Pawn confrontations: capture, push past, or leave the tension?

Question

When your opponent moves a pawn to a position where it can be captured by one of your pawns, how should you determine whether to capture it, push past it or leave the tension on the board and make a different move?

I appreciate that the answer may vary with pawn structure, game phase, and style of play (e.g. a preference for open or closed games), and I know that pushing past is not always an option (break moves, pushing to unsafe squares). But are there any guiding principles to make the decision easier? Are there any books or videos that cover this subject?

Ideally I'd like an answer involving general principles but – in case it helps to illustrate them – here are some sample positions you can refer to if you'd like. (Using your own positions instead is fine too, though!)

Game 1: Black plays d5, White to move

r1bqk2r/pp2npbp/2n1p1p1/2pp4/4PP2/1PN2N2/P1PPB1PP/R1BQ1RK1 w kq - 14 8

Should White capture on d5, push past to e5, or leave the tension?

Game 2: Black plays d5, White to move

rnbqkbnr/ppp2ppp/4p3/3p4/3PP3/8/PPP2PPP/RNBQKBNR w KQkq - 4 3

Capturing (exchange), pushing past (advance), and leaving the tension (Nc3/Nd2 etc.) are all popular lines against the French. Are there any common principles that can be applied to help determine the most favourable line? (Nc3 is most common, but what principles explain why that's favourable to capturing or pushing?)

Game 3: Black plays d5, White to move

rnbqkb1r/ppp2ppp/4pn2/3p4/2PP4/5N2/PP2PPPP/RNBQKB1R w KQkq - 6 4

Should White capture on d5, push past to c5, or leave the tension?

Game 4: White plays e4, Black to move

r1bbr1k1/pppn2pp/3ppn2/5p1q/2PPP3/BPN2NP1/P1Q2PBP/3R1RK1 b - - 23 12

Pushing the pawn to f4 gives up the pawn with no compensation, so should Black capture on e4 or play another move?

Answer 1

This is too complex to have straight principles. Of course there are some patterns that you are going to recognize during your improvement and there are also easy things. I'm going to mention a few at the end of this post. First of all, let me refer to positions cited by you.

Position #1 Key is calculating, always, and this is great example. First thing you should do is asking yourself: what can I do? Can I not react, keep the tension? The answer is 'No.'. Your e4 pawn is hanging. You can't play d3 because you'd lose your knight then. Bd3? Too facticious obviously. So now comes the question: e5 or exd5? Well, after exd5 - Nxd5 c3 is hanging, f4 is hanging, I don't really like it. There are moves like Ba3 but somehow I don't like playing such moves. To sum up, after a moment of fast calculation, I'd choose e5.

Position #2 You mentioned all the possibilities. Why do people choose 3. Nc3 frequently? It's most aggressive, probably giving best chances. But it's also most complicated, definitely. Nd2 is also quite nice, if I recall correctly it's Micheal Adams' favourite choice. If you want a draw just exchange and develop your pieces. Positions after 3. exd5 are mostly drawish. e5 are for closed-positions-lovers. You should know what fits your play-style. If you are willing to be better at french, I suggest you nice video series on this topic by Rustam Kasimdzhanov, I think it's chessbases' stuff.

Position #3 It's also all theory. You can play exchange variation or keep tension. That's also something you should fit to your play-style. One thing is for sure, never play 4. c5 here. That's losing advantage on the spot. Simple 4. ... - b6 and you are not white anymore after few moves.

Position #4 It's calculation...again. As you correctly mentioned: playing f4 is pointless. It's giving up a pawn for literally free. So again, two choices here. If we don't take, what do we play? f5 is hanging, so let's defend it. We can play g6 and create additional holes or move our Nd7 to f8 or b6 to discover your Bc8. Once we jump anywhere (same after g6) white is going to play e5. Black is too squeezed. His pieces are passive, his Queen is on h5 doing nothing. It's hard to find a continuation. And again, after few moments we are sure we should capture on e4. So ... - fxe4 is a move here, then best to exchange Knights since when you are the passive one, you should look for exchanges.

Now few easy positions with patterns or principles.

[fen "4k3/pp3ppp/3p4/4p3/3PP3/8/PP3PPP/4K3 w - - 0 1"]

You rather don't want to exd4 because your d6 pawn is weak then. (assuming there are more pieces of course.

[fen "8/1p6/2p5/1PPp4/3P4/8/8/8 w - - 0 1"]

You rather don't cxb5 because then your d5-pawn and b7-pawn are weak. (assumption like above)

Those 2 above were pretty easy, now something more difficult (but not too difficult) and illustrative.

[fen "8/p5pp/1p1bk3/PPp4P/2P1K1P1/8/4N3/8 w - - 0 1"]

As white you should play a6 here. Whole point is in the future your plan will be something like that: Nc1-b3-a5-c6. Taking advantage of impossible bxa5 because of b6. Of course this must be calculated (again!) and well prepared. This is just and example of pattern. Unfortunately, this is probably impossible to paste you 1000 examples here. This comes along with experience and you will notice that for yourself. Those were just few examples, hope you get my point. Good luck!