Let's invent some very weird pieces

right general: 
Range: moves unlimited amount of squares diagonally backward left or forward right or directly forward. 
Step: can move 1 square backwards
worth 3 points

Train: moves like a rook, bot can jump over the opponents pieces and captured all of the pieces that stand on the squares it passed

After the train is moved, it becomes a rook

Springer: Can only move to the edges of the board for it's first turn, but after that it moves 3 squares in any direction. Captures any piece that is touching it after it's third move, including it's own pieces. If it touches your king you lose, if it touches the opponent king you win.

The Marshall, moves like a rook but blocks the first attack the useThe paladin moves like a knight and then a pawn. It moves like a knight first and then a pawn or attacks like the pawn.

Back and forth pawn: pawn that doesn't promote, but once it hits the last rank, it can move 1 square backwards, and capture diagonally backwards, and so until it reaches the 1st rank again, then it reverts to a regular pawn. It can only move 2 squares on its very 1st move.

The absorber pawn: pawn that absorbs the power of captured pieces. If, let's say, it captures a rook, a bishop, and a knight, then it will become an amazon. If it doesn't capture anything on its way to the last rank, then it can promote just like a regular pawn. But if it has already captured something, then no.

The helium piece : Each player has 2*#spectators, but nobody knows which pieces are helium. If you try to capture it, then it's (the helium piece) pushed back, instead of being captured. The pushing is determined based on the direction of the piece, so if a rook moved up onto E5 to capture a helium piece, then it would be pushed onto E6 instead of being captured. It can't be taken by a knight. If it is pushed off the board then it pops, and it pushes every piece within a king's move away one square in a line with one point being the popped piece and the other being the pushed piece. If it gets pushed into another piece, then it just stays there. If a helium piece captures, then the piece that it tries to capture is instead pushed like it was a helium piece. If a helium piece takes a helium piece, then they both pop, but instead of pushing, they pop any helium pieces next to them, and they do the same. If a king gets pushed into double check, then it immediately counts as checkmate for the side with more people rooting for it/ the amount of helium pieces left. Also, helium pieces can check only in a 2 square radius. They also can't be pawns. (I posted this on a different forum too, but I think it is a really weird piece so I posted it on this forum.). 

My Custom Piece: Princess

Starting Position

Replaces the original Rook space, so each player begins the game with 2 Princess pieces.

Movement

Moves like a Queen, but her range is limited to 2 tiles.

Abilities

- If a player's Queen is captured, the player can use a Princess to be the next Queen. The coronation event takes 2 turns and the player's King must move to 1 tile within the new Queen (unless they cannot do so because all of them are occupied by other pieces). However, the player must do this within 1 turn or this chance is lost.

- If the Princess is next to (within 1 tile) the opponent's King, the opponent's King and the Princess cannot move but also cannot be captured. However, the opponent's King won't be in check, since the Princess cannot move anyway. However, if there are 2 Princesses that are next to the opponent's King, the King is under check (since one immobilises the King and the other attacks)

- The only piece that can capture a Princess is another Princess (including their own Princess but why would anyone do so)

- A Pawn can promote into a Princess, but a player cannot have more than 2 Princesses at any given time. Also, if a player uses the Princess, they cannot promote a Pawn into a Queen.

Penalty Rule (since it would be quite OP)

- If a player using the Princess loses both Princesses and the Queen, they automatically lose, unless they can promote a Pawn into a Princess within 5 turns (the number of turns it takes to move a pawn from 2nd rank to 8th rank).

- During this time frame, the player is also forced to move only Pawns during this time frame, unless they are in check.

- If they don't have any Pawns (or lose all while trying to achieve this), they immediately lose the game. If they can't move any Pawns (most likely because opponent's pieces are blocking the way), it is a stalemate draw.

Wizard

It can teleport but not capturing pies and not checking the king but it can be used as any piece except a knight and a king.

Interesting

Wikipedia has a comprehensive web page on the subject, discussing Betza notation for fairy chess pieces.
But imagine pieces that can transform. For example, imagine pawns that can be promoted to a minor piece at the end of any move (so if you move the pawn, you can immediately promote it), but then they last for 3 moves and then disappear.

I like the idea of a spy.

(I haven't figured out the name yet) piece. This piece can move in two different ways:

1. It can move like a king.

2. It can go through a group of friendly pieces like this:

Not capture the Bishop on c5?

It can only capture when it moves like a king.

It can't check.

I was not clear enough.

Also, do you have any name ideas for this piece?

Very nice invention. Reminds me of one of the pieces from the abstract board game Hive but I forgot that name.

Get the name from your favorite SF/Fantasy book or anything - it's your honor