[ Help | Earliest Comments | Latest Comments ][ List All Subjects of Discussion | Create New Subject of Discussion ][ List Earliest Comments Only For Pages | Games | Rated Pages | Rated Games | Subjects of Discussion ]Single Comment Monster Chess Variants. A Discussion of the value of Double-Move pieces. (8x8, Cells: 64) [All Comments] [Add Comment or Rating]Jeremy Lennert wrote on 2011-03-29 UTCExcellent ★★★★★The obvious possibility for the number that would be squared to value a doublemove piece would be the piece's mobility; or rather, you'd expect the mobility of a doublemove piece to be related to the square of the regular piece's mobility (but lower, due to overlap). The average mobility of a Knight on an 8x8 board is 5.25. (This counts moves to occupied spaces, on the grounds that the move either threatens or protects a piece, but naturally not moves off the board.) Assuming a board where 15% of spaces are occupied by friendly pieces and 15% by enemy pieces (leaving magic number = 70% of spaces empty), a Double-Knight's mobility is increased by 15.5 for the spaces two N moves away (I have laboriously calculated), plus 8 * .15 = 1.2 average 'shooting' moves, for a total of about 22, just over four times the normal Knight. (That goes up if you count different routes to the same destination as different moves when you capture different pieces along the way.) That's not far off from your estimate that a Double-Knight is worth '3 or 4 normal Knights'. That suggests mobility may be a reasonable predictor of doublemove value (though it's a royal pain to calculate). However, the ability to continue after a capture does seem like it should add quite a bit more than the ability to move through enemy pieces, even though they result in the same mobility. So there's probably something more complex than just mobility changes going on.