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Why is this position checkmate?

[FEN "2kr1bnr/1pQ5/p3pp2/2Pp2pp/3P4/3qPN1P/PP1N1PPB/5RK1 w - - 0 19"]

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    How do you propose that black get out of check? – Ross Millikan Mar 2 at 6:02
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    Yeah, I never see the far away bishop, too... – lvella Mar 2 at 14:02
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    Because the king is in check and unable to move out of check - doesn't matter what image is posted ;) – TCooper Mar 2 at 17:33
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    What do you think checkmate means? One way to think of it is: "for every possible move black could make, the next white move is [king captured]." So pick a black move. Anything besides capturing the white queen results in the queen capturing the king. Then maybe you should capture the queen! But if you do this, there is another piece waiting to capture the king. – The Chaz 2.0 Mar 2 at 20:04
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    I sometimes wish the win condition in chess was simply "capture the opponents king", and the whole concept of 'check' would be eliminated, which would be so much simpler. The game would be subtly different (no stalemate, more liberal castling options), but I think overall for the better. – orlp Mar 3 at 21:16
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The queen is protected by the bishop on h2, so the black king cannot take the queen. Nothing else can take the queen and the queen covers b8 and d7.

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Your king is mated when you are in check and no legal move gets you out of check, meaning that all three of the following conditions are met:

  1. You cannot capture the attacker.
  2. You cannot block the check by interposing a piece between the king and the attacker.
  3. There is no safe square to which your king can flee.

The black king is currently in check. He cannot capture the white queen because she is protected by the bishop on h2. (A king may not move to a square in which he would be in check.) No other black piece is in a position to capture the white queen. Therefore, condition 1 is met.

The white queen is adjacent to the black king, so there are no squares available for interposing. Therefore, condition 2 is met.

The only squares the black king could move to that are not already occupied by friendly pieces are b8 and d7, both of which leave him still in check by the white queen. Therefore, condition 3 is met.

Since all three conditions are met, this is checkmate.

EDIT: I've made some minor edits to my answer to address the following two things mentioned in the comments:

  1. You forgot rule 0: "You are in check." You're correct; these rules don't matter if you're not currently in check. I felt this was implied by rule #1, but I edited the answer slightly to be more explicit.

  2. Wouldn't it be simpler to say that checkmate is when you're in check and no legal move gets you out of check? Yes, that is simpler. However, it's not as helpful to a beginner, as they might ask, "Okay, but how do I know if no legal move gets me out of check?" My answer helps said newbie out. I've edited the response to be more explicit that the three rules I give are to determine whether any legal move exists to get out of check.

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  • Even though checking(!) off the three points on your list correctly determines if checkmate is reached, it is even simpler: If you cannot end the move without the king still being in check. - Your points are merely checking for the three possible actions that could end a check. – I'm with Monica Mar 3 at 13:07
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    0. You are in check – user253751 Mar 3 at 14:12
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    The rules are much more succinct than these 3 rules: 1) you are in check, and 2) no legal move gets you out of check. – TKoL Mar 3 at 16:33
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    @TKoL sure, but enumerating a little what "no legal move" means is much more helpful for a beginner – llama Mar 3 at 18:14
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    @user253751 I figured it out. For the benefit of everyone else: The post includes a list of conditions for checkmate, numbered 1 to 3. But there should be another condition above them (numbered 0), which says: “You are in check”. – Brian Drake Mar 4 at 3:03
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When your king is in check, it has 3 options to escape - either interpose a piece, run away, or capture the attacker. In this position there is no intervening square, so interposing is impossible even if a piece were available to do so. Nor can the king run away since it is blocked by the edge of the board and its own pieces, and the remaining empty escape squares are attacked by the queen. Finally, capture of the queen is impossible since it's protected by its own bishop on h2. Hence the king is in checkmate.

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    Also the queen cannot be captured by any other piece. – Brian Drake Mar 3 at 7:03

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