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I beat a NM in an OTB classical game with the Sokolsky Opening

5...e4 is unnecessary.
If black is happy with equality he can play 5...exd4
After 6.Bxd4 c5 it should be equal and 6.Qxd4 a6 seems fine for black.

"This is what higher rated opponents will usually play against you."

Maybe, and maybe not. There are all sorts of lines against the Polish (besides the couple you mentioned).
@mrbasso 5. ... exd4 is perfectly playable and the engine likes it. It has never been played in the Lichess Masters Database but that's mainly because this line is quite rare. 5. ... Nd7 is also a fine move here and is a bit more principled: Black's main edge lies in their big centre so it makes sense to try to support it as opposed to trading it away. I agree with you that I don't think that 5. ... e4 was good, though it has been played by titled players before.

@MrPushwood Perhaps I should provide some statistics. Of the 1935 games in the Lichess Masters database that start with 1. b4, in 971 of them (about 50%) Black responded with 1. ... e5. That of course means that Black has a 50% chance of doing something else (and there are some interesting sidelines like 1. b4 c6 with the idea of 2. ... a5 or 2. ... Qb6 that are worth learning about) but 1. ... e5 is the most critical line. If White doesn't know what they're doing in 1. b4 e5 then they can lose very quickly whereas the other lines are often more forgiving.
It is true though: one of the practical problems of playing the Sokolsky is that Black has many good choices including a choice between going for boring equality vs. going for dynamic equality. 1. b4 e5 is very popular among higher-rated opponents because it will often give Black the latter (or even better, an advantage if White doesn't know what they're doing).
Fantastic.
I really enjoyed looking into this.
This is not a system I know much about and you made me realise I ought to.
I cloned it because I intend on analysing it further.
I'll have more to say in a few days but for now I wanted to say two things:
1. I disagree with the comments that 5...e4 is bad. I don't think it's bad at all (considering the system chosen).
2. That your opponent didn't play 8...f5 is very strange. I reckon even 1400 players will intuitively, at the very least consider it. For your opponent's rating, not playing f5 is very strange indeed. More som he seem to have missed its positional necessity several times throughout the game.
@DrFlagenstein

1. 5 ... e4 is playable though I personally prefer Black's alternatives. Titled players have won with 5. ... e4 so there may be some merit to it, though I personally enjoy playing White's side of the position.

2. I think the reason why my opponent didn't play f5 has to do with playing style. I have seen my opponent play the London System before and that often suggests an inclination towards being very solid. They might have misevaluated f5 as being very weakening when in reality, White has no concrete way to use it to attack Black's king. I think it's similar to why I played 20. Bf3 when 20. e4 would have lead to a winning endgame (i.e. I saw the move and the line but didn't play it because I'm not a strong endgame player). For me, the only thing that really confused me about my opponent's play was 20. ... Bxf3. I feel that Black's light-squared bishop was doing a great job of holding their position together whereas my bishop is probably my worst piece.

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