1.e4 d5
2.exd5 Qxd5
3.Nc3 Qa5
4.d4 c6
5.Bc4 Bf5
6.Nf3 e6
7.Ne5 Nf6
8.g4 Be4
9.f3 Bd5
10.Bd3 Bb4
11.Bd2 Nd7
12.a3 Bd6
13.Ne4

Black resigns 1-0

I've never seen that, and it's not in the Openings Explorer. It does not look trustworthy--exposing the queen while blocking the effective development of the ♗c8 and all that--but there appear to be some points as well.

The natural continuation would be <4.d4 Nc6 5.Bd3>:

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But after 5...Qa5 things get a little awkward for White. His ♗d3 blocks the defense of the d-pawn, and 6.Nf3 Bg4 is also annoying. If White resists tempation and plays 5.Nf3 first, then 5...Nb4 is annoying.

Perhaps White shouldn't bother driving the queen off f5, where she's not that well placed. 4.Bc4 and 5.d3 would eliminate many of Black's cheapos, and he would still have to spend time untangling.

1.e4 d5 2.exd5 Nf6 3.Nf3 Bg4 4.Bb5+ Nbd7 5.h3 Bh5 6.g4 Bg6 7.Ne5 a6 8.Nxg6 hxg6 9.Bc4 Ne5 10.Bb3 Nexg4 11.d4 Qd7 12.Nc3 0-0-0 13.Qf3 Nh6 14.Bxh6 Rxh6 15.Qe3 e6 16.dxe6 Qxe4 17.exf7 Qxf3+ 18.fxe3 Bb4 19.a3 Bxc3+ 20.bxc3 Ne4 21.Be6+ Kb8 22.Rb1 Nxc3 23.Rb3 Ne4 24.Bd5 Nd6 25.0-0 Rf8 26.Kh2 g5 27.c4 Rf6 28.Rxf6 gxf6 29.c5 Nxf7 30.Rxb7+ Kc8 31.Ra7 Kd7 32.Rxa6 Ne5 33.a4 Nd3 34.Bc4 Nxc5 35.Bb5+ Kd8 36.Ra8+ Ke7 37.Rxf8 Kxf8 38.a5 Ke7

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39.Bd3(!?) I don't know if this is ! or ?. It's good for him if I take it but since I didn't, doesn't it just waste a move?

I returned the favor with <52...Kd6??>

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It's an interesting position, and I think 52...Kd6 is actually the right move. After 52...Kd4, White wins after 53.e5 c4 54.e6 c3 55.e7 c2 56.e8Q c1Q 57.Qd8+!. Now Black cannot play 57...Ke3 58.Qxg5+ winning the queen, but also losing is 57...Kc3 58.Qc8+ followed by trading queens and winning on the kingside.

52...Kd6 doesn't seem right at first glance, since it allows the pawn to advance with check. But Black has enough time to survive this, and his king is headed to c7 to stop any skewer checks by White on the c-file.

After <53.Kf6>, the fatal error was <53...Kd7?>. Black draws after 53...c4 54.e5+ Kd7! 55.Kf7 c3 56.e6+ Kc7 57.e7 c2 58.e8Q c1Q. Now White cannot trade queens, and even if should he be able to win the g-pawn that won't be enough to win the game.

The problem with 53...Kd7 was that it allowed White to take the g-pawn while his king was still in the square of the c-pawn and his pawns far enough apart to protect each other.

I notice that after <1 e4 d5 2 exd5 Qxd5 3 Nc3> Tiviakov always chooses <3 ... Qd6> whereas the popular <3 ... Qa5> is the move that so often finds black in trouble.

I was thinking I recently (6 months or so?) saw a game with 3. ...Qd6 where white introduced a move giving black some new problems?

There are approximately 43,405 games in the database that end decisively in 25 moves or less, which is about 7.33% of the entire database. Of these, White wins 26,903, Black wins 16,502. That's 62% White wins, or 1.63 White wins for each Black win.

Now let's look at the figures for Black's move one responses to 1.e4:

Miscellaneous (ECO B00)
W 231 B 123 65% 1.88

Scandinavian (B01)
W 435 B 178 71% 2.44

Alekhine (B02-B05)
W 313 B 173 64% 1.81

Modern, Pirc, etc. (B06-B09)
W 990 B 511 66% 1.94

Caro-Kann (B10-B19)
W 939 B 429 69% 2.19

Sicilian (B20-B99)
W4985 B3174 61% 1.57

French (C00-C19)
W1720 B 900 66% 1.91

1.e4 e5 (C20-C99)
W6428 B4107 61% 1.57

By this criteria, the Scandinavian does appear to have the highest risk of losing a miniature game with Black. Of course, by this criterion, the Caro-Kann is the 2nd most dangerous, which I think most would find counter-intuitive (though it does back up <parisattack>'s comment about their similarity). The equality of the Sicilian and 1.e4 e5 is also interesting.