Caro Kann advance with Bf5 and c5

Trying to play Caro Kann against computer and now I'm stumped. Against humans I like to play 3... Bf5 and the later 6 ...c5 against humans, but 7. c4 and 7. Be3 seem like really awesome responses for White, with really bad winrates for black on 365chess statistics, and I don't know how to proceed

Thanks for any enlightenment! 

If it helps, I prefer 5...c5

That does help, actually! Feels like there's more options when I can move knight to c6

Actually, about doing 5.. c5, not sure how to proceed. If I take the d pawn after 6. Be3, knight takes back and threatens the bishop which is annoying. Defend bishop with knight e7 and block in my other bishop, or retreat the bishop to g6? Or I could do the steps in the board above, but I look underdeveloped compared to white...

Yeah, it tries to take advantage of your lack of development / knight on d7.  Consider playing one (or two) development moves first and it really takes the bite out of c4.  e.g. just play 6...Ne7 and c5 the next move or the move after that.

8.Re1 at the end of your line is a non-move.  White's point is to start a fight and open some lines when black's development may cause him problems.  He needs to look at moves like Nc3 and dxc5.

edit, I see you already got that advice, nvm heh.

I also agree playing it before Nd7 is better.  You can also consider 3...c5 which I find to be a really annoying line to face as white FWIW.

5...c5 6.Be3 cxd4 7.Nxd4 Ne7 8.Nd2 (8.c4 is another mainline and here 8...Nbc6 9.Qa4 dxc4 scores well for Black while 9...a6 is solid) 8...Nbc6 9.N2f3 Be4 (better than Bg4 here) 10.O-O and here either 10...Ng6 or 10...Bxf3 approach equality.I've never had problems defending Black's position but it can be hard to win.

You don't play 6... Nc6 after 6. Be3, but instead either 6... cxd4 or 6... Qb6. 6... cxd4 is probably more considered the "main" line given it's recommendation by Schandorff in his grandmaster repetoire book on the Caro. You need to know your stuff here though if your opponent knows what he's doing.

Alternatively, you can play 5... Nd7 as you did in your first game and that will lead to a more manuevering type game. Just don't play 6... c5 right after. This line is recommended by Lakdawala in his Caro book, and imo is less harsh on you for not knowing the theory. You do however have to know common manuevers such as Ne7-c8-b6(a7), or Bg6, Nh6-f5. You also need to get use to f6 breaks in some situations, since c5 might open the game up too much.