Danish Gambit: What Each Rating Plays After 3.c3, and the 5...d5 Pawn Return

The Danish Gambit is 1.e4 e5 2.d4 exd4 3.c3, and White is offering one or two pawns for quick development and open lines toward the black king. Guides list the lines and tell you it is fun against unprepared opponents. What they do not tell you is what Black players at your level actually do after 3.c3, or how the main defence works once the pawns come back. We ran the maia3-5m checkpoint, see how Maia chess actually works, on two positions in the opening at seven rating bands from 1000 to 2200, and graded every legal move with Stockfish 18. Then we ran quick local Stockfish checks on a dozen further lines past those two positions. Percentages on this page are Maia3's predicted probability that a player at that rating chooses the move. They are not game counts.

Two conventions. Every evaluation is from White's side, so +0.50 means White is better by half a pawn and -0.33 means Black is better by a third of a pawn. The dataset tables come from Stockfish at depth 20. The line checks are separate quick runs of ten seconds per line, which reached depths between 15 and 24, so treat those scores as rough guides and expect a position to differ by several hundredths between the two methods.

What the Danish Gambit is

After 3.c3, Black can take with 3...dxc3 and White chooses between recapturing at once with 4.Nxc3, the one-pawn version, or sacrificing a second pawn with 4.Bc4 cxb2 5.Bxb2, the two-pawn version. Wikipedia files the opening under ECO code C21. As of October 2026, Chess.com calls 4.Bc4 the most popular variation when Black accepts and 4.Nxc3 slightly more conservative but still dangerous. House of Staunton says the one-pawn line is not especially scary for Black, which makes the two-pawn line the sharper one. In the two-pawn line White has two bishops pointing down the long diagonals at the black king.

Black can also decline with 3...d5, known as the Sorensen or Capablanca Defence. Some forum posts and roundups call 3...d5 the Schlechter, so here is the split we use, following Wikipedia. The Schlechter Defence is 5...d5 inside the accepted gambit. The Sorensen or Capablanca Defence is 3...d5. They are different positions.

Where it came from, and who played it

Wikipedia says Martin Severin From, a Danish player, essayed the gambit at the Paris 1867 tournament and is usually given credit for the opening. It also says the Swede Hans Lindehn played it regularly from 1857 at the latest, and it cites an earlier correspondence game, London against Edinburgh in 1824. Wikipedia calls the historical naming very confusing. In Denmark the opening is the Nordic Gambit, so the name Danish is not the Danish one.

House of Staunton lists Mieses, Marshall and Alekhine among those who played it. We found no verifiable Alekhine quotation about the gambit, so we attribute none. Wikipedia says that as more defensive lines for Black were found and improved, the gambit lost favor in the 1920s, and today it is rarely played in top level chess. Chess.com also calls it rare among the elite, though aggressive players still use it at lower levels.

The first decision: how Black answers 3.c3

In the position after 1.e4 e5 2.d4 exd4 3.c3, Stockfish 18 at depth 20 ranks 3...dxc3 first, at -0.33. Behind it come 3...Qe7 at -0.26, 3...d5 at -0.10, 3...Ne7 at -0.08 and 3...Nc6 at -0.03. So the engine thinks Black can take the pawn and stand a third of a pawn better, or decline and stand about level. Here is what Maia3 predicts people play.

In the table, "out" means the move was outside Maia's top five at that band. It does not mean zero probability. Taking the pawn is both the engine's best move and the likeliest human move at every band, and the evaluation gap between the two is zero at all seven. In our set of 13 openings, only the Smith-Morra Gambit also has a gap of zero at every band.

That is the surprise, and it comes with a catch. Black does not stumble by declining. The trouble is that taking the pawn gets less popular as players improve, from 72.7 percent at 1000 and 74.0 at 1400 to 65.2 at 2000 and 51.1 at 2200. At 2200 almost half of the predicted choices are something else. 3...Nc6 is the runner up at every band from 1000 to 1800, then shrinks to 6.5 percent at 2200, while 3...d5 climbs from 1.3 percent at 1200 to 24.3 percent at 2200 and is second at 2000 and 2200. So the model's strongest players often skip the pawn question, while its weakest almost always take the pawn and keep going.

One more detail. 3...d3 is a move that only enters Maia's top five from 1800. It rises from 3.1 percent at 1800 to 8.1 at 2200, and it gives White an edge of +0.75 in the dataset. Our depth 24 check agrees at +0.77 after 4.Bxd3. Stronger players are more likely than weaker ones to try this sharp pawn push, and it is not a good one.

One pawn or two: 4.Nxc3 or 4.Bc4

After 3...dxc3, our quick check scores 4.Nxc3 at -0.36, 4.Bc4 at -0.45 and 4.Nf3 at -0.82. The two versions are under a tenth of a pawn apart. At 1400 the model picks 4.Bc4 at 80.2 percent, which is the continuation the dataset followed. We only measured that one rating for White's move, so we do not claim how the choice shifts across bands.

The one-pawn line has a famous cousin. After 4.Nxc3 Nc6 5.Nf3, the position is the Goring Gambit, which White can also reach through the Scotch move order 1.e4 e5 2.Nf3 Nc6 3.d4 exd4 4.c3 dxc3 5.Nxc3. Wikipedia notes that Goring's own move order, with Nf3 before c3, avoids Schlechter's Defence. Our check of that position gives -0.22, with 5...Bb4 first, 5...Bc5 at -0.15 and 5...d6 at -0.02. If you like this structure, the Scotch Game page covers the quieter relative.

After 4.Bc4: do you take the second pawn?

This is the second position in our data. White has played 4.Bc4, Black has the move, and 4...cxb2 is the engine's best at -0.60 from White's side. Everything else trails by at least four tenths of a pawn: 4...Nc6 at -0.20, 4...d6 at -0.18, 4...Nf6 at -0.17, 4...d5 at -0.15 and 4...Bb4 at -0.13. The one move to avoid in the table is 4...Bc5, which gives White +1.04.

Again the engine's move is the likeliest human move at every band, gap zero. And again findability falls with rating. The capture is predicted at 56.4 percent at 1000 and 39.6 at 2200, losing a little at every step along the way. The runner up changes along the ladder: 4...Nf6 at 1000 and 1200, 4...Nc6 at 1400 and 1600, 4...d6 at 1800 and 2000, and 4...Nc6 again at 2200. Stronger players decline the second pawn more, and the declines that carry the weight are all within half a pawn of the best move. The average of the two positions tells the same story: the chance of the engine's move is 64.5 percent at 1000 and 45.3 percent at 2200.

Why stronger players decline more is something the data cannot say. What the numbers show is the behaviour: if you reach 4.Bc4 at 1400, about half the time Black will take the second pawn, and at 2200 about three times in five they will not.

The Schlechter 5...d5 pawn return

Suppose Black does take both pawns. After 4...cxb2 5.Bxb2, a quick check puts the position at -0.52 from White's side. Black is up two pawns and better by half a pawn, and the best replies are 5...Nf6 at -0.52, 5...Bb4+ at -0.49 and 5...c6 at -0.41. Black's extra material is only safe if White's initiative can be stopped. The Schlechter Defence, 5...d5, is the way Black gives a pawn back to do that.

Wikipedia says Carl Schlechter recommended returning a pawn with 5...d5 as one of the most reliable defences for Black, with positions rated equal or slightly better for Black thanks to the queenside majority in the endgame. Here is the line our check followed: 5...d5 6.Bxd5 Nf6. White is now to move, and the quick check finds one reasonable move. 7.Bxf7+ scores +0.02. The next two candidates, 7.Nge2 and 7.Nc3, score -0.90 and -0.94, so White is close to forced to take on f7.

After 7.Bxf7+ Kxf7 8.Qxd8, Black has the in-between check 8...Bb4+, and the check line then runs 9.Qd2 Bxd2+ 10.Nbxd2 Rd8 11.Nf3 Kg8. White has only one move there: 9.Nc3 and 9.Bxc3 score -3.33 and -4.18. The score for 8...Bb4+ is 0.00 from White's side at depth 22. Queens are off and the check scores it level. That is the answer to the question the other pages leave open. The gambit does not fail to a refutation here. It simply gives White nothing more than an equal endgame, and White has to play 7.Bxf7+ on the way. The price is Black's edge. The same check gives 5...Nf6 at -0.52, so the Schlechter trades half a pawn of advantage for a simple, level ending.

The other fifth moves for Black are worth knowing, because a pawn return is not forced. Each position below has White to move after the Black reply.

• 5...Bb4+ leaves White with 6.Nc3 at -0.39 as the best reply. 6.Nbd2 and 6.Kf1 are at -0.89 and -0.90, so White should block with the knight on c3.
• 5...Nf6 gives 6.Nc3 at -0.52, then 6.e5 at -0.65, whose line runs 6...Ne4 7.Bxf7+ Kxf7 8.Qf3+ Ke8. That one is a shallow depth 15 check, so take it as a sharp idea and not a verdict.
• 5...Nc6 is much easier on White: 6.Nf3 scores -0.14, against -0.53 for 6.Nc3.
• 5...Qe7 is worse for Black: 6.Nc3 scores +0.58. The alternatives 6.Qe2 and 6.Bb3 score -0.20 and -0.56, so White needs the knight move here.

Last, a line from the two-pawn gambit where White develops quickly and Black does well anyway: 5...Bb4+ 6.Nc3 Nf6 7.Ne2 is -0.80 for White with 7...O-O best, and 7...Bxc3 at -0.62. If you are Black, castling at the first chance is the idea to carry from this.

Declining with 3...d5

Here is the other main road, and the one Maia3 shows rising with rating. After 3...d5, White's best is 4.exd5 at 0.00, with 4.Qxd4 next at -0.17 and 4.Qa4+ at -0.80. The usual run is 4.exd5 Qxd5 5.cxd4, and the quick check gives +0.02, with the top three Black replies (5...Nc6, 5...Bb4+ and 5...Nf6) tied at that score. White has recovered the pawn and the position is level, with Black developing freely. The Wikibooks theory table marks 5...Nc6 6.Nf3 Bb4+ 7.Nc3 Bg4 8.Be2 Bxf3 9.Bxf3 Qc4 as equal, and our numbers do not argue.

One forum poster called 3...d5 a risk-free, very slight technical edge for Black in the ending. Our check scores it level rather than better for Black, but either way it is a quiet ending, which is hard on a player who wants the attack.

What to play by rating band

If you are White, the engine says 3.c3 is playable but not an attempt at an edge. Below 1800, about three Black players in four take on c3 in our model, so your gambit is accepted and the main question becomes which bishop line you know. Learn the 4.Bc4 cxb2 5.Bxb2 position well and prepare for 5...d5 6.Bxd5 Nf6, where 7.Bxf7+ is the move that holds the balance. Sources name Bxf7+, Ne5+ and the Qb3 double threat on f7 and b7 as the recurring tactical themes, and those are worth drilling alongside the opening. We did not check any trap line, so we show none. At 2000 and above, expect 3...d5 about one game in eight at 2000 and one in four at 2200, so the Sorensen line deserves the same attention as the main line. If you want a calmer bishop on c4, the Italian Game page shows the same diagonal without the pawn deficit.

If you are Black below 1800, take the pawn, take the second pawn, and know how to give one back. Your best path is the capture on b2, then a quick 5...Nf6, which keeps the larger edge in our check, or 5...d5 if you would rather head for a level ending. Avoid 4...Bc5. At 2000 and above, the engine's capture is still best at -0.33 and -0.60, but declining with 3...d5 or 4...Nc6 costs you little, so choose by what you can play. Our chess openings by rating dataset uses the same method for other openings. For learning the ideas in place of memorising the lines, why you should stop memorizing openings and learn plans fits this opening well, since the plan, bishops and open lines against the king, is the same in every branch.

Do club results favor White?

House of Staunton says human results at club level heavily favor White, and it states no pool or rating band. We cannot confirm or refute that, because our dataset predicts moves and does not count results. What we can say is narrow. At every band we measured, the model expects Black to find the engine's best answer more often than any other single answer, but the share falls with rating, and the quick checks put Black's best lines at level or better. As of October 2026, chess.com lists as a con that Black can easily equalize with some theory, which fits that picture.

Where other pages are better

This page is narrow on purpose. The dataset holds two positions, the one after 3.c3 and the one after 3...dxc3 4.Bc4, and nothing past move four. The dozen line checks are quick local runs, not deep analysis, and they are no substitute for an opening database. We have no game results by rating and did not open the Lichess explorer. Wikipedia is the better reference for history and the full variation list, and chess.com is better for browsing the lines. None of the pages we opened splits Black's replies to 3.c3 by rating, or walks through the Schlechter pawn return with engine scores, which is the gap this page fills.

What to take from it

The Danish Gambit is a pawn sacrifice that the engine says is sound but not better for White. The headline is human, not theoretical: taking the pawn is both the best and likeliest reply at all seven bands, and yet it falls from 72.7 percent at 1000 to 51.1 at 2200 as 3...d5 climbs to 24.3, and the second capture on b2 falls from 56.4 percent to 39.6. Black's safest answer to the full gambit is the Schlechter 5...d5, a pawn back and a level endgame, while 5...Nf6 keeps more of the edge and asks for more precision. Maia3 is a model of human choice from the maia3-5m checkpoint, not a count of real games, and every percentage above should be read that way.