user25509: I know popular openings like the Queen's Gambit can be accepted with an initiative for white. Is there any gambit where accepting it would lead to a forced mate for the player that accepted it?

user29548: I would say that in lower levels, the Blackburne-Shilling Gambit is a gambit that you should never accept as the capturing the pawn on e5 can lead to a lot of traps.
[FEN ""]

1. e4 e5 2. Nf3 Nc6 3. Bc4 Nd4


user17330: I would add that there are situations where one side "offers" the material that cannot be taken, but it is not really intended as a trap, it happens in the course of a logical development of the opening. The most "mainstream" example is perhaps the Berlin defense:
[fen ""]

1.e4 e5 2.Nf3 Nc6 3. Bb5 Nf6 4.O-O Ne4 5.d4 Nd6 (5... exd4 6. Re1 d5 Nxd4) 6.Bxc6 dxc6 7. dxe5 Nf5 8. Qxd8 Kxd8 

White's 4. O-O and 5.d4 seems to offer black a pawn, however if black accepts, the pin is a problem. White threatens both f3. and Nc6. It is not quite a forced mate but Black will have to give up material without complete compensation. "Everyone knows" that it's better not to take the pawn.

user4418: Yes. In this line in the Dutch Defence black cannot take the offered bishop
[fen ""]

1. d4 f5 2. Bg5 h6 3. Bh4 g5 4. e3 gxh4?? 5. Qh5#


user15221: While it's not generally given as part of the explicit definition, the term "gambit" usually refers to an offer of material that can be accepted. If it can't be accepted, then it's a trap.
You can look through chess traps and see that many of them involve apparently giving up material.

25509: <p>I know popular openings like the Queen's Gambit can be accepted with an initiative for white. Is there any gambit where accepting it would lead to <strong>a forced mate</strong> for the player that accepted it?</p>
 29548: <p>I would say that in lower levels, the Blackburne-Shilling Gambit is a gambit that you should never accept as the capturing the pawn on e5 can lead to a lot of traps.</p>
<pre><code>[FEN &quot;&quot;]

1. e4 e5 2. Nf3 Nc6 3. Bc4 Nd4
</code></pre>
 17330: <p>I would add that there are situations where one side &quot;offers&quot; the material that cannot be taken, but it is not really intended as a trap, it happens in the course of a logical development of the opening. The most &quot;mainstream&quot; example is perhaps the Berlin defense:</p>
<pre><code>[fen &quot;&quot;]

1.e4 e5 2.Nf3 Nc6 3. Bb5 Nf6 4.O-O Ne4 5.d4 Nd6 (5... exd4 6. Re1 d5 Nxd4) 6.Bxc6 dxc6 7. dxe5 Nf5 8. Qxd8 Kxd8 
</code></pre>
<p>White's 4. O-O and 5.d4 seems to offer black a pawn, however if black accepts, the pin is a problem. White threatens both f3. and Nc6. It is not quite a forced mate but Black will have to give up material without complete compensation. &quot;Everyone knows&quot; that it's better not to take the pawn.</p>
 4418: <p>Yes. In this line in the Dutch Defence black cannot take the offered bishop</p>
<pre><code>[fen &quot;&quot;]

1. d4 f5 2. Bg5 h6 3. Bh4 g5 4. e3 gxh4?? 5. Qh5#
</code></pre>
 15221: <p>While it's not generally given as part of the explicit definition, the term &quot;gambit&quot; usually refers to an offer of material that can be accepted. If it can't be accepted, then it's a trap.</p>
<p>You can look through <a href="https://en.wikipedia.org/wiki/List_of_chess_traps" rel="noreferrer">chess traps</a> and see that many of them involve apparently giving up material.</p>
