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This question already has an answer here:

In what situations is it impossible to win for a player? For example due to not enough material or the composition of the material is not useful. I guess for example when you only have a king and a knight left or so and the opponent has far more pieces? I'm looking for the (few) hard cases where "you can't win". For example when you only have a king.

marked as duplicate by Glorfindel, SmallChess, Cleveland, GloriaVictis, limits Oct 11 '15 at 21:06

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    Title and question in the text don't really match, please edit it appropriately. There are lots of positions where one side cannot win but still hold a draw even against superior material on the other side. – jknappen Oct 8 '15 at 8:36
  • @jknappen I have edited the title to match what I think the intent is. – dfan Oct 8 '15 at 14:34
  • How is this supposed to be a duplicate? When it is time to resign and when to forget about winning is completely different! – BlindKungFuMaster Oct 12 '15 at 13:42
  • Exactly what @blindkungfumaster says – Folkert van Heusden Oct 12 '15 at 14:19
  • I agree with @BlindKungFuMaster . In this question the main subject is drawing, while in the other one the main subject is losing. Not exactly the same... – lodebari Oct 12 '15 at 16:43
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There are very few positions in which it is actually impossible to win although you are up material. Basically only KN vs K or KB vs K.

Then there are positions which can be won, but this would require such egregious errors by your opponent, that in practice a draw will inevitably be agreed. Examples are KNN vs K, KBB vs KB, KR vs KB.

And then there are theoretically drawn positions which give you very real winning chances even against strong players. KR vs KN, KRB vs KR, KQ vs KNN.

There are also known "fortresses" where the stronger side cannot break through once the weaker side has achieved a certain setup. Here is one famous (and relevant) example:

   [White "The wrong"]
   [Black "bishop"]
   [FEN "k7/8/8/PK2B3/8/8/8/8 w kq - 0 13"]
  • There are non-trivial situations in KR vs KB. – Cleveland Oct 9 '15 at 1:55

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