How much is a piece worth?

One of the more attractive, yet frustrating parts about chess is that the most interesting games are the ones where the normal 'rules' are broken. We jealously guard our pieces, up until we decide to sacrifice them, understanding that the side with the stronger army doesn't always win. While knowing when to 'break the rules' is normal for experienced players, it can be very confusing for new players.
But knowing when to take a piece can even be tricky for GM's. The first day of the GCT Rapid in Belgium saw a stark example of this in the Giri - Aronian game. Giri left his knight on the edge of the board as bait for Aronian, who decided to trap it with 8. ... g5. White Giri got in return was not an immediate win, but a lead in development and a strong enough attack that Aronian was only able to avoid mate by eventually returning more material than was initially captured.


Giri,A (2771) - Aronian,L (2793) [A29]
GCT Rapid YourNextMove Leuven BEL (3), 28.06.2017

1. c4 Nf6 2. Nc3 e5 3. Nf3 Nc6 4. g3 Bb4 5. Nd5 e4 6. Nh4 O-O 7. Bg2 d6 8. b3 g5 9. Bb2 Nxd5 10. cxd5 Nb8 11. Qc2 gxh4 12. Bxe4 Re8 13. Bxh7+ Kf8 14. Qc4 Na6 15. gxh4 Re5 16. Qf4 Qe7 17. Rg1 Rxe2+ 18. Kd1 Rxd2+ 19. Qxd2 Qxh4 20. Rg8+ Ke7 21. Qe3+ Be6 22. dxe6 Qh5+ 23. Kc1 Rxg8 24. exf7+ Kxf7 25. Qf4+ Ke8 26. Bxg8 Nc5 27. Bc4 d5 28. Bb5+ c6 29. Qxb4 Qg5+ 30. Qd2 1-0