Not really a review, but a few comments about the last parts of the game.
The bottom is very large. If we count that as your territory (which might be rather optimistic, although white should probably have invaded much earlier than they did in the game), you were not behind, but ahead by a solid margin. If you did mentally consider that territory, and still thought you were behind, it'd probably be good to practice counting;
these lessons might be helpful. In games like these where the territories are huge, it's very tempting to rely entirely on simple multiplication ("this area looks like a 6 by 10 rectangle.."), but this can easily be misleading. It's worth it to count "properly" at least once during a game so you can take into account dead stones and friendly stones inside territories.
Beyond that: the fight at the end worked out very well for you. After the fight had escalated to a certain point, that life and death situation was clearly worth more than 22.5 points, so you could say that this was where you finally won the game. Mistakes were made on both sides here, though obviously all in all you made fewer and came out on top

. One thing I noticed was a sequence at the end that shows off some moves that might be worth knowing about.
Here's what was played in the game:
- Click Here To Show Diagram Code
[go]$$Bcm1 1 and 4 are mistakes - cancel out in your favour
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$$ | . . . , . . . . . , . . X X X O X 3 . |
$$ | . . . . . . . . . X O O O X O X X 2 5 |
$$ | . . . . . . . . X . X O . O O X O O 1 |
$$ | . . . . . . . . . X . O X . O O X 4 . |
$$ ---------------------------------------[/go]
You ended up killing, but 1 was not a good move. You should usually have a clear plan before playing on the first line. White could've answered like this:
- Click Here To Show Diagram Code
[go]$$Bcm1 White lives
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$$ | . . . , . . . . . , . . X X X O X 3 . |
$$ | . . . . . . . . . X O O O X O X X 2 4 |
$$ | . . . . . . . . X . X O . O O X O O 1 |
$$ | . . . . . . . . . X . O X . O O X . . |
$$ ---------------------------------------[/go]
However, there
was actually a move that did kill: 1 at 2.
- Click Here To Show Diagram Code
[go]$$Bcm1 White dies - r1 is a false eye
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$$ | . . . , . . . . . , . . X X X O X . . |
$$ | . . . . . . . . . X O O O X O X X 1 . |
$$ | . . . . . . . . X . X O . O O X O O 3 |
$$ | . . . . . . . . . X . O X . O O X 2 . |
$$ ---------------------------------------[/go]
A more interesting sequence:
- Click Here To Show Diagram Code
[go]$$Bcm1 White captures...
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$$ | . . . , . . . . . , . . X X X O X . . |
$$ | . . . . . . . . . X O O O X O X X 1 . |
$$ | . . . . . . . . X . X O . O O X O O 2 |
$$ | . . . . . . . . . X . O X . O O X 3 4 |
$$ ---------------------------------------[/go]
Note that 3 here is a good move even though it's self-atari. If white gets to play at all three points around the corner without actually playing
in the corner, they'll get an eye there. 3 prevents that since it can only be captured by white actually playing in the corner.
As long as you respond, white can't get an eye where the captured stones were, either:
- Click Here To Show Diagram Code
[go]$$Bcm5 ..but black kills with the throw-in.
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$$ | . . . , . . . . . , . . X X X O X . . |
$$ | . . . . . . . . . X O O O X O X X X . |
$$ | . . . . . . . . X . X O . O O X O O O |
$$ | . . . . . . . . . X . O X . O O 1 . O |
$$ ---------------------------------------[/go]