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Pirc position analysis?

This weekend I played in a classical tournament and lost in the following position as white against a higher rated opponent (1950 vs. 2150 USCF).

Before making a series of bad moves we had the position after 11... d5. Can someone help me understand why white might be better after 12. exd5 and what some plans for white could be?

Thanks!

lichess.org/study/e5QYVcp2/R7tYN4fi
e2 seems like the best square in general though it is blocking the rook. I know you don't want the bishop on d3 with the black side fianchetto structure. The plan with Bc4 seemed artificial to me though I rarely get this structure with white or black. And the only other two options just seem wrong. b5 since it allows the opponent to trade his bad piece immediately. Bf1 seems passive.

A line I was looking at involved Bd3 Bf5 Bxf5 gxf5 seems rather bad at first but actually it could be good for black getting the open g file. Though since the rook has already moved from the castled position it seems like this never crossed blacks mind and probably should not have. It looks a lot like play in the Larsen Caro Kann where black intentionally doubles the pawns to get activity along the g file.

White should be better in general since the b pawn is backwards though the inclusion of both d4 and a4 together make it harder to generate queenside play and black is the one playing there with Rc8 and Qb6.

Just some food for thought you are higher rated than I am but ideas are ideas.
Yes, white is better because of the a5 pawn and the resulting b5 weakness. Black can not start the usual minority attack with b5 and also f6 and e5 is not easy as white has this square well under control. However the white advantage seems not to be gigantic, but havent asked the fish. The best move is probably Bb5 or every other bishop move which controls b5.
addon, i like 13...Nxd5 more, which keeps b5 protected. After this move the white advantage should be not too big.
Another addon, it is general not trivial to find a good square for the Bf1 in the Pirc. Thats why i like Setups with 4.Be3 and 5.Qd2 and keep the bishop on f1 for a while. Kaspy also played that often. Eg. his famous Wijk game against Topi was played in this line:

de.lichess.org/yJlIjXRs#9
My first thought was Bd3 & then stabilizing the q-side with c3 and going Ne5. I think the bishop is reasonably well placed on d3 as it looks at the weak b5 square and prevents both Bf5 and Ne4. (Though, black could still try to go Bf5, accept the doubled pawns and then go Ne4.)
I'd also consider going 14. Bb5 first, provoking 14...Bd7, and then going back to d3. (The point would be that now black's knight can't use the d7 square to challenge white's knight on e5.)

I like white's position here as black's pieces seem to be not doing anything, and it looks difficult to find an active plan for black.
However, I'm not sure how white can make much progress either.

Therefore, another idea would be to go 14. Bb5 Bd7 15. Qd3 with the idea that after 15...Bxb5 16. Qxb5, black's b7 pawn becomes a target. You can attack it a second time with Ra3-Rb3, and because of the bishop on the h2-b8 diagonal, it can be awkward for black to defend this pawn. Also, if black advances the pawn to b6, Ne5-Nc6 (hitting a5 and e7) will be possible.

Nothing of the above has been engine-checked, so it might be all garbage. :p
without calculating anything (so if stockfish disagrees with me you know whom to trust:) )I would play Bd3 playing against the c8 bishop. Sure black can do Bf5 but having an airy king means no equality in the near future.If black doesnt go for this structure,then some standard moves like Qd2,c3 maybe Bh6, maybe Ne5, maybe Ra3-b3-b5 if some pieces get off, maybe h3-h4-h5 later. seems like a pleasant position for white
Thanks everyone! I appreciate the engine-free advice!
По-моему, рыба правильно подсказывает - ставить слона на d3! Чтобы встретить оппонента готового выскочить на f5. Белые ничего особенного не добиваются, а только играют на ограничение активности чёрных фигур. Это правильная стратегия против игрока с более высоким рейтингом.
PS. Почему то Сc4! хороший ход.
@ujcn yes, Bd3 is the fishs first choice, and @MorningCoffee s suggestions are further more or less his choice. it is something like a permanent +0.5 to +0.75. If black gets rid of his bishop by playing ..b6 and ..Ba6 his position is holdable.

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