user2299: [FEN ""]

1.e4 e5 2.f4 exf4 3.Nf3 c5

What's the refutation of Black's unusual third move, or anyway the best way to play against it? Which is stronger, the Open Variation 4. d4 cxd4 5. Bxf4, or the Closed Variation 4. Bc4 Nc6 5. d3?
If there is no refutation (as seems to be the case), then why is 3...c5 hardly ever played, or mentioned in the books? Is it because there are so many good lines against the King's Gambit that nobody needed another one? Is it that the people who like to play c5 usually play it on the first move?

user4418: White's f4 sacrifices a pawn for rapid development and the possibility of an attack against the uncastled black king. c5 as a response from black addresses none of the issues in his position and just wastes a move making the gambit all the more effective. White's plan remains on track - Bc4, O-O, win the pawn back on f5 and smash through on f7.

user19877: My initial reaction is that 3...c5 is very weak just by looking at it, which is why it is so rare. The ECO key that comes with ChessBase's Mega databases is very detailed, but even this does not even have its own specific sub-key.
There are 112 games in Mega 2020 database with 3...c5. The most popular response, played in 87 of the 112 games was 4.Bc4, which had a winning percentage of 64.9%, followed by 4.d4, which was played in 17 games and had a winning percentage of 61.8%). 4.d3 (6 games/33.3%) and 4.Nc3 (2 games/50.0%) were also played.
Obviously, 4.Bc4 and 4.d4 are the choices, but you also have to think about what to play stylistically: If you play the King's Gambit, you like open, tactical, positions, so it does not make sense to play the latter two moves at all unless they eventually become the natural move to finish development later. You still want to strive for the quick development of the kingside, and play down the f-file and open center.
3...c5 is weak, but as I looked through the games, the only plan that white needs to fear is the Be7 and g5 plan (possibly g5 first), holding the pawn. Black scored in the 40-50% range in most of those lines. That might bode well for the 4.d4, and early Bxf4 plan by white.
Now that I have discussed what humans play, I am going to see what Stockfish 11 says. After looking at many lines, a lot of which are below, but that is only a small fraction of what I actually looked at, I cannot say that Stockfish found any pure refutation, but I suspect that the you will do well following the main line because if black plays 3...c5, it is because black is a weak player to start with...deny black holding f4, and you will probably win most of the time as the human stats above show.
4.Bc4 and 4.d4 early on both come in with the same evals, but as the depth gets deeper (depth 33), 4.Bc4 is preferred by Stockfish, but they are both the typical minor pluses that computers typically give white in the opening, about +.5, but as I force in lines, and go deeper, everything levels out a lot. Here are some sample lines.
One last note about the play: The reason that white can play the early Bc4 in these lines, and not worry about g5, it that it seems tactically refuted if black tries to save it. White is playing a gambit line, so I was not really worried about trying to get the pawn back simply because we are down a pawn, but the computer might be; nevertheless, I was concerned because it gets in the way of developing the Bc1 and opening the f-file, so I did lean toward recovery.
Please note that there are also extensive comments within these lines.
 [FEN ""]

 1. e4 e5 2. f4 exf4 3. Nf3 c5 4. Bc4 Nc6 5. d3 {This is Stockfish's favorite, and is indicative of trying to stop the early g5 plan. It still is not the most human move, which I will also cover.} (5. d4 cxd4 6. Bxf4 Nf6 7. O-O Nxe4 8. Bd5 $1 {This leads to mind-boggling complications.} (8. Re1 d5 $17) 8... Nf6 9. Ng5 Nxd5 10. Nxf7 Qf6 (10... Kxf7 11. Qh5+ Ke6 12. Nc3 {And the other rook comes in and wins...+8.}) 11. Bg5 Qg6 12. Qe1+ Be7 13. Bxe7 Ne3 14. Rf2 Nxe7 15. Nxh8) (5. O-O $6 {This is slow, but leads to typical positions.} g5 6. d4 cxd4 7. Bxf7+ (7. g3 $5) 7... Kxf7 8. Nxg5+ Qxg5 9. Bxf4 Qg6 10. Be5+ Ke8 11. Bxh8 b6 {With wild play that the computer likes barely for black, but I do not believe that a human will survive.}) 5... Bd6 $5 (5... g5 $2 6. h4 g4 7. Ng5 $18) (5... Be7 6. Bxf4 Nf6 7. Nc3 d6 8. O-O O-O 9. Qd2 $16) 6. O-O Nf6 (6...Nge7 $4 7. Ng5 O-O 8. Qh5 $18) 7. Nc3 (7. Qe1 $5) (7. e5 $2 {This does not work due to tactics and threats of smothered mate, and the Qd1 and Bc1 hanging if the queens get traded.} Nxe5 8. Re1 O-O 9. Nxe5 Bxe5 10. Rxe5 d5 11. Bb3 c4 12. dxc4 Ng4 13. Re2 dxc4 14. Qxd8 Rxd8 15. Nc3 cxb3 16. axb3 g5 $17) 7... O-O 8. Bd2 a6 9. a4 {And the computer thinks this is roughly equal, but white is more fun to play.}


2299: <pre><code>[FEN ""]

1.e4 e5 2.f4 exf4 3.Nf3 c5
</code></pre>

<p>What's the refutation of Black's unusual third move, or anyway the best way to play against it? Which is stronger, the Open Variation 4. d4 cxd4 5. Bxf4, or the Closed Variation 4. Bc4 Nc6 5. d3?</p>

<p>If there is no refutation (as seems to be the case), then why is 3...c5 hardly ever played, or mentioned in the books? Is it because there are so many good lines against the King's Gambit that nobody needed another one? Is it that the people who like to play c5 usually play it on the first move?</p>
 4418: <p>White's f4 sacrifices a pawn for rapid development and the possibility of an attack against the uncastled black king. c5 as a response from black addresses none of the issues in his position and just wastes a move making the gambit all the more effective. White's plan remains on track - Bc4, O-O, win the pawn back on f5 and smash through on f7.</p>
 19877: <p>My initial reaction is that 3...c5 is very weak just by looking at it, which is why it is so rare. The ECO key that comes with ChessBase's Mega databases is very detailed, but even this does not even have its own specific sub-key.</p>

<p>There are 112 games in Mega 2020 database with 3...c5. The most popular response, played in 87 of the 112 games was 4.Bc4, which had a winning percentage of 64.9%, followed by 4.d4, which was played in 17 games and had a winning percentage of 61.8%). 4.d3 (6 games/33.3%) and 4.Nc3 (2 games/50.0%) were also played.</p>

<p>Obviously, 4.Bc4 and 4.d4 are the choices, but you also have to think about what to play stylistically: If you play the King's Gambit, you like open, tactical, positions, so it does not make sense to play the latter two moves at all unless they eventually become the natural move to finish development later. You still want to strive for the quick development of the kingside, and play down the f-file and open center.</p>

<p>3...c5 is weak, but as I looked through the games, the only plan that white needs to fear is the Be7 and g5 plan (possibly g5 first), holding the pawn. Black scored in the 40-50% range in most of those lines. That might bode well for the 4.d4, and early Bxf4 plan by white.</p>

<p>Now that I have discussed what humans play, I am going to see what Stockfish 11 says. After looking at many lines, a lot of which are below, but that is only a small fraction of what I actually looked at, I cannot say that Stockfish found any pure refutation, but I suspect that the you will do well following the main line because if black plays 3...c5, it is because black is a weak player to start with...deny black holding f4, and you will probably win most of the time as the human stats above show.</p>

<p>4.Bc4 and 4.d4 early on both come in with the same evals, but as the depth gets deeper (depth 33), 4.Bc4 is preferred by Stockfish, but they are both the typical minor pluses that computers typically give white in the opening, about +.5, but as I force in lines, and go deeper, everything levels out a lot. Here are some sample lines.</p>

<p>One last note about the play: The reason that white can play the early Bc4 in these lines, and not worry about g5, it that it seems tactically refuted if black tries to save it. White is playing a gambit line, so I was not really worried about trying to get the pawn back simply because we are down a pawn, but the computer might be; nevertheless, I was concerned because it gets in the way of developing the Bc1 and opening the f-file, so I did lean toward recovery.</p>

<p>Please note that there are also extensive comments within these lines.</p>

<pre><code> [FEN ""]

 1. e4 e5 2. f4 exf4 3. Nf3 c5 4. Bc4 Nc6 5. d3 {This is Stockfish's favorite, and is indicative of trying to stop the early g5 plan. It still is not the most human move, which I will also cover.} (5. d4 cxd4 6. Bxf4 Nf6 7. O-O Nxe4 8. Bd5 $1 {This leads to mind-boggling complications.} (8. Re1 d5 $17) 8... Nf6 9. Ng5 Nxd5 10. Nxf7 Qf6 (10... Kxf7 11. Qh5+ Ke6 12. Nc3 {And the other rook comes in and wins...+8.}) 11. Bg5 Qg6 12. Qe1+ Be7 13. Bxe7 Ne3 14. Rf2 Nxe7 15. Nxh8) (5. O-O $6 {This is slow, but leads to typical positions.} g5 6. d4 cxd4 7. Bxf7+ (7. g3 $5) 7... Kxf7 8. Nxg5+ Qxg5 9. Bxf4 Qg6 10. Be5+ Ke8 11. Bxh8 b6 {With wild play that the computer likes barely for black, but I do not believe that a human will survive.}) 5... Bd6 $5 (5... g5 $2 6. h4 g4 7. Ng5 $18) (5... Be7 6. Bxf4 Nf6 7. Nc3 d6 8. O-O O-O 9. Qd2 $16) 6. O-O Nf6 (6...Nge7 $4 7. Ng5 O-O 8. Qh5 $18) 7. Nc3 (7. Qe1 $5) (7. e5 $2 {This does not work due to tactics and threats of smothered mate, and the Qd1 and Bc1 hanging if the queens get traded.} Nxe5 8. Re1 O-O 9. Nxe5 Bxe5 10. Rxe5 d5 11. Bb3 c4 12. dxc4 Ng4 13. Re2 dxc4 14. Qxd8 Rxd8 15. Nc3 cxb3 16. axb3 g5 $17) 7... O-O 8. Bd2 a6 9. a4 {And the computer thinks this is roughly equal, but white is more fun to play.}
</code></pre>
