A neat idea from L. Breiman

[Tom Dietterich]

   >  hold {d_2, ..., d_{k-1}} constant ...by re-making decision d_1
   How can you hold d_2 ... etc constant if they might depend on d_1, like in
   a game tree ?

   Cheers, Henrik

   IBM Research 
   Lawrence Livermore National Labs

Suppose d_1' is an alternative way of making d_1.  You can now
evaluate the "board position" corresponding to {d_1', d_2, ...,
d_{k_1}}.  In some cases, of course, this will not be a legal position
(and it should get a bad evaluation), but in many situations, it will
be legal and possibly superior to {d_1, d_2, ..., d_{k-1}}.

--Tom