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Why is the best move in continuation Qxd3 instead of Qxa1+ assuming KC1?

Hey everyone (first time posting in the boards so not sure how this will work). I played a game recently as black and I'm trying to figure out the continuation of the game. I think the best move is Qxa1+ but the computer wants Qxd3 (assuming King to C1 to get out of check which is what the computer calls best move for white). Running a further analysis with best moves being made, the difference is a checkmate in one less move with computer continuation, but I'm not sure if I would have been able to see this continuation down the line, whereas the other checkmate (with the move I want to make) is a lot easier for me to read and plan for down the line.
[Event "Rated Classical game"]
[Site "lichess.org/hZhuqSE0"]
[Date "2020.06.29"]
[Round "-"]
[White "roman_vorotilov"]
[Black "iggywriter"]
[Result "0-1"]
[UTCDate "2020.06.29"]
[UTCTime "21:24:13"]
[WhiteElo "1382"]
[BlackElo "1346"]
[WhiteRatingDiff "-6"]
[BlackRatingDiff "+24"]
[Variant "Standard"]
[TimeControl "1800+0"]
[ECO "D00"]
[Opening "Queen's Pawn Game"]
[Termination "Normal"]
[Annotator "lichess.org"]

I guess never mind now. I looked at the analysis again and it gave me a different move for white to get out of check (which I think would have likely been played; it's a much better move than kc1). I was just confused because in the first analysis I swear it recommended kc1 and then the series of moves I described, and I was confused about that sequence because it didn't seem to make much sense.

Still, I guess given the idea that king goes to C1, I'm still thinking the Queen Check with A1 is a better move that'll capture both rooks. I'll lose the knight, but whatever; I'm plus 2 on the exchange and have a huge material advantage through the rest of the continuation.

Thanks for looking at this relatively useless post. Again, it was more of a question of why as to anything else. I'm relatively new to the game and trying to develop into a more consistent player, and for the most part I feel like I played well in this game (despite the blunder and the "inaccurate" moves).
It is best not to get too wrapped up in computer assessments of very lopsided positions.
At that point any move wins. You should rather look what you would have done if he went 5 b5 and why you allowed that.
@tpr
i don't think he's in a great position to avoid b5 since a6 runs into a4 (if White is really that intent on playing b5) when White can eventually get it in after Bb2 or something. of course e5 by Black is bad timing cause b5 can come immediately. However, disregarding the immediate e5, i don't think b5 is something to necessarily worry about because of the weaknesses on the light squares and white's lack of development. Black can either reply Na5, and start applying pressure to the hole on c4, or even Nb8-d7-b6, again eyeing c4. the white pawns on the queenside end up being overextended and the long term weaknesses aren't worth the short term inconvenience for black, especially since white isn't developed at all yet.

But the better question is why play so timid when White is playing with his pawns and weakening his light squares. Play should've been 2. ...c5 followed by b6 and Bb7 eventually, aiming at e4. White's only option playing this way (with an early e3) is to play an eventual e4, otherwise his dark squared bishop faces serious problems. This is a common motif in queen's pawn openings that's leads to caro-kann like pawn structures. Otherwise, the Bishop is best deployed outside the pawn chain before e3 (in which case White can focus on the c-file after c4), or in some cases traded off quickly via Bc1-a3 or Bc1-d2-b4.

hope this helps!
@tpr

I wasn't worried about Bb5 because I had plenty of counter play if white decided to make that move. I likely would have played c3 to block and then tried to pressure later on in the game . I could have also played the NC3 to block or even the bishop and offered an exchange (which would have favored me if taken; I would have been able to position the queen out and then the knight and castle. I should also note that right now I am incredibly uncomfortable playing with Bishops and almost always favor bishop trades that allow me to develop more with my knights or position my knights in favorable squares).

I'm not all that familiar with this opening, and if I'm being honest, I played the way I did because usually as black I try to create a slow, positional game. Until recently, my opening ideas for black almost always included some sort of Indian game (and I generally play well in Indian games). Had white's opening move been e4 I likely would have played the Scandinavian Defense because it's something I've been trying more and more (and with fairly mixed results for me. I'm still learning most of this stuff obviously :)

Here, I think I just wanted to try something different. For example, the Bishop trades was something that I just did because I wanted to see what white's response was going to be (and that was likely a really bad idea because a ton of things could have gone wrong; and if he would have taken with the Knight, he would have started development and had the edge); I actually figured he'd take the bishop on d2 with the knight, but once he played the Queen, I felt like I had an opening for an attack because I was positive he was going to take the other bishop with the Queen instead of the Knight giving me the idea (11. Ne4 and then the pawn coming into play which I didn't think would be the response, so the retreat on 12. But the pawn again moved me back to that initial idea and then I played the queen to complete the idea. Here, I should probably consider what would have happened if he didn't push the pawn) and figured that positional advantage with the knights would, in worst case, at least give me an edge, even if his response would have been 12. Ne2 (I still would have had development with an additional knight and the castle. I would have looked for a way to get my Queen and Rook into play and continued trying to push the knights).

Or I could have done something completely different. Again, looking at the game, I wonder if maybe I should have played the Kings pawn opening or Nf6 to start the game and seen where it went from there. Had I played Nf6 I would have likely tried to get into a variation of an Indian game, which again wasn't what I wanted to do in this game.

@intro_bard_bot
The timid play most of the time is due to lack of familiarity and learning. I haven't figured out how to play aggressively as black, and like I've said above, I usually end up trying to play some variation of an Indian game. The advice above is golden, and I'm certainly looking for ways to improve consistently throughout the game. I've started reading Karpov's "Find the Right Plan" and could use suggestions for a reading list, if you have anything you think would be useful to look at and would be something a relatively advanced novice could understand. Mostly, I'm learning new things right now, and hoping to find more consistent play down the line. I think that the last week or so has been good for me (also corresponds to when I started with the Karpov book; the big idea I've kinda taken to heart is to play with a plan rather than respond to whatever my opponent plays using the seven basic principals outlined in the introduction to the text . I've also taken more notice with pawn structure and how to use that to an advantage earlier in games. This game isn't really a good example of what I've been learning from that book save for the idea that eventually led to the resignation).

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