How do you meet d4-d6 when your opponent doesn’t play the Old Indian, and the setup is d6-Nbd7-e5, which is Pirc territory?
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1. d4 d6 2. null Nd7 3. null e5
When this happens, can I play the London System, possibly with d4-Bf4, and so forth?
Planning to play the Old Indian (Be7 for black) against the London System has no bite since white can control e5 more easily. The Be7 does not aim at e5, of course, but as important, it inhibits Re8, and its control of e5 also. So minus two pieces helping play e5, and you are not likely to get that freeing move in. You would also have to play (after d6) e6 since e5 loses a pawn to any reasonable white development, Be7, and only then, figure out how to enforce e5 gaining some space in the center. In reality, you would probably have to play for c5 instead.
As a defense against the London System, the King's Indian (g6 and Bg7) is much more logical since the Bg7 can help fight for control of e5, and the Re8 immediately helps too with a potential e5. In those lines, white usually plays Bf4, but then h3, and Bh2 to anticipate black's eventual e5.
When this happens, can I play the London System, possibly with d4-Bf4, and so forth?
Simple answer is "Yes, provided you play 3. Nf3"
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1. d4 d6 2. Bf4 Nd7 3. Nf3 e5 4. dxe5 dxe5 5. Nxe5
Just leaves black a pawn down for no compensation. So, black can't play 3 ... e5
If you like playing the London system, then it is playable:
1.d4 d6 2.Nf3 Nd7 3.Bf4. Now if Black plays 3...g6 then you just go for 4.e3, 5.h3, 6.Be2, etc. And as Brian noted, 3...e5 is poor.
However, if you don't like the London then you need another line. If you want to remain completely in d4 waters then you could go for:
1.d4 d6 2.Nf3 Nd7 3.c4 e5 4.Nc3. Now against most moves Black can play (4...Nf6, 4...g6, 4...c6, etc) you just play 5.e4. And on 4...exd4, you recapture with 5.Nxd4 and then fianchetto with 6.g3.
I wouldn't recommend London against 1...d6 or 1...g6. They can do 1.d4 d6 2.Nf3 g6 3.Bf4 Bg7 4.e3 Nd7 5.h3 (or whatever) e5 which is if anything more comfortable for black imho. Black normally has to do some contortions such as Nfd7 to get e5 in whereas now he gets it in one go.
Play 2.e4 and learn some small amount of theory in one of the main lines (whichever suits your style best) - will give you a nice position without too much work. If opponent continues with Nbd7 etc. (Philidor) then you could choose between the sharp Shirov Gambit (1.d4 d6 2.e4 Nf6 3.Nc3 Nbd7 4.Nf3 e5 5.g4) or play positionally with 1.d4 d6 2.e4 Nf6 3.Nc3 Nbd7 4.Nf3 e5 5.Bc4 with ideas of 0-0,Re1 a4 Ba2 (prophylaxis against b5 and Nb6 and d5 ideas) and a small pull.
