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.