Chess Piece Essay: Hoppers

We now enter a realm almost solely within the world of generalized chess. A class of chess pieces unknown to those familiar only with the usual chess pieces.

Hoppers are the name given to a class of chess pieces that require another piece to move and set the direction of movement. A piece a hopper uses to hop is called a hurdle. This means that a pure hopper cannot move alone on an otherwise empty board.

In this piece I will cover linear hoppers, mainly sorted by its action before and after hopping. Long hoppers ride after their hop, while short hoppers stop after landing on its destination square. Leaper hoppers can only start their hop with a single leap, while rider hoppers can ride before they jump. 

Conditional hoppers require a specific hurdle or require a hurdle to fulfill a different task, the latter form usually used in hybrids. The hurdle can remain unscathed or may change state after a hop, the latter making the hopper a hurdle-changing one.

Some Starting Examples

Since the concept of a hopper is relatively alien to anyone not into chess variants, let's start with the quintessential hopper, the grasshopper. A short directional hopper, it jumps over any piece moving as a queen, landing at the square just after the piece and stopping there.

Chinese cannons are pieces in Xiangqi that take a rook's move but needs to hop on a third piece to capture (thus making this a hybrid). Korean cannon hops are long as they need to hop onto a piece before moving continuously, thus making them akin to long grasshoppers.

For a more general approach, the line a hopper takes need not be constrained by rook and bishop lines. The simplest example is the Equihopper, whose hop consists of a leap over a hurdle and landing the same distance. 

Capturing the Gist of It

Hoppers generally capture the (first) piece beyond the hurdle within its range, but some hopper types might put this into question.

In most cases hoppers takes as they move, whether long or short, through replacement. A long hopper stops on the square where it captures. 

Now if a piece has to land on the square before a hurdle, can it capture? This is more a question of how chess spaces work.

It Takes Three to Tangle

Two-hurdle hoppers are very specialist and used usually to prove a point. The obvious development from this is making a hopper jump over exactly two pieces.

A piece that needs to move between two pieces still counts as a hopper, though how this would work is beyond this essay's capabilities.

Let's Make Weird Things Happen

Hoppers can give rise to unusual situations in generalized chess geometry. The requirement that a hopper have something to hop leads to cases where a piece cannot move to a square as it would be check, what is usually called an anti-pin. Anti-pins also happen when a check cannot be responded by a recapture as the recapturing piece will become a hurdle enabling a hopper to capture the royal piece.

It's assumed that the hurdle doesn't change when it is hopped upon, in order to spare many a headache. Hurdle-changing hoppers affect the hurdle, independent of replacement capture capabilities. How the piece changes can range from a simple transformative cycle to a progressive one (i.e. there's a point the hurdle stops changing). What a piece can change into may even depend on the direction of the hop. This classification also counts capturing hurdles as a hurdle change.

Legality of a hop of this kind depends on whether the change in the hurdle creates a legal position, this is independent of the legality of the hop as a move.