user8527: In developing a computer chess program, would it be reasonable to automatically declare a draw match for these two scenarios:
A.  Player 1 has a king and a knight, player 2 has only a king left.
B.  Player 1 has a king and a bishop, player 2 has only a king left.

user9030: It would be absolutely reasonable, because there is only one way to end such positions, draw.
There are other positions like these as well. And for this, there is a rule called dead position rule in FIDE. It's a superset of the older concept of draw by insufficient material.
It's draw automatically if any following situation happens:

King vs king
King vs king + knight
King + zero or more bishops vs king + zero or more bishops, where all bishops stands on same colored squares
Any combination of pieces in a position where stalemate is unavoidable.
Any combination of pieces in a blocked position where checkmate is impossible.
Any combination of pieces in a position where it's inevitable to end up in a position described above.


user4362: Yes, in these two cases there is insufficient mating material and the game will always end in a draw.

user3831: Yes, since it is not possible to produce a checkmate in these circumstances.
See also the FIDE rules:

1.3 If the position is such that neither player can possibly checkmate the opponent’s king, the game is drawn (see Article 5.2 b).
5.2 b The game is drawn when a position has arisen in which neither player can checkmate the opponent’s king with any series of legal moves. The game is said to end in a ‘dead position’. This immediately ends the game, provided that the move producing the position was in accordance with Article 3 and Articles 4.2 – 4.7.


8527: <p>In developing a computer chess program, would it be reasonable to automatically declare a draw match for these two scenarios:</p>

<p>A.  Player 1 has a king and a knight, player 2 has only a king left.</p>

<p>B.  Player 1 has a king and a bishop, player 2 has only a king left.</p>
 9030: <p>It would be absolutely reasonable, because there is only one way to end such positions, draw.</p>

<p>There are other positions like these as well. And for this, there is a rule called <a href="https://www.fide.com/fide/handbook.html?id=208&amp;view=article" rel="nofollow noreferrer"><em>dead position rule</em></a> in FIDE. It's a superset of the older concept of <a href="http://www.e4ec.org/immr.html" rel="nofollow noreferrer"><em>draw by insufficient material</em></a>.</p>

<p>It's draw automatically if any following situation happens:</p>

<ol>
<li>King vs king</li>
<li>King vs king + knight</li>
<li>King + zero or more bishops vs king + zero or more bishops, where all bishops stands on same colored squares</li>
<li>Any combination of pieces in a position where stalemate is unavoidable.</li>
<li>Any combination of pieces in a blocked position where checkmate is impossible.</li>
<li>Any combination of pieces in a position where it's inevitable to end up in a position described above.</li>
</ol>
 4362: <p>Yes, in these two cases there is <a href="http://www.e4ec.org/immr.html" rel="nofollow">insufficient mating material</a> and the game will always end in a draw.</p>
 3831: <p>Yes, since it is not possible to produce a checkmate in these circumstances.</p>
<p>See also the FIDE rules:</p>
<blockquote>
<p>1.3 If the position is such that neither player can possibly checkmate the opponent’s king, the game is drawn (see Article 5.2 b).</p>
<p>5.2 b The game is drawn when a position has arisen in which neither player can checkmate the opponent’s king with any series of legal moves. The game is said to end in a ‘dead position’. This immediately ends the game, provided that the move producing the position was in accordance with Article 3 and Articles 4.2 – 4.7.</p>
</blockquote>
