First piece to move must be the king.
What strange chess rules can you think up?

Playing blindfolded.
I have played four games blinfolded against 1000 to 1100 players and won three drew one

You can move your king on top of your rook. This counts as a move, and you put your king on top. Your king is still exposed to checks against that square, it's like K+R became one.
At your turn, you can decide to move your king down, or you can move your rook carrying your king away. You cannot go through a square controlled by the enemy (same rule as castling), but it's a really useful maneuver to escape enemy attacks.
The "not in my house!" Rule. Once during any part of the game when your opponent makes a move that gives check you can declare the "not in my house!" Rule and your opponent has to make a different move that does not give check. This rule could influence perpetual checks, sacrificial combinations, end game positions, ect.

Every time you push a pawn there's a one in (number of remaining pawns) chance that it will go rogue and flee to Russia

Battlenet Rigmarole: Before the game begins, each player names a Pokemon, a drug, or a philosopher, and the other player must guess which category it is from. If you correctly guess your opponent's phrase, you may replace a piece of theirs with a pistachio, which can only move one space backwards. If you guess incorrectly, you must play the entire game without pants or underwear, and you must eat a spoonful of baked beans after each move.
lol

Here is what I use with my son . He gets a time advantage of 7 minutes to my 5 minutes. We start at say $1 per game.
At any time during the game either player can say "DOUBLE!' then the other player has to immediately resign or play for double stakes.
After the "Double" the player who did not say "DOUBLE" but kept on playing can at any time say "REDOUBLE!" This means the other player must resign immedately at double stakes or if he does not resign then he is playing quadruple stakes.
This really adds an element of reality to the game. No playing out lost games. Adds a lot more "thinking" to the game.
i think this is what they do in backgammon.

1. Quadrant mate. Divide the board into 4 quadrants. At the beginning of the game the players will pinpoint the exact quadrant the opponents king will be checkmated. The player to do it will receive 4 points per win, while the player that won but did not mate the opponent's king in the quadrant that he predicted will receive one point instead. It will result into an interesting game.

If a player wishes to capture en passant, s/he must first stand up and perform the Hokey-Pokey. The part where they put their Whole Self un, and then their Whole Self Out.......
I think it might be more historically appropriate to force the player of en passant to don a curly white wig and speak in an affected french accent for the rest of the game...

Playing blindfolded.
I have played four games blinfolded against 1000 to 1100 players and won three drew one
How is that possible?

The king may castle with ANY unmoved piece if there is nothing between the pieces and room to do it. The king moves two squares right or left, and the other piece moves where the rook would go for "normal" castling. For example:
Or perhaps pawns can capture diagonally two squares forward with their first move. For example:
Here is what I use with my son . He gets a time advantage of 7 minutes to my 5 minutes. We start at say $1 per game.
At any time during the game either player can say "DOUBLE!' then the other player has to immediately resign or play for double stakes.
After the "Double" the player who did not say "DOUBLE" but kept on playing can at any time say "REDOUBLE!" This means the other player must resign immedately at double stakes or if he does not resign then he is playing quadruple stakes.
This really adds an element of reality to the game. No playing out lost games. Adds a lot more "thinking" to the game.