Decoy into fork (3 moves)
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Explanation
The following diagrams illustrate the most common ways to decoy a piece into a fork:
In the first diagram, White can lure the queen into a knight fork by trading rooks: 1.Rxh4+ Qxh4 2.Ng6+ Kg7 3.Nxh4.
The second diagram shows that this still works with a decoy. White can sacrifice the exchange to lure the queen into a knight fork: 1.Rxh4+! Qxh4 2.Ng6+ Kg7 3.Nxh4.
In the third diagram, the rook sacrifices itself on an empty square. The decoy still works: 1.Rh4+! Qxh4 2.Ng6+ Kg7 3.Nxh4.
Decoy is often combined with deflection, as illustrated by the fourth diagram. Initially, the queen guards the square where the fork is going to happen. The decoy not only lures the queen into the knight fork, but it also lures the queen away from guarding the square where the knight gives the fork: 1.Rh4! Qxh4 2.Ng6+ Kg7 3.Nxh4.
Examples
White can sacrifice the exchange with 1.Rxf6+. Recapturing with 1...Kxf6 lures the king to f6, where it can be attacked with the fork 2.Ng4+, giving check and attacking the rook on e3 at the same time. After capturing the rook, in the end White has won a knight and is a knight up in a winning endgame.
Sometimes a decoy can be combined with additional motifs:
The queen on b8 is protecting the knight on d6, and the square e8. It is overloaded, and White can win with 1.Qxd6!, combining decoy and deflection. After the queen recaptures with 1...Qxd6, it is deflected away from protecting e8, and also decoyed to d6. White can then win the queen back with the royal fork 2.Ne8+, having won a knight in the end. This combination of decoy and deflection happens quite frequently, even in games of strong players.
Related combinations
Trade into fork is similar to decoy into fork, but the first move is a trade instead of a sacrifice. It is also possible to decoy a piece to a square where it can be attacked in a subsequent tactic other than a fork. And you can decoy the king into checkmate.