[figjrzma] binary valued chess royal pieces

chess variant:

each player has one king, worth 2^N points.  each player has 2 pieces (names and abilities TBD) each worth 2^(N-1) points.  4 pieces each worth 2^(N-2), and so forth, down to 2^N pieces each worth 1 point.  (levels of nobility or officer ranks offer names for various N.)

optionally, any number of additional pieces each worth epsilon points.  optionally, additional pieces worth 0 points.  (enlisted ranks or commoners.)

the game ends when one player has captured opponent pieces totaling 2^N points or more.  this can be accomplished by capturing the king just as in orthodox chess (details about stalemate TBD), or some other combination of lesser valued pieces.

or, set the threshold to 2^N+1.  the king may be sacrificed if every other noble lives.  or, also increase (only) the value of the king to 2^N+1: capturing just the king is enough to win, but capturing (say) both of the two second highest-value pieces is not quite enough; at least one more piece must be captured.  let there also be one more 1-point piece so that victory may also be achieved by capturing every 1-pointer.

or 2^N+epsilon: this is where the epsilon-valued pieces come into play.  in practice, these small threshold differences are unlikely to matter, because chess is normally full of exchanges: no one plays damageless chess.

in general: any monotonic boolean function, not just addition.  do game design to make the function not too complicated for humans to compute.