DanQuigley: 1.e4 e5 2.f4
This move initiates the King's Gambit.
Black accepts the gambit.
This is the most popular move, no doubt because it follows Lasker's "Knights before Bishops" rule. However 3.Bc4 does every bit and even a little better for White in practical tests.
This is called the Cunningham Defense and has been played since the beginning of modern chess. It is the fourth most popular move in this position, behind 4...g5, 4...d5, and 4...d6, but it has just as much bite for Black as the alternatives.
White proceeds with his development by bringing the Bishop out to a spot where it can bear down on f7. If White could take another move now it would no doubt be 0-0, whereupon the pressure on Black's f7, after the Knight moves the the fifth rank, would be all but unbearable.
The point of Black's last move. He gets in this annoying check in order to complicate White's plans. Euwe and others demonstrated keeping the Bishop instead and playing 4...Nf6 is probably even stronger for Black, but Larsen's opponent probably apparently didn't get the memo, or wasn't convinced, and plays classically instead. Taking the h4 Bishop and playing Kf1 after Black recaptures with the Queen is also perfectly playable for White, though very seldom tried.
Computer programs consider White's better line to be 5.Kf1 Be7 6.d4 Nf6 7.e5 Nh5 8.Ng5 Bxg5 9.Qxh5 g6 = -0.08 (36 ply). However, 5.g3 turned out fine for Morphy, so Larsen must have figured he could make it work too.
5...fxg3 ⩱ -0.64 (29 ply)
At last! White gets this move in.
6...gxh2+ 7.Kh1 Nh6
This move at least puts a stop to all Bxf7+ sacrifice ideas. The fearless computer programs consider 7...d5 8.exd5 = -0.44 (26 ply) to be better for Black, but Morphy chose 8.Bxd5 against Bird in 1859 with a good result due to later mistakes by Bird. Black here is playing in the style of Von Der Lasa, circa 1839. Von Der Lasa didn't have success with this move either, but Black's position is somewhat playable. Bilguer (who had White versus Von Der Lasa) was simply the stronger player.
8.d4= +0.06 (21 ply)
This position has been reached only a few times over the centuries, though by some pretty famous names. There is no consensus whatsoever on how Black should best proceed here.
Computer programs prefer 8...d6 9.Nc3 O-O 10.Bxh6 gxh6 11.Qd2 Bg5 12.Qxh2 Bg4 = +0.22 (21 ply) Other moves have been tried by Black, the most popular of which is 8...d5. There is also 8...Ng4 by Von Der Lasa and 8...Qe7 as played by Von Dory against Reshevsky in 1920. Castling here appears to be Lauridsen's dubious theoretical novelty. Chessbase provides nine subsequent tries with the move, the score being 7-2 in White's favor.
9.Bxh6 ⩲ +0.93 (27 ply)
9...gxh6 10.Ne5 Qe7?
This mistake proved to be fatal. Essential for Black was getting his other pieces in the game with 10...d5 11.Nxf7 Qe7 12.Bxd5 Nc6 13.Nxh6+ Kg7 14.Rxf8 = +0.47 (26 ply)
11.Nc3+- +3.95 (26 ply)
11...d6 12.Nxf7 Be6 13.Nxh6+ Kg7 14.Bxe6 Kxh6 15.Qd2+ +- +3.54 (26 ply)
The wrong piece takes on f7. Easily winning is 12.Nxf7 d5 13.exd5 Qe3 14.d6 Bf2 15.Qe2 Qxe2 16.Nxe2 b5 +- +7.02 (29 ply)
12...Kg7 ⩲ +1.07 (28 ply)
13...d6 14.Rxf8 Qxf8 15.Nf7 Be6 16.Qf3 Kg8 17.Rf1 Qg7 ⩲ +0.65 (29 ply)
14.Qxf1 ± +1.62 (30 ply)
White gives Black his chance to equalize rather than put him away with 15.Nf7 Be6 16.Qg2+ Bg5 17.Rf1 Bc4 18.Rf3 Nd7 19.b3 Bxf7 ± +2.00 (28 ply)
15...Bg5= -0.08 (27 ply)
16.Qf2 Be6 17.d5 cxd5?
Black goes astray and misses his opportunity to stay in the game with 17...Bg8 18.Rd1 Kh8 19.Nxg5 hxg5 20.Qd4+ Qg7 21.Qxg7+ = -0.50 (25 ply)
18.exd5 ± +2.50 (30 ply)
Not of much help either was 18...Bd7 19.Re1 Qf8 20.Ne4 Kh8 21.Qd4+ Qg7 22.Qxg7+ Kxg7 +- +2.66 (28 ply)
Not crisp. White finishes Black off with 19.Re1 Bxh5 20.Rxe7+ Bxe7 21.Nd4 Kh8 22.Qf5 Nd7 23.Qxh5 +- +6.75 (27 ply)
Black can put up more resistance with 19...Bxh5 20.Ne6+ Kg8 21.Re1 Bg6 22.Qg3 Kh8 23.Kxh2 Qf7 ⩲ +1.28 (28 ply)
20.Re1+- +5.53 (29 ply)
20...Qf6 21.Qxf6+ Kxf6 22.Rf1+ Kg7 23.Bxf7 Nd7 24.Be6
In view of 24...Rf8 25.Rxf8 Nxf8 26.Bc8 Kf6 27.Ne4+ Ke5 28.Nxg5 b6 +- +3.70 (33 ply) Black resigned.