra move (the one you skipped).

Take this postion for instance.  White just played Nf3.  Find and prioritize white's threats:

One might look at this position and see white's "threat" to play Nxe5, winning a pawn.  But before we start calculating how to deal with that "threat", let's skip our move and visualize the position after Nxe5.  Is it any good?  Has white just won a pawn?  Are we just sacrificing our pawn for some sort of initiative?  Anyone who has studied some tactics should quickly find that black has the immediate queen fork (Qa5+) hitting the king and the now loose knight on e5.  There is no way to deal with the check and defend the knight at the same time, so black wins a knight for a pawn.  Therefore, black does not/not need to address the threat to e5, and can go on with any regular move that doesn't block his queen fork, such as 0-0.

You could also say that the pawn on e5 is tactically defended, but in order to see that you have to allow the "threat" to play out in your mind (unless you already know the pattern, or the specific opening in this case...that all comes through training and experience).

Keep in mind both of these steps as you play:  (1) find and prioritize all threats, and then (2) make sure the threats are REAL!!  Cecil Purdy calls this "recognizing the unreality of their unreal threats".

IM Andrew Martin has a great YouTube video on this topic as well:

And here is a fun position I came across today.  White just played 1. Rd1.  Is 2. Rd8+ a threat?