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?