Chess Opening Theory/1. e4/1...e5/2. f4/2...exf4/3. Nf3/3...g5/4. h4/4...g4/5. Ne5

The Kieseritzky Gambit has been considered the main line of the King's Gambit for a long time. The continuations that follow this position have interesting strategic possibilities for both sides. It was popularized by Lionel Kieseritzky in the 1840s. It was used very successfully by Wilhelm Steinitz, and was used by Boris Spassky to beat Bobby Fischer in a famous game at Mar del Plata in 1960. This motivated Fischer into developing his own defense to the King's Gambit (the Fischer Defense). It's been out of favour at high levels for a few decades now though, as analysts with computers have found mistake after mistake in the old Victorian books.

Black's pawn on g4 is attacked, but Black is still a pawn up, so giving back one of the two pawns on f4 and g4 wouldn't be a disaster. As a secondary consideration, f7 is also attacked and White may be able to intensify the attack with Bc4 if given the chance.
 * That f7 weakness is why the mechanical attempt to protect the pawn with 5...h5 doesn't work too well. 6.Bc4 would leave Black resorting to awkward defensive moves like ...Nh6 and ...Rh7.
 * 5...Nf6 is the most common move, not to defend the g4-pawn (because it doesn't) but to counter-attack e4 and so deny White the necessary tempo to capture on g4. If White takes a move to defend e4, Black can then unleash the c8-bishop with ...d6, which does defend the g4-pawn and drives away the White knight.
 * 5...d6 is the main alternative to 5...Nf6. After 6.Nxg4 Nf6 it looks as though Black has just played the moves in the wrong order, but the point is that after exchanging knights on f6 it will be Black who has come out of the King's Gambit with a lead in development. This is the perennial problem with playing gambits: can your opponent gain more by giving the material back than you gained by sacrificing it?
 * 5...Bg7 prepares to set a dastardly trap if White takes the pawn, but an alert White player has a couple ways of dodging it.
 * 5...Qe7 generally wins the pawn back but at the cost of trading off the queens, which blunts Black's attacking potential and makes the weak f-pawns into more of a factor.

Theory table
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1.e4 e5 2.f4 exf4 3.Nf3 g5 4. h4 g4 5. Ne5