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K-B-N vs. K : I have read that the maximum number of moves needed is 33,
but the sequence must be extremely precise, an slight error can be enough
for surpasing the 50th. move, so it is difficult win the game in every
case.
I have also read an old article that K-Q vs. K-R is a victory for the
superior band in at most 36-40 moves, but the analysis is too complicated,
even with computers, to be enterely sure, by cause of the high branching
factor...And the article conclusion was based on a particular strategy by
part of the K-R team. It is also certain that slight errors are enough for
a draw by the 50 moves rule, playing under optimal defensive sequence. In
the game Svidler-Gelfand 2001 world championship eliminatories, Svidler
commited a slight error, but also Gelfand essayed a novel strategy, with
the Rook close to his King amost all the time as theory suggests, but
moving the Rook sometimes far from his King to precise squares in very
precise moments. By curiosity, I made an experiment with Chessmaster 9000
playing against itself, with a far-from-trivial initial position I have
found in Internet. The result: draw, by the 50 moves rule. This is not a
conclusive remark, but may be an indicative of the difficulties for the
superior band. This problem is a good exercise to be tested using
high-level programs running on powerful computers.