Why does the computer recommend this trade?

I am in learning mode, and when I played vs. the computer, it said that the best move for my Bishop on b5 was to capture black's Knight on c6.  I would really appreciate hearing from you folks as to why this is the best move for me (white).  I tend to avoid trading pieces;  perhaps I should not.  Thanks, Richard

Ah, I think I have seen the computer do this before as to doubling pawns.  By this, I assume that two pawns, one behind the other on the same file, are less potent than two pawns side by side;  is that correct?  And, there is the double benefit of removing the guard on E5.  Got it.  All makes sense.  Thank you TT.   ~~~Richard

From a tactics perspective, 1. Bxc6 … wins the e5 pawn (2. Nxe5 …).

As TumpaiTubo mentioned, capturing White's Bishop also forces Black to double pawns on the c-file. While doubled pawns can be fine in certain positions, they are generally considered to be a weakness because they cannot defend each other. One of the doubled pawns usually becomes a target for capture.

In addition to the material gain, capturing the e5 pawn (2. Nxe5 …) weakens Black’s pawn structure even further, since Black will suddenly have three pawn islands, versus White’s fully intact pawn structure. The player with the most pawn islands generally has the weaker pawn structure because they become difficult to defend, particularly in the endgame. Sometimes pawn islands can be created with compensation though, such as providing a semi-open file for Rooks.

Doesn't white just win the pawn on e5? Black probably cannot capture a pawn back, because he is behind in development. A pawn is a pawn, especially when there is little compensation for the opponent.

What you fellows say makes good sense.  Thank you very much for joining in.

So good to learn this stuff.

Richard

Santa Cruz, CA

It really is this simple - the op shouldn't overthink this

1. Bxc6 removes the defender of the e5 pawn. A sample line is 1. Bxc6 dxc6 2. Nxe5 and White just wins a pawn for no compensation! Also note that Black can't "win back" the pawn with e-file pressure via the dubious 2...Qe7?! because 3. f4! secures the outposted Knight and gives White a lot of play. 

Normally, moves like Bxc6 are not so great when unprovoked because you are giving up the Bishop pair for little to nothing - however, winning a pawn outright is "something" enough to justify conceding the Bishop pair. Hope this analysis helps

Thanks for posting your question. I learned from the answers as well. Kudos to all.

Isn't it blacks move in this position?

White has made 5 moves = 3 minor pieces, e-pawn, and castles.

Black has made 4 moves = 2 minor pieces, and 2 pawns.

Good try, but you overlooked ...Qd4 met with Nf3 and White is much better. If after Nf3, then ...Nxe4?? doesn't win back the pawn due to Nxe4 ...Qxe4 Re1 and White picks up the pinned Queen.

The FEN for the position agrees with your thoughts.

r1bqkb1r/pp1p1ppp/2n2n2/1Bp1p3/4P3/2N2N2/PPPP1PPP/R1BQ1RK1 b kq - 1 5

Additionally, if 1. Bxc6 dxc6 2. Nxe5 Qd4 3. Nf3 Nxe4??, Black's Queen can be captured right away with 5. Nxd4 ... There is no way Black can capture the e4 pawn without a serious loss of material.

Based on how the op described the situation in the first post, the position appears to be White to move (hence 1. Bxc6 the Stockfish recommendation in question). If the diagram is set to Black to move, then that is likely just them misplacing the right to move into the diagram when they created it. 

My analysis based off of White resulting much better (even after the ...Qd4 idea) is only based on White moving first via 1. Bxc6

My comments are also based on the understanding it is White to move (1. Bxc6 ...). Strangely, the FEN also specifically says it is move #5 for Black, which perfectly aligns with IMBacon's move count observation.

I don't know? Maybe the diagram was edited at one point and that is why we may have analysis discrepancies; either way, the op should just learn opening principles and follow tactical themes like "remove the defender" to be wary of moves like the recommended way to win a central pawn. Perhaps we annotate slightly differently (due to calculation or differences in diagram), but hopefully the op understands what we are all attempting to express

I apologize if perhaps I fiddled with the setup before copying the FEN.  You all have certainly answered what I wanted to know based on it being White's move.   Thanks a bunch ~~~R

because of double pawns and ded queenside, and white can eat pawn.

Op that position to understand exchange is above beginner level. You should start with simple middle game exchange and know the logic. Don't blind read what book says.  Just don't read prose where they tell no more than 10% of the truth. You need to keep yourself pristine fresh , and eat good food so that you can catch it.