user20863: I saw the game Firouzja vs Carlsen in world blitz championship in which Carlsen flagged Firouzja. Carlsen won because even though he had only a bishop, there could be a possible mate position.
I am asking if there a chess position in which both players have at least one piece, not including the kings, and there is no possible future mate position?
An obvious one is if both players having only one bishop moving on the same color squares. But is there something else?
I am actually looking for a complicated position, not obvious to humans at all, which needs something like 30-50 moves deep analysis for proving there is no any possible mate position.

user19877: I think that is limited to just a few positions.

A lone king vs. king.
king and bishop vs. king.
A king and bishop vs. king and same colored bishop as the other side.
A king and multiple bishops of the same color vs. king.
A king and knight vs. king.
Any barrier position, where neither side can cross over to the other side.

Even king and knight vs. king and knight you can get a mating position.
Here is a wonderful position that I "stole" from chess.com that illustrates why that FIDE rule exists. Yes, it was probably not fair for Carlsen to get the full point, but imagine having this position, and not getting the full point.
 [FEN "6rk/4NP2/7K/8/8/8/b7/8 w - - 0 1"]

  1. fxg8=Q+ Bxg8 {By USCF, and chess.com rules, this is a draw here.} 2. Ng6#




 [FEN "6nk/5N2/6K1/8/8/8/8/8 b - - 0 1"]


20863: <p>I saw the game Firouzja vs Carlsen in world blitz championship in which Carlsen flagged Firouzja. Carlsen won because even though he had only a bishop, there could be a possible mate position.</p>

<p>I am asking if there a chess position in which both players have at least one piece, not including the kings, and there is no possible future mate position?</p>

<p>An obvious one is if both players having only one bishop moving on the same color squares. But is there something else?</p>

<p>I am actually looking for a complicated position, not obvious to humans at all, which needs something like 30-50 moves deep analysis for proving there is no any possible mate position.</p>
 19877: <p>I think that is limited to just a few positions.</p>

<ol>
<li>A lone king vs. king.</li>
<li>king and bishop vs. king.</li>
<li>A king and bishop vs. king and same colored bishop as the other side.</li>
<li>A king and multiple bishops of the same color vs. king.</li>
<li>A king and knight vs. king.</li>
<li>Any barrier position, where neither side can cross over to the other side.</li>
</ol>

<p>Even king and knight vs. king and knight you can get a mating position.</p>

<p>Here is a wonderful position that I "stole" from chess.com that illustrates why that FIDE rule exists. Yes, it was probably not fair for Carlsen to get the full point, but imagine having this position, and not getting the full point.</p>

<pre><code> [FEN "6rk/4NP2/7K/8/8/8/b7/8 w - - 0 1"]

  1. fxg8=Q+ Bxg8 {By USCF, and chess.com rules, this is a draw here.} 2. Ng6#




 [FEN "6nk/5N2/6K1/8/8/8/8/8 b - - 0 1"]
</code></pre>
