I often come into a position where I fork a rook and a bishop. Until now, I always chose to capture the rook and then I get recaptured by another piece. But if you look at the value of those pieces, it's better to get a free bishop. So, what do you think, should I capture the rook or the bishop?

Bishop. No question about it.

If you're up in material, it's better to have the same pieces he has plus some extra (two rooks + knight vs two rooks), than to have an unbalanced situation (in this case, two rooks vs rook and bishop). The first is more likely to lead to a clean win.

Also, since his recapture moves his a8 rook to e8, it's basically the rook on a8 (currently not doing much) you're exchanging vs your hyperactive knight on f6. Much better to take the free active bishop in the center...

Thanks for your help Scarblac! I never looked at it the way you do.

In that position, you ought to win no matter what you take.

take the king =)

aw man, it  says black to move =(

Hehe, that diagram was just an example.

Aye, just simple counting really. Bishop = 3 points, Exchange = 2. So the bishop is better.