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Chess/Can't understand why Black won't take a piece

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Question
QUESTION: I'm being guided through a game offered by a certain chess
teaching program. Currently, the board is configured as such
(in FEN notation):
3r1rk1/p2P1ppp/1p6/n7/5Q2/5N2/q4PPP/3RR1K1 with Black to
move. According to the software, the next (and apparently
'correct') move is ...Qc4 to try for a trade. Now, I'd
expect ...Rxd7 to eliminate the passed pawn, and while that
leads to Rxd7, can't Black counter with ...Nc6 to keep white
from taking a7 and won't the other rook probably keep white
from taking f7? It seems that'd be a better option than
trying a queen trade (which ends up being unsuccessful with
White choosing Qf5).

ANSWER: I'm afraid I'm having a bit of trouble setting up this position.  I'm not overly familiar with FEN (and truthfully find it a bit confusing), so perhaps it would be better to describe the position this way (and let's see if I have it right):

White:  Kb1, Qc4, Re1, Rd1, Nc3, Ps a2, b2, c2, e7

Black:  Kb8, Qh2, Rc8, Re8, Nh5, Ps h7, g6, c7, b7, a7

If that is in fact the position you have in mind, please resend me the question and I'll do the best I can to answer it for you.

---------- FOLLOW-UP ----------

Layout
Layout  
QUESTION: Not quite the position. I have, however, generated a standard
chess diagram from the FEN, so hopefully this will be more to
your ease of use.

Answer
After 1... Rxd7 2 Rxd7 Black would be down a rook in material.  The win for White would then only be a matter of time.  In fact, not all that much time, from the looks of it, since 2... Nc6 3 Qd6 is very strong.  Playing the knight back to a5 here loses to 4 Qxf8+ Kxf8 5 Rd8 mate.  Protecting the knight with 3... Qc4 (or Qc2) loses it to 4 Rc7.  And finally, if 3... Qa4 White has the resource 4 Rxf7:  4... Kxf7 (4... Rxf7 5 Re8+ mates) 5 Ng5+ Kg8 6 Qd5+ and the Philidor's-legacy mate occurs (6... Kh8 7 Nf7+ Kg8 [7... Rxf7 8 Re8+] 8 Nh6+ Kh8 9 Qg8+ Rxg8 10 Nf7 mate).

If you allow yourself to be down an entire rook, you must have a great deal of compensation for it; otherwise, your position will most likely prove hopeless.

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Tony D'Aloisio

Expertise

I've read a good deal on the subject and I can answer a lot of chess history questions (or at least I'll know where to look them up). Also questions regarding analyzing specific positions (although with the advent of powerful chess software, this isn't likely to have the importance it once did).

Experience

I was a national master in the US for a number of years. My peak USCF rating was 2290, and I was ranked in the top 150 in the state of California. My current published rating is 2177.

Education/Credentials
B.A. Sonoma State University 1984 (English major with Communications emphasis)

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