Here is a little game I played today. It really helps to illustrate the trade-off between material and time. By sacrificing a pawn, I was able to get a vicious attack against the white king while most of his pieces were stuck on the back rank. Although it is a correspondence game, with one day per move, my opponent and I finished the game within a couple hours.
1. e4 c6
I almost never play the caro-kann; I like open, tactical positions. However, I had about 6 different correspondence games open, and I wanted to mix things up and try a different opening every game. As it turns out, this relatively defensive opening quickly exploded into tactics.
2. d4 d5
3. e5 Bf5
4. Ne2
Obviously the point to Ne2 is to play Ng3, followed by h4. This is meant to gain space with tempo on the light-squared bishop.
4. ... e6
5. Ng3 Bg6
6. h4 h5!
Most of the time players will go for h6 here, allowing white to play h5 and tuck the bishop on h7. However, I decided to go for this pawn sacrifice and then attack the center, gaining a couple developing moves and opening the game up with white's pieces out of position and his king unprotected in the center. It is a pawn sacrifice because the h5 pawn cannot be defended after Be2.
7. Be2 c5
8. dxc5
White could have defended the pawn with c3, and I would have followed up with Nc6, attacking the center again.
8. ... Bxc5
9. Bxh5
9. ... Ne7
Allowing the recapture of the bishop with further development. White giving up the light-squared bishop is a mistake here, since it is a crucial defensive piece, and allows me to grab the initiative, with pressure on the e-pawn.
10. Bxg6 Nxg6
11. Nh5 Qc7
White is getting greedy here. He is trying to snatch another pawn, and open up my king while neglecting his own. I welcome the pawn capture with check. Once my king moves to f8, I will be attacking the knight and the pawn on e5. He can't retreat the knight, since Qxe5+ will fork the king and knight.
12. f4
White wisely protects his e-pawn instead of going for the reckless check and pawn grab. However, his position is already untenable.
12. ... Kf8
Calmly defending the pawn. I don't castle, because I like my rook on the half-open file, ready to aid the coming attack.
13. Qe2 Nc6
14. g4 Nd4
15. Qd1
What do you do when you have a lead in development and your opponents king is helpless in the center? You attack. You bust open the center and open lines by any means necessary.
15. ... Nxe5!
16. fxe5 Qxe5+
17. Kf1
Nothing else can be done, the king has to run for it. I knew if I gave white one more move, he could play Bf4, attacking my queen and helping consolide his position. I couldn't let that happen.
17. ... Rxh5!
We begin to see the real danger white is now in. Once he recaptures, Qf5+ will draw the king closer to oblivion. My bishop and knight are working perfectly together, the knight covering the light squares against the queen, and the bishop prepared to give a deadly discovered check if the king ventures onto a dark square.
18. c3
White decides not to recapture the rook and allow my check.
18. ... Rf5+!
But I force the issue! That g-pawn has to go so that I can hop on the light-squares. If white doesn't capture, I get a whole extra rook added to the attack. So he has to capture.
19. gxf5 Qxf5+
20. Kg2 Qe4+
21. Kh2 Qxh4+
Clearing the h-file for the rook. Later engine analysis revealed Ne2 or Nf5 to be forced mates in 9. However, white is is now in so much trouble, any line is good enough for the eventual win.
22. Kg2 Qe4+
23. Kh3 Ke7
Making way for the rook, so that every piece participates in the attack.
24. Qf1 Rh8+
25. Kg3 Rxh1
26. Nd2 Qh4+
27. Kg2 Qh2#
It's not often you get to enjoy a 27 move checkmate, especially in a correspondence with the caro-kann opening. Remember: Time and initiative are often far more important than a single pawn. A pawn advantage is only game winning if you can reach the endgame, which won't happen if your king is under deadly assault.
Hope you enjoyed the game!