Just post an idea for a new chess piece, and estimate how many "points" it would be worth. Also, I have given rough point values to the pieces below, but am willing to change them according to suggestions.
Assume pawns are 1 point, Bishops 3, Knights 3, Rooks 5, and Queens 9.
Here are some well known "nonstandard" pieces along with a few I made up:
Superqueen: Moves like a queen or a knight. 14 points
Hawk: Moves like a bishop or a knight. 7 points
Elephant: Moves like a rook or a knight. 9 points
Sidekick: Moves like a king (only you don't have to protect this like the king). 2 points
Chinese Knight: Moves like a knight but can't jump over pieces. 2 points
Chinese Elephant: Moves like a bishop, but exactly two squares (no jumping over pieces either). 1.5 points
Blocker: Can move like a rook as many times as desired in one move, but without the capability of capturing. 4 points
Cannon: Moves like a rook, but to capture, jumps over a piece before capturing the enemy piece behind. 5 points
Wild Knight: Has the option of moving exactly 3 squares horizontally or diagonally, OR moving 3 in one direction, 2 in another (the same way a normal knight moves 2 in one direction, 1 in another). 5 points
Triple Knight: Moves like a knight, three times in one turn and without repetition. 8 points
Treacherous Bishop: Moves like a bishop, but with the option of moving one square horizontally or vertically (not stuck on one color any more). 5 points
Also, if you can come up with better names for the pieces I came up with, please present them here.
That's called a chancellor as well.
Just post an idea for a new chess piece, and estimate how many "points" it would be worth. Also, I have given rough point values to the pieces below, but am willing to change them according to suggestions. Everything I post in red is an edit in this post. Everything I post in this color is an edit made starting 10/15/2011 at 2:45pm.
Assume pawns are 1 point, Bishops 3, Knights 3, Rooks 5, and Queens 9. Also assume for the sake of rating pieces, that each new piece faces only itself and the standard pieces, since including other nonstandard pieces in an actual game will have an effect on the worth of each.
Here are some well known "nonstandard" pieces along with a few I made up:
Superqueen: Moves like a queen or a knight. 14 points
Hawk (aka Archbishop): Moves like a bishop or a knight. 7 points
Elephant (aka Chancellor): Moves like a rook or a knight. 9 points
Defender: When behind the middle line (between ranks 4 and 5), the defender is a queen. When it crosses the line, it becomes a rook. It cannot move diagonally across the line. 7 points
Sidekick (aka General): Moves like a king (only you don't have to protect this like the king). 2 points
Avenger: Moves like a knight, but when captured, is replaced by a checker, and the enemy piece placed on top. On the player's (owning the captured Avenger) turn (any turn, not necessarily the following), the player has the option of removing the checker (unless his/her own piece occupies it). If an enemy piece is on the checker, that piece is also removed from the board. This takes the turn. The checker does not move. 6 points.
Occupant: Controls the square it rests on and no other. If an enemy piece captures it, the enemy piece is also removed from the board. Although it doesn't move, it can "move" by moving into the square it already occupies (essentially zugzwangproofing the army). This piece is placed on the board by both opponents immediately after move seven, provided the game lasts that long, and cannot be placed on an occupied square. 3 points.
Monk: It moves like the king. If an enemy piece is next to it, the monk may convert the piece to the other's army. It's abilities are not affected by the conversion. A conversion counts as a move. If an enemy piece captures it, it is not converted upon capturing. The monk may not convert the enemy king. It also cannot deliver check or assist in checkmates. It may convert and be captured by any enemy piece. 5 points
Chinese Knight: Moves like a knight but can't jump over pieces. 2 points
Chinese Elephant: Moves like a bishop, but exactly two squares (no jumping over pieces either). 1.5 points
Blocker: Can move like a rook as many times as desired in one move, but without the capability of capturing. 3 points (previously 4 points)
Teleporter: Can teleport anywhere once per one turn, cannot teleport onto an occupied space (and therefore cannot check). 4 points (previously 5 points)
Cannon: Moves like a rook, but to capture, jumps over a piece before capturing the enemy piece behind. 5 points
Wild Knight: Has the option of moving exactly 3 squares horizontally or diagonally, OR moving 3 in one direction, 2 in another (the same way a normal knight moves 2 in one direction, 1 in another). 5 points
Triple Knight: Moves like a knight, three times in one turn and without repetition. Only captures on final destination square. 14 points (Old estimate: 8 points)
ThreeKnight: Moves like a triple knight, but is subject to "en passant" which in this case means that the opponent may capture this knight if it landed (on one of its knight jumps) on a square the opponent may capture on. Note that if the ThreeKnight later captured on this move, the opponent may replace the piece, since the ThreeKnight never made it that far. Only captures on final destination square. 8 points
Treacherous Bishop: Moves like a bishop, but with the option of moving one square horizontally or vertically (not stuck on one color any more). 5 points
Squire: Shares a square with the knight and enables this joint piece to move either once or twice if desired. Upon the knight's first capture, the Squire is forfeited, and if captured, both are captured. 3 points
Esquire (aka Page; Gentleman): Moves like a pawn, but may always move 1 or 2 squares forward. If it moves 2 squares, it may jump over a piece. It captures like a pawn, and promotes to a knight. 3 points
Deathknight: Moves like a queen, can jump over pieces, can sacrfice itself to capture all pieces around it, can move two times in one turn but cannot check or capture on the second move. 19 points
Jedi-Knight: By sacrificing itself, this knight first gets the opponent to make a forced (legal) move, i.e. on the opponent's turn, the player can declare that the opponent has to move a certain piece to a certain location, followed by the player then having to move that (jedi) knight...and regardless of that knight making a capture or not, it is promptly removed from the board. 14 points
Wall: Takes up a 2x2 square, cannot move, you can place it anywhere behind the "4" line.Can only be captured by a queen or rook (on any of the four squares). 2 points
Nuker: Does not move, but sacrifices itself to capture 3 pawns or one bishop/knight, you can sacrifice 2 nukers to capture a rook or a bishop and knight. 6 points
Striker: Moves like a rook but cannot move horozontally. When it reaches the 8th rank, it becomes a regular rook. 3 points
Cavalier: It moves just like a knight, except that it has twice the range. It may make two standard knight moves in a row, or it may combine them to make one large move. In a large move, instead of "up one and over two or up two and over one", it is "up two and over four or up four and over two". It is able to check, deliver checkmate, and assist in checkmates and can capture and be captured by any enemy piece. 5 points
Siege Tower: It moves just like a rook. It is made up of two segments, one on top of the other. Each attack on it removes one segment, so it must essentially be "captured twice" to be removed from the board. Siege towers can damage and capture each other. The loss of one segment does not affect its abilities. It may check, deliver checkmate and assist in checkmates, and it can capture and be captured by any enemy piece. 9 points
Robot: Moves like a queen, but can't stop until it's obstructed, either by a piece in the same army, by the side of the board, or by capturing an enemy piece. 5 points
Pikeman: Moves forward one square at a time. Like a pawn, it can move forward two squares on its first move if desired. However, also like pawns, it cannot move backwards or sideways. It may capture any piece (only one, not all three at once) on the three squares immediately in front of it, meaning it can capture diagonally up to the left and right, or straight forward. It may check, deliver and assist in checkmates, and capture and be captured by any enemy piece. If a pikeman reaches the eighth rank, it is promoted to a Champion. 1 point
Champion: It possesses the same abilities as the pikeman, but is able to move backwards one square per turn. It may not move sideways. It also may not move backwards to the first rank. If a champion reaches the eighth rank, it becomes a General (a.k.a. Sidekick), which retains all of the champion's abilities, but may move like a king. 2 points
Bigot (aka Madman): Moves like a bishop, but with the option of capturing pieces in the same army. 3.5 points
Traitor (aka Whip): Moves like a rook, but (see above). 6 points
Kitty (aka Commander): Moves like a queen, but (see above). 10 points
Trojan Pony (aka Sadist): Moves like a knight, but (see above). 3.5 points
Wizard: Moves like a king, but has the option of creating an opponent's piece (not a king, and no pawns on first or eighth ranks) on the square he left. 3 points
Bloody Saint: Moves like a bishop, but can jump over pieces like the knight. 5 points
Bully: moves like a rook, can only capture pawns. 3 points
Morpher: Can morph into rook/bishop/knight, but morphing into another piece takes a turn. 6 points
Secretive Queen: When checking the King, you dont have to announce that you are checking their King. If their King doesnt move, then you could capture it. 9.1 points
Mine: Moves 1 space at a time. when Detonated, it explodes everyting within a radius of 2 squares. 8 points
Drunken Bishop: Moves like a rook but may only occupy squares of a certain colour. Can jump over (multiple) pieces. 3.5 points
Chinese Drunken Bishop: Moves like a rook but may only occupy squares of a certain colour. Cannot jump over pieces. 2.5 points
Paladin: Moves two squares in any direction diagonally, then 1 square horizontally or vertically. 8 points
Time Pawn: Moves like a pawn, bet when you capture a piece with it, it adds 20% extra to your time limit. Correspondence: 1.1 points; 30min: 1.5 points; blitz: 2 points; bullet: 3 points
Boulder: Moves like a King. Cannot capture. Its purpose is to block attacks. Can be only captured by the Queen. 1 point
Blader: Moves like a queen; if it captures a piece, then it has the ability to capture any one piece in the surrounding 8 squares, by moving into the square of that piece. 15 points
Also, if you can come up with better names for the pieces I came up with, please present them here.