Go: How to count territory in this example?

Question

I am very new to go and therefore I have some problems to count the territories. In the following example (13x13) in my point of view black wins.

But I still have some questions:

1. Does the black territory (marked with grey) take half of the board? What's with the red marked area? Doesn't white has an eye here and hence is still alive? So how many points are there for black? 27? Or 36?

2. Does the white area (marked with white, right side of the board) make 23 points here? And does white get one point for the red marked area?

3. How to handle the blue marked area? Is it neutral territory?

4. During the game black caught 24 white stones and white caught 21 black stones. Do they simple add up to the total points?

We played a subset of a larger 19x19 board, so in this photo our 13x13 area is delimited by the dots.

For ease of reading, here's the same board position rendered with markdown:

$$ +-------------+
$$ |.X.X.X.XXXOX.|
$$ |X..X.XXX.XOOO|
$$ |XX.X.XOXXXO..|
$$ |.X.,XXOX.,XOO|
$$ |..XXOOOX.XXXO|
$$ |.XX.XO.OXXXO.|
$$ |X.XXXO,OO..OO|
$$ |..XXOOO..OOOO|
$$ |XXX.XOO..O..O|
$$ |..XXXXOO.OXXX|
$$ |XXOOXXXO.OOXO|
$$ |XOOOOXOOOOOOO|
$$ |.XO.OXO.O.O..|
$$ +-------------+

Answer 1

The white stones in the lower left are dead, the black ones in the lower right and the one stone in the upper right are dead.

Using Chinese scoring (stones on the board plus territory,) black wins 95 (59 stones + 36 territory) to 78.5 (49 stones + 23 territory) + 6.5 (komi).

To use Japanese scoring, we'd have to know how many stones were captured during the game, but we can guess based on what is on the board. Black has 64 stones on the board and white only has 57, so presumably black captured 7 or 8 stones during the game? That would mean that black has a score of 36 (territory) + 7 or 8 (captured) + 8 (dead on board) = 51 or 52. White has 23 (territory) + 5 (dead on board) + 6.5 (komi) = 34.5.

Either way, black won by at least 16.5 points.

Another note regarding the two blue spaces. They are neutral and don't count for either side in either scoring system. If you had been using Chinese scoring, then the players would want to fill them for extra point. It is likely that each player would get one of the spaces and therefore the relative score would be unchanged.

Answer 2

I'll assume you're using Japanese scoring, which is more popular in the U.S. In that case, you count the open spaces you have surrounded.

This game is a little hard to count, because I can't see the edges of the board. If we're pretending that the edges of the board are the outermost lines where stones have been played, then I count 24 points for Black, ignoring the lower left corner and the captured white group. Since that group only has one eye, it is dead. The easiest way to handle prisoners is to put the captured stones into the opponent's territory - taking points away. We can also count each captured stone as two points - one for the space it's covering, and one for the opponent's space it will fill in when moved to their territory. We'll get the same result either way. Taking this into account, Black gets 16 points for the captured white stones, and two more for the open spaces in the lower left.

The blue area is neutral, so nobody gets points for that.

I count the white area as 28 points, including the dead black stones.