Suppose a new variant of chess is played on a board with alternating black, white, and grey squares. What are some potential rule changes or variations in piece abilities that could be applied to this board, and how might they affect the gameplay and strategies used by the players?
A new variant of chess played on a board with alternating black, white, and grey squares can introduce exciting rule changes and variations in piece abilities. Here are some potential ideas:

Piece movement restrictions: Assign each piece a specific colour it can move on. For example, bishops could move diagonally only on black squares, while knights could only move to white squares. This would limit the mobility of pieces and introduce new challenges to both offensive and defensive strategies.

Grey squares as teleportation zones: When a piece lands on a grey square, it can teleport to any other unoccupied grey square on the board as a single move. This would create dynamic gameplay, as players could set up surprise attacks or escape from dangerous positions.

Colour-specific power-ups: Pieces could gain specific abilities or powers when on a certain coloured square. For example, a pawn on a white square could move two spaces forward instead of one, or a rook on a black square could move diagonally as well as vertically and horizontally. These power-ups would encourage players to strategically position their pieces on the board to maximize their potential.

Grey square immunity: Pieces on grey squares cannot be captured, providing a temporary safe zone. This would introduce a new layer of strategy, as players would need to decide when to risk moving their pieces out of the safe zones and how to effectively attack pieces protected by grey squares.

Colour-specific piece promotions: When a pawn reaches the opposite end of the board, it can promote to a more powerful piece based on the colour of the promotion square. For example, promoting on white square results in a knight, on black square results in a bishop, and on grey square results in a queen. This would require players to consider the implications of the promotion square colour when advancing their pawns.

These potential rule changes and variations in piece abilities could significantly impact gameplay and strategies, forcing players to adapt and rethink traditional chess tactics. The introduction of grey squares and new piece dynamics would create a fresh, challenging, and engaging chess experience.
The teleportation idea seems overpowered.  Can you suggest a way to tone it down?
Yes, the teleportation idea can indeed be overpowered, depending on how it is implemented. Here is a way to tone it down:

Limit the number of times a piece can teleport: Instead of allowing pieces to teleport an unlimited number of times, you could limit the number of times a piece can teleport during a game. For example, each piece could have a set number of teleportation moves they can make, or a certain number of teleportation moves could be allocated to each player at the start of the game.

Introduce a cooldown period after teleportation: After a piece has teleported, it cannot teleport again for a certain number of turns. This would prevent players from repeatedly teleporting their pieces back and forth and would require them to carefully plan their teleportation moves.

Add limitations to teleportation zones: Not all grey squares could be teleportation zones, or there could be restrictions on which grey squares can be used for teleportation. For example, only certain grey squares could be used as teleportation zones, or teleportation could only be allowed to specific regions of the board.

By introducing limitations to the teleportation ability, players would need to carefully plan and use their teleportation moves strategically, rather than simply relying on them as an easy escape or surprise attack tactic. This would help to balance the gameplay and make it more fair for both players.