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Excepting the variations where there is a capture or fork possible for the defending side. Is a position possible where this kind of endgame will last more than 50 moves? Is somewhere a calculation in moves done what is the worst possible situation?

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It takes at most 33 moves to win this endgame from any position (excluding positions where bishop or knight can be captured). See https://en.wikipedia.org/wiki/Bishop_and_knight_checkmate and references there.

So, no, a forced draw is not possible in this endgame. However if the defending side is playing perfectly (e.g. an engine with tablebase), it could be very hard to win this for a human within 50 moves if you start from one of those 33-moves-to-mate positions.

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    I would not say that it;s hard in terms of technique, but humans get tired, and a single slip can cost you 5 or 6 moves. – DanielWainfleet Jan 24 '18 at 6:41
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    @DanielWainfleet That's exactly what I wrote: hard to win ... within 50 moves. As for technique, indeed, it is pretty easy once you know how the knight is supposed to move... – user1583209 Jan 25 '18 at 19:56
  • Many years ago Scientific America had a brief note about the old Q of whether in general R+B could win against 2 Knights, with no pawns or other pieces left (except of course the Kings). Regressive analysis by computer (basically analyzing backwards from winning positions) said YES, but only if the 50-move rule is waived. The longest variation took 233 moves to a forced win of one of the Knights, followed by about 20 more moves to mate – DanielWainfleet Jan 27 '18 at 2:39
  • The following ending even requires 545 moves to be won by white : W: Kd3 Qh1 Nh2 vs B: Kf4 Ra7 Bd1 Nh7 with black to play. – Emphyrio Jan 28 '18 at 3:29
  • Important to know as well : in chess endgame studies, the 50move rule doesn't apply (unless expressedly specified, but it 's rarely the case). Many engame studies have some secondary lines whose validity depends of some tablebase result giving a win longer than 50 DTZ. That s why usually composers don't use syzygy tablebases but rather Nalimov or Lomonosov. The 50move rule does apply in other chess composition genres though (for instance it's very much the case in retrograde analysis where many problems are based around it). – Emphyrio Jan 28 '18 at 3:38

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