This actually sounds like a nice variant! It would take a while to learn though.
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This proposal I've been thinking about is a fairly simple varient of chess960.
Firstly, you set up a chess960 postion like normal.
Then you roll a d6, or choose a number 1-6 using a random number generator.
Depending on what you roll:
1) Play a normal game of chess960.
2) Swap both players' the queenside-most knight with the king. The objective of the game is now to checkmate this knight (and not the King). The knight can now castle, and the King cannot.
3) Same as 2 but with the kingside-most knight.
4) If there are bishops not between the rooks, swap them with the nearest rook so they become between the rooks. The objective now is to checkmate either bishop (and not the King). This means, for example, a fork of both bishops is checkmate. Both bishops can individually castle, and this can include castling one queenside and the other kingside. The king cannot castle.
5) The objective, similar to 4, is to checkmate either rook (and not the king). Castling is normal.
6) White can choose any of the above 5 positions/rulesets for their side of the board and declare it, then black does so so for their own side of the board. If a chess clock is being used, the chess clock starts before white chooses and choosing counts as a move. Then e.g. if white chooses position 2 and black chooses position 5; black will try to checkmate whites' queenside knight and white will try to checkmate one of blacks' rooks.
So my question is: how fun/balanced would this varient be?
Any weaknesses in how the rules are set up?
How many positions total would this varient have, if you count each distinct one of the 6 rolls as a different position? I know it must be less than 5760 because the bishop swap rules leads to identical positions from different chess960 start postions, but I don't know how many less.
As a quick note, the reason I had 2 rooks/bishops as checkmatable is because I think on their own they would be too difficult to checkmate. If you think that's not the case, or conversely that they're still too difficult to checkmate, tell me and I can make amendments.