Bishop's Opening: Why 3. d3 instead of 3. Nc3?

In the Bishop's Opening the much preferred 3rd move for White is 3. d3 instead of 3. Nc3. Black is attacking White's e4-pawn on the 2nd move so it's understandable that White will defend it on the 3rd move, but 3. Nc3 seems more natural than 3. d3. I have never heard the reasoning for this, but this is what I *believe* might be the reason: 3. Nc3 would allow the bishop move 3...Bb4 to put pressure on that knight at c3, whereas Black wouldn't consider playing 3...Bb4+ after 3. d3 because that bishop would just get driven off with 4. c3. Does anybody know if this is the real reason, or is there some other logic behind the preference for 3. d3?

P.S.--I just realized that 3. Nc3 transposes to the Vienna Game, so another possible explanation is that if White wanted to play the Vienna Game he could have done it on the 2nd move instead of waiting (1. e4 e5 2. Nc3), so by the 3rd move maybe White is less inclined to play 2. Nc3. Could this be the reason?

We can write long reasonings, justifying one or other option, but both 3. d3 and 3. Nc3 are equally good.

If they're equally good then why is one much more popular than the other?

3. d3 {"Hendriks Attack." #1 pop. 7208/10913 = 66% frequency. w 41%.}
3. Nc3 {Vienna Game. #2 pop. 1451/10913 = 13% frequency. w 41%.}

It proves that the majority of chess masters believes in traditions and statistics (3. d3 has an essentially better statistical evaluation).

Nc3 allows the fork trick (which could be the best move; it's what I play anyway,) though that can lead to stuff like the Frankenstein Dracula Variation and surely sometimes White players enter that stuff on purpose... the main point is as you said Nf6 attacks a pawn. Nc3 does sort of defend it because Black can still take the pawn but White can get it back with tactics, but d3 defends it in a clearer way.

Oh my gosh, you're right. I'm so used to White being the one doing the Fork Trick that I didn't consider Black could do it here. I think you nailed it: that's the best answer so far, and I believe the best we'll get. Thanks!

3.Nc3 is playable but risky. 

Wow, I didn't think this opening could get so complex so fast. I guess I should have guessed that since the Italian Game (1. e4 e5 2. Nf3 Nc6 3. Bc4) has that character, too, largely due to White's bishop at c4 that can launch all kinds of combinations: all peaceful and logical and then suddenly the fireworks start! Thanks, Logozar.

Alright, I'm gonna give a beginner's perspective...

D3 not only defends E4 and C4, but also allows the development of the black bishop.  

Both the Vienna Game (which 3 Nc3 transposes into) and the Bishop's Opening are basically attempts to play an early f4 and achieve a favorable-for-White position of the King's Gambit Declined.

THE reason for 3 d3 in the Bishops Opening, which was THE opening the the high school team I coached rode to multiple county championships and state trophies, is to prevent the Frankenstein-Dracula Vienna after 3 Nc3 Nxe4 4 Nxe4 d5!

With 3 d3, Black can't prevent f4 from beinhg played before Nf3 - although ...Bc5 usually makes that a difficult plan to carry out.

Yes and no. The fork trick is not so good here cuz of 4. Qh5+! => 3...Nxe4 is suboptimal.

After 3.Nc3 White has few good options. The so-called Frankenstein Dracula is just plain risky for White and so is 3.Nc3 Nxe4 4.Nc3 so White plays 3.d3 instead.

I prefer 3.Nc3 Nc6 though because 3...Nxe4 4.Qh5 Nd6 5.Qxe5+ is a way to bail out of any complications.

The Frankenstein-Dracula is fine for White - Black does get a big attack, but theoretically I think that White should emerge with an edge. The problem is that 5...Be7! 6. Nf3 Nc6 (not 6...0-0? - that loses to 7.h4!) 7.Nxe5 g6 8.Qe2 Nd4 and Black has equality. 5.Qxe5+ gives White a small edge, according to "The Modern Vienna Game" (Ovetchkin & Soloviov), although I'm not completely convinced by this, it must be said. Other options all allow White the game he wants - an early f4 and a sort of KGD position (or a nice bind on the light squares after 3...Nc6 4.d3 Na5 5.Nge2 +/=), not to say that that's necessarily bad for Black. I can give lines if anyone wants.

Meanwhile, 3.d3, while undoubtedly fine for White, does allow 3...c6 followed by ...d5. If Black tries to play this against 3.Nc3, he meets 4.d4! with a White advantage (hence why the d-pawn is not yet moved). Basically it's a toss-up between allowing the Frankenstein-Dracula lines or the 3...c6 line, both of which probably equalise, objectively speaking.

4...Ng5 is close to be an inaccuracy, the correct move is 4...Nd6.

3.Nc3 allows 3...Nxe4......similar to...

https://www.chesskid.com/video/player/most-common-opening-traps-1-the-fork-trick

I didn't realize I was opening up Pandora's Box of frankenworms with this topic! The free database I'm using didn't label the variation that everyone is mentioning--the Frankenstein-Dracula Variation--so I didn't realize so many people already knew about it. I'd only seen that name in passing on these forums before. I found it on Wikipedia today, though:

https://en.wikipedia.org/wiki/Vienna_Game,_Frankenstein-Dracula_Variation
"The Frankenstein–Dracula Variation is a chess opening, usually considered a branch of the Vienna Game, but can also be reached from the Bishop's Opening."
"The line is seen extremely infrequently in top-level play."

This must be one of those openings like the Fried Liver Attack that interests mostly novices and mostly is played by non-GMs, so I assume the statistics are mostly from games by lower rated players. Below are the statistics I found. Once at Black's 3rd move the database appears to use the same page from both transpositions (Bishop's Opening and Vienna Game).
----------
1. e4 e5
2. Bc4 {Bishop's Opening.} Nf6 {Bishop's Opening Berlin Defense.}

3. d3 {"Hendriks Attack." #1 pop. 7208/10913 = 66% frequency. w 41%.}
3. Nc3 {Vienna Game, "Mieses Attack." #2 pop. 1451/10913 = 13% frequency. w 41%.}
-----
1. e4 e5
2. Bc4 {Bishop's Opening.} Nf6 {Bishop's Opening Berlin Defense.}

3. Nc3 {Vienna Game, "Mieses Attack."}

3...Nc6 {#1 pop. 1685/4820 = 35% frequency. w 39%.}
3...Bc5 {#2 pop. 1365/4820 = 28% frequency. w 45%.}
3...Nxe4 {Frankenstein-Dracula Variation. #3 pop. 790/4820 = 16% frequency. b 38%.}
----------
1. e4 e5
2. Nc3 {Vienna Game.} Nf6 {Falkbeer Variation.}

3. f4 {"Brodie Attack." #1 pop. 4016/12912 = 31% frequency. w 47%.}
3. Bc4 {"Mieses Attack." #2 pop. 3370/12912 = 26% frequency. w 42%.}
3. g3 {Paulsen-Mieses Variation. #3 pop. 2577/12912 = 20% frequency. w 43%.}
3. Nf3 {Petrov Three Knights Game. #4 pop. 2568/12912 = 20% frequency. b 39%.}
-----
1. e4 e5
2. Nc3 {Vienna Game.} Nf6 {Falkbeer Variation.}
3. Bc4 {"Mieses Attack."}

3...Nc6 {#1 pop. 1685/4820 = 35% frequency. w 39%.}
3...Bc5 {#2 pop. 1365/4820 = 28% frequency. w 45%.}
3...Nxe4 {Frankenstein-Dracula Variation. #3 pop. 790/4820 = 16% frequency. b 38%.}
----------
1. e4 e5
2. Bc4 {Bishop's Opening.} Nf6 {Bishop's Opening Berlin Defense.}
3. Nc3 {Vienna Game, "Mieses Attack."} Nxe4 {Frankenstein-Dracula Variation.}

4. Qh5 {#1 pop. 600/790 = 76% frequency. w 38%.}
4. Bxf7+ {#2 pop. 80/790 = 10% frequency. b 55%.}
4. Nxe4 {#3 pop. 61/790 = 8% frequency. b 39%.}

http://www.chessmail.com/xtras/frank_drac.html I remember reading somewhere someone thought though John Nunn "put this variation to bed" but it seems many people these days think it should favor White if White is able to defend like an engine. There are also "cop out" early Queen trade variations for both colors to consider so it might be that it's not attractive at the top level because it can be avoided so playing into this neither player knows whether the game will be very dry or something Tim Harding might write into another chapter.

In a world where there's a toilet variation I'm not surprised lol.