Yeah, I think 4. d3 can be safely filed under "non-critical."

It's interesting to recall that Karpov gave 3...d5 as dubious after he got in trouble with it against Ljubojevic in the mid-'70s.  ECO in the '90s gave the line Kaufman recommends (4...Bd7 and later ...Nf6 rather than ...Bd6) as slightly better for White; they were quoting Romanishin, but what they gave was certainly incomplete/unconvincing.

The Ponziani was a pet opening of mine a long time ago.  What led me to give it up were some lines of the sort 3...d5 4. Qa4 f6 5. Bb5 Ne7 6. ed Qxd5 7. d4 Bd7 followed by ...ed plus ...Ne5 or ...a6 and ...Na7, where Black basically tries to trade some pieces and leave White with an iffy IQP position.  Though later it appeared to me that White has some aggressive tries in such lines that I might not have been aware of.

Some time later, when playing Black against a Ponziani-playing opponent, I intended to try the line mentioned by CheckMate (which has been played by Spassky and some other strong players).  Later still I noticed that one Ponziani book seemed to think that 6. Qb3 (which had been played a few times by the Bulgarian-US IM Minev) should lead to an edge for White, a claim of which I grew somewhat skeptical.

What about 1. e4 e5 2. Nc3 Nc6 3. c3 Nf6 4. d4 exd4!? 5. e5 Nd5 ?



Definitely not a refutation of "the Ponz", but an interesting position to play,  which can also arise out of the Göring.

I too am skeptical of such strong "anti-Ponziani" claims.  I notice that Kaufman, in his best-play line, only claims that Black has "full compensation for the pawn" (though he adds some other verbiage such as "at least White isn't clearly worse").  Another bit I notice is that earlier in that line he doesn't mention the way White played in Planinc - Mariotti 1970 (two GMs of that decade).  Planinc won; after about 20 moves it was maybe equalish though my inclination is to prefer White.

After 1 e4 e5 2 Nf3 Nc6 3 c3 d5 4 Qa4, Larry Kaufman in the Chess advantage in Black and White believes that 4...Bd7 comes close to refuting 4 Qa4.