DESTROY AND BUD

1. Basic chess rules apply, except:
2. When a piece makes a capture, it buds off a piece one rank lower,
   leaving this behind on the exit square.  Ranks  KQRBNP-.

Game Sample:
                        
r . b . k . n r     |  1. e4    e5         10. Kg1  Rh:h2
p p p p . p p p     |  2. d4    Nc6        11. R:h2 Q:g3+
. . B . . . . .     |  3. d:e5  Bc5        12. resign!
. N n . r . . .     |  4. Bb5   B:f2
. . . . . . . b     |  5. K:f2  Qh4+
. . . . . O q .     |  6. g2    Q:e4    
O O O . r . . R     |  7. Nf3   N:e5  
R N B Q . . K B     |  8. N:e5  Q:e5  
                       9. B:c6  Re2+

As people can see in the game sample, the ploriferation of pieces allow for strong and dealy attacks against the adversary force. Since there is a demotion mechanism on the captures, the game converges to an end.