Well, it doesn't do anything to defend d5, and it weakens b7. So the first thing to look at is some combination of Qb3, Nc3 and cxd5. Compare with the Baltic Defence (2...Bf5), where 3.cxd5 is always followed by 3...Bxb1.
So what's your idea after 3.cxd5? If 3...Qxd5, then 4.Nc3 and white is well on his way to get a rather nice pawn center.
It doesn't look very solid to me.
I was about to write essentially the same thing as Scarblac.
In addition, you say in your post that the bishop can be traded for a knight on f3. Except that white isn't forced to play Nf3. White can play f3 with tempo on the bishop and then e4.
Those are good points. I haven't played this opening before, and there's very little data on it, so I didn't know what to expect.
I suppose after 3.cxd5 there are 2 possible responses: 3...Qxd5 of 3...Nf6. If 3...Qxd5 4.Nc3, I wonder if you could put the Queen at c6 (keeping an eye on the possible skewer, of course, possibly playing a6 the instant the e-pawn moves, such as 5.Nf3 Bxf3 6.exf3 a6.
However, 3...Nf6 may be the safer response. Now if 4.Qb3 Qxd5, protecting the b pawn as well. If 4.Nc3 Nxd5 then either 5.Nxd5 Qxd5 and Black seems okay to me or 5. Qb3 Nb6. Either way the b pawn seems okay.
Again, I'm just trying to feel out this opening; I'm not defending it because I've never played it, I'm just curious why it isn't played. But I'm happy to hear feedback as I'm not yet great at analysis.
To respond to Loomis:
Nf3 is not forced and may never need to be played; I merely assumed that if White played f3, Black would not complain.
My idea if 3.f3 is 3...Bh5. This is probably horrible, but I would like to keep the pin on the queen, because it prevents 4.e4 (4...cxe4 and the f pawn is pinned).
> I merely assumed that if White played f3, Black would not complain.
White gets to support a big fat pawn center with gain of tempo on the bishop.
1. d4 d5 2. c4 Bg4 3. f3 Bh5 4. cxd5 and now white is threatening to just push e4 and own the center. 4. ... Nf6 5. Qb3 relieves the pin with tempo on the b7 pawn, so e4 is coming next and black is just down a pawn. 4. ... Qxd5 5. Nc3 Qc6 (this doesn't feel right to me, either) 6. e4 a6 (if you have to play non-developing moves like this, something has gone wrong) 7. Bf4. White is easily developing his pieces, has plenty of space, owns the center, and Rc1 might be coming up, continuing to harass the queen.
Just some thoughts on the position to help you work through understanding 2. ... Bg4.
Loomis,
I appreciate your help and effort! This is one thing I love about chess.com: bringing together numerous points of view to advance everyone's understanding of the game.
In my opinion, 5. Qb3 is not so bad in light of 5... Qxd5, protecting the b pawn and simultaneously attacking the d4 pawn and Queen. This seems to me to force White to choose between exchanging Queens or protecting the d4 pawn. White could play something like 6. e3 instead, but after 6... Qxb3 axb3, I would probably prefer Black. If White instead initiates the exchange with 6. Qxd5 Nxd5 7. e4, Black has to retreat, but the resulting position doesn't seem terrible for Black. It may be cramped, but with Queens off the board, there don't seem to be immediate threats, and Black's pawn structure remains flexible. If instead on White's sixth move he chooses to protect the d4 pawn by moving the Queen, say 6. Qc3 (not 6. Qd3 Bg6), 6... Nc3 and Black seems okay.
What do you think?
Well, since I can't find any information on this opening at all, and it appears to be unclaimed, maybe we can name it? Any suggestions?
I have a feeling Loomis and Scarblac might vote for "Wrong Defense." 
so u lose a tempo for no reason after cxd and nc3? or even just h3 to kick back bishop not to mention qb3 attacks d5 and b7
What's to stop
bg4 LOSES A PAWN AFTER qb3
iaeuy,
Check the above discussion. I think it's better for Black not to take with Qxd5 in that situation, but rather to play Nf6 first.
EDIT: I just saw your move list variation. Let me think about it and see if I ca find a response.
CJ,
What about 1. d4 d5 2. c4 Bg4 3. Qb3 Nc6?
iaeuy,
I've been looking at it for a while now, and I think you're absolutely right that, with best play, that's the diagram we're looking at. However, I'm not quite ready to quit on this idea without testing it in game situations first; to my amateur mind, after 6... e6, this thing is far from decided. White has a massive center, true, and it's unclear that Black has achieved, well, anything, but I would like to see if it's a playable position. Unfortunately I don't have Rybka or a similar engine, so the best I have is an online analysis engine. For someone with an engine, can you tell me what the computer scores the position after 1. d4 d5 2. c4 Bg4 3. cxd5 Qxd5 4. Nc3 Qd8 5. f3 Bh5 6. e4 e6? Thank you.
However, I'm beginning to think I'm probably better off sticking with my usual 1. d4 d5 2. c4 e6. While I don't like hemming in the Bishop, I'm not going to abandon an otherwise solid defense just because I'm bored.
Thanks Anthony. I'm starting to think that Bg4 might make more sense after 2. Nf3 and not 2. c4. 3. Ne5 seems to be the common response, but I'd need to look to see if 3... Bh5 is a viable option or if 3... Bf5 must be played instead.
Thanks all for the responses and analysis. In light of all the discussion, I think I'll let 1. d4 d5 2. c4 Bg4 continue to rot away. What I've forgotten in all my boredom is that my philosophy of play, whether White or Black, is that if Black can keep a pawn on d5, Black has equalized. That's why I play the French, why I (normally) play 1. d4 d5 2. c4 e6, and why I play the English as White (I prefer c4 to e4 for a number of reasons which I won't get into here).
Thanks Anthony. I'm starting to think that Bg4 might make more sense after 2. Nf3 and not 2. c4. 3. Ne5 seems to be the common response, but I'd need to look to see if 3... Bh5 is a viable option or if 3... Bf5 must be played instead.
The problem here is that you're playing a Trompovsky a tempo down, which is a risky strategy indeed.
Try the Tango (two nights out)
Or the Nimzo Indian.
Besides specific lines cited by others, there are some general considerations that help explain why the 2. ... Bg5 has seldom been seen. First of all, it has traditionally been held as an opening principle in general, "knights before bishops." The short-range piece needs to be developed first, needing more steps to get somewhere, while one waits with the longer-range piece to see where it should go. Second, historically it was felt that in the Queen's Gambit Declined the queen bishop was usually needed on the queenside (for both black and white). So strong was this belief that even Pillsbury's 4. Bg5 was greeted in 1895 as being an astounding innovation.
Hello,
I have been looking for a defense to 1.d4 that I find satisfying and interesting, but also solid. From my perspective, 2...Bg4 after 2.c4 or 2.Nf3 or most any other second move seems solid and natural, as it allows Black to play e6 at some point without hemming in the Bishop (I also play the French Defense as Black, but the light squared Bishop is becoming a thorn in my side in that defense as well).
My question is: why is there such little data on this move sequence? I've found 42 games in the database, and the opening has no name. Is it that positionally crippling as to be unplayable, and if so, how?
Here are the pluses I see with this opening:
1. As said before, the light squared Bishop is not trapped by e6.
2. White's e pawn is momentarily pinned.
3. Black will be able to trade with a Knight at f3, doubling white's pawns, which seems more useful than having it stuck on c8 or b7 with a pawn on d5.
It seems that this may transpose into more commonly known d4 openings, but why is this viewed as a bad way to get there?