user17540: One sometimes sees the claim that in every chess position, either White has a forced win, or Black has a forced win, or both players can force a draw.
While this claim is "morally" correct, it is technically not quite correct.  To be pedantically correct, in the third case, we should say that both players can force at least a draw.  The point is that there can exist positions in which neither White nor Black can force a win, but White can force Black to win, and Black can force White to win.  In such a scenario, neither player can "force a draw" in the sense of guaranteeing that the game will not terminate in a win for either player.
My question is, has this observation been made before (most likely, by chess problem composers)? I would be surprised if the observation is original, but I have not seen anyone state it explicitly before.
Below is a position (with White to move) that I came up with to illustrate the point.  The position is theoretically drawn, and this can be seen without tablebases; the only defense to Black's threat of 1...d1Q+ is 1.f4, after which Black can avoid defeat only with 1...d1Q+ 2.Qxd1 Qxf4+ or 1...Qxf4+ 2.Qxf4 d1Q+ with a draw in either case.  But White can force Black to win with 1.Qg2+ Qxg2#, and if White tries to "force a draw" with 1.f4 then Black can force White to win with 1...Qg2+ 2.Qxg2#.
[FEN "8/8/8/8/6Q1/5P2/3p3q/5K1k w - - 0 1"]


I contacted Noam Elkies and he said he had not seen this stipulation before, but he noted that the  (known) five-man minimum for a selfmate (see below) also achieves "my" task.  White can selfmate with 1.Qg7+ Qxg7#.  Either of the alternatives 1.Kf6 or 1.Kh6 leads to a tablebase draw, but also allows Black to selfmate with 1...Qg7+.
[FEN "6qk/4Q3/6K1/8/6b1/8/8/8 w - - 0 1"]


user8201: I have never heard your point before, and it might be original.
There is a famous theorem by Ernst Zermelo (more famous for his set theory work), see https://en.m.wikipedia.org/wiki/Zermelo%27s_theorem_(game_theory) which when applied to chess means that either White can win, Black can win, or both players can force at least a draw. To regular chess players, and even apparently to Wikipedians, the words “at least” might not seem necessary but to problemists they are essential, as the questioner’s elegant counter-examples show.
If Black is forced to mate, then he/she has gained at least a draw, so Zermelo’s theorem is not violated.

17540: <p>One sometimes sees the claim that in every chess position, either White has a forced win, or Black has a forced win, or both players can force a draw.</p>
<p>While this claim is &quot;morally&quot; correct, it is technically not quite correct.  To be pedantically correct, in the third case, we should say that both players can force <b>at least</b> a draw.  The point is that there can exist positions in which neither White nor Black can force a win, but White can force Black to win, and Black can force White to win.  In such a scenario, neither player can &quot;force a draw&quot; in the sense of guaranteeing that the game will not terminate in a win for either player.</p>
<p>My question is, <strong>has this observation been made before (most likely, by chess problem composers)?</strong> I would be surprised if the observation is original, but I have not seen anyone state it explicitly before.</p>
<p>Below is a position (with White to move) that I came up with to illustrate the point.  The position is theoretically drawn, and this can be seen without tablebases; the only defense to Black's threat of 1...d1Q+ is 1.f4, after which Black can avoid defeat only with 1...d1Q+ 2.Qxd1 Qxf4+ or 1...Qxf4+ 2.Qxf4 d1Q+ with a draw in either case.  But White can force Black to win with 1.Qg2+ Qxg2#, and if White tries to &quot;force a draw&quot; with 1.f4 then Black can force White to win with 1...Qg2+ 2.Qxg2#.</p>
<pre><code>[FEN &quot;8/8/8/8/6Q1/5P2/3p3q/5K1k w - - 0 1&quot;]
</code></pre>
<br>
I contacted Noam Elkies and he said he had not seen this stipulation before, but he noted that the  (known) five-man minimum for a selfmate (see below) also achieves "my" task.  White can selfmate with 1.Qg7+ Qxg7#.  Either of the alternatives 1.Kf6 or 1.Kh6 leads to a tablebase draw, but also allows Black to selfmate with 1...Qg7+.
<pre><code>[FEN &quot;6qk/4Q3/6K1/8/6b1/8/8/8 w - - 0 1&quot;]
</code></pre>
 8201: <p>I have never heard your point before, and it might be original.</p>
<p>There is a famous theorem by Ernst Zermelo (more famous for his set theory work), see <a href="https://en.m.wikipedia.org/wiki/Zermelo%27s_theorem_(game_theory)" rel="nofollow noreferrer">https://en.m.wikipedia.org/wiki/Zermelo%27s_theorem_(game_theory)</a> which when applied to chess means that either White can win, Black can win, or both players can force <em>at least</em> a draw. To regular chess players, and even apparently to Wikipedians, the words “at least” might not seem necessary but to problemists they are essential, as the questioner’s elegant counter-examples show.</p>
<p>If Black is forced to mate, then he/she has gained at least a draw, so Zermelo’s theorem is not violated.</p>
