This can be the least forcing type of threat possible because the defender has a broad range of options to consider. However, the options are not unlimited and the most interesting responses fall into the broad category of counter-attack.
The basic defensive options are very similar to those for defending against check and mate-in-1, with a few additions and expansions. Let's compare the options against checks and mate threats.
When in check, you can:
- Capture the piece giving check
- Block the path to your king
- Move your king
When there is a mate threat, those three options are expanded to:
- Do something to the piece/pieces threating to give mate (pin, deflect, capture).
- Block access to the mating square of either/any of the pieces threatening to give mate, or reposition one of your pieces to be able to block the check.
- Move your king, create an escape square, or move the king to allow a block.
- Defend the mating square.
- Counter-attack the king with the goal of:
WIN - delivering your own mate
DRAW - forcing draw by repetition, stalemate, or
DEFEND - rearranging your pieces to allow one of the other basic defenses listed above.
Defending against an attack by a piece against a piece is very similar to defending against a mate-in-1 threat -- the exact same 5 options are available. The major difference is the much broader range of counter-attack possibilities. Counter-attacking to win against a mate-in-1 threat can ONLY be an attack against the king that starts with a check. Counter-attacking to win against a piece threat does not have to start with a check.
Many authors will say you should first try to "ignore" your opponents threat at first, but I would make two points. First, they are usually talking about broad "attacks" (eg, white's pawn storm on the king side is faster than black's attack down the c file) and not usually in relation to a basic attack by a piece against a piece. Second, when they say "ignore", what they really mean is to create a greater threat...and that is the key.
Counter-attacks must create an equal or greater threat than your opponent's threat. And vice-versa...if you are considering attacking your opponent, look to see if they have an equal/greater attack they can counter with, and calculate the line to the end.
Some of this is pretty easy, like an attack against a pawn can easily be countered by an attack against anything -- from a pawn all the way up to the king. An attack against a minor piece can be countered by an attack against another minor piece, rook, queen, or king. And on up the ladder until you get to an attack against your queen, where the options are pretty limited (you rarely want to "defend" your queen against an attack by a rook or minor piece).
One interesting point to remember is that if you are counter-attacking the same target with a piece of lesser value than your opponent is using (say he attacks your Queen with a Bishop, and you counter-attack against his Queen with a Pawn), that is a GREATER threat than your opponent's if the queens are both defended. If the queens are not defended it is just an equal trade.
But when counter-attacking it is absolutely vital that you calculate, especially when a series of captures is involved (ie, both targets are defended). I would note that most of the world's top players prefer to counter-attack. Play through games of Fischer, Morphy, and Kasparov, and you'll find many games were won because they were incredibly stubborn and chose to counter-attack instead of retreating or passively defending.
So the moral is to make sure you consider the full range of defensive ideas availabe when you are under attack or are considering an attack. These defensive "candidate ideas" should give you a lengthy move list to actually calculate -- then, you will calculate each option to the end, evaluate the final position, and pick the best defensive reply.
Here is one of my favorite examples from a Fischer game in 1968. Fischer had the Black pieces against Matov.
White is preparing to shift his rook to the king-side, and just moved his knight from c3 to a4 attacking Black's queen -- a nice tempo gaining attack on the queen that will allow Matov to get his rook where he wants it. Fischer can't capture or pin the knight, can't block it, and defending the queen doesnt' make any sense, so Matov expected Fischer to retreat his queen to c7 -- the only safe square.
But Fischer was incredibly stubborn and attacked White's queen right back with Nc4. That not only attacks White's queen with an equal valued piece but also discovers an attack against the d4 knight. Fischer found a way to counter-attack with a GREATER threat!
Right away you can see that White can't go ahead with his threat of capturing the Queen because after 1. Nxc5 Nxd2 both of White's Rooks are forked and he'll drop the exchange. He now has to defend, so let's look at the basic defensive options for White. White can capture the knight with 1. Bxc4, but after 1....Qxc4 both of White's knights and the rook on f1 are hanging, and he'll lose a piece. You can't block a knight, and defending the queen doesn't make sense. So White retreated the queen with 1. Qd3, doubling up on the c4 knight and renewing the threat of Nxc4.
Black consolidated with a series of equal trades in the center 1....Qxd4 2. Qxd4 Bxd4 3. Bxc4. So a queen for a queen, and knight for a knight. All's well that ends well, right? If you can visualize that final position, can you find the simple tactic that forced Matov to resign?
Highlight for the answer: [ Fischer played 3....b5 forking the knight and bishop.]