Also isn’t your Petrov play just the Urusov? I’m curious what you play if black declines the gambit. Do you just transpose into your Italian or something different?
It's not quite the same as the Urusov, that happens when you play d4. Formally 3.Bc4 is called the "Italian Variation" of the Petrov (Lichess incorrectly calls it the Urusov), and 4.Nc3 is called the Boden-Kieseritzky Gambit.
If Black declines the gambit with 4...Nc6, then I'm very happy because this just transposes to the Two Knights Defense and I'm back in Italian territory. If they play 4...d6 then you can go 5.d4 dxe4 6.O-O and you're in some kind of Philidor (5.Ng5?! has the highest winrate here actually, but if your opponent has the psychological willpower to play d5 after playing d6, then you may get a bad position). If they grab the pawn but let you recapture afterwards (5...Be7), well, then it becomes kind of dry but there's not much you can do about that. I think the variation I would dislike facing the most is 4...d5, where you either lose the bishop after 5.Bxd5 or your pieces get awkwardly shoved around with 5.exd5 e4.
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I'll expand some more on my earlier post and share more of my opening repertoire. I have been struggling a lot vs the Scandinavian, because the position opens up really quickly and I can't "squeeze" the opponent like I tend to do in the Italian / Alapin after getting 2 pawns in the center. So what I'm trying now is Levy Rozman's suggestion, 3.Nf3, with the idea to go Be2 / c4 / d4 / maybe d5. From what I can tell Black has to play a very specific way to prevent this plan, 3...Bg4 / 4...Nc6 / 5...O-O-O.
Versus the French, I don't want to be "that person" who plays the Exchange and sucks the life out of the position. I initially tried the Advance with the Milner-Barry Gambit, but I was having trouble because assuming Black knows how to defend properly, it ends up being IMO too passive and it's hard to know what pawn breaks to play for (I know you're supposed to get your f-pawn moving in the French, but your knight is blocking it and it's kinda hard to move it since your d-pawn is so weak). I'm planning to switch to the Tarrasch.
Against the Caro-Kann, I like playing the Exchange with Bd3 / c3 / h3 (used at grandmaster level) which makes it very hard for Black to develop their light-squared bishop as they're used to doing in the Caro.
As Black, I'm currently trying out the Kan Sicilian / (Hyper)accelerated Dragon against 1.e4, which both feature more positional play than other types of Sicilians. Against everything else I play the KID. In the future, I might look more into the Caro / French against e4 and Dutch against non-e4.