Can this game still be won?

Question

I am black and white has expanded more than I thought. It’s almost at tie at this stage but I can’t see how to win.

Can this game still be won?

Answer 1

Edits: corrected my miscount of Black area, possible White gain
If my calculations are right, you seem to have lost or won depending on the rules in force, but you had a chance in any case!

Your score

In your position, using area scoring, I count your central group as 40 points as follows:
_{Counting in vertical pairs left to right two horizontal lines at a time (numbers in diagrams can only go up to 10; f, s, e stand for 4, 6 8; the 40th point is the marked ◯ at J1).}

$$Wcm1 Counting
$$ +---------+
$$ |...XXXO..|
$$ |24680OOO.|
$$ |OOXX.XXO.|
$$ |O2fs80OO.|
$$ |O2X4X6O.O|
$$ |OOOOMXOOM|
$$ |XOXO802OX|
$$ |.X.OX..4s|
$$ |...OOXeXP|
$$ +---------+

Note that the SE corner is yours as far as J3, which White cannot capture, but White should get J4.

Your problem

Since you needed 41 points to win (unless the next paragraph applies), you were there, if you took one of the two neutral points (marked with crosses), namely E4, making it ⬤41:◯40½.

However, some rule sets award White a point for each handicap stone¹, meaning you would need 5 or 6 more points than White to win for a 4- or 5-stone handicap respectively, i.e. 43:38 or 44:37.

¹ _{See the section on Handicap go at [https://senseis.xmp.net/?TerritoryAndAreaScoring#toc6]}

Your chance

But you had a chance to

win anyway, by making a seki² in the SW, if White blundered by answering ⬤E4 immediately at ◯J4: you could then play ⬤A2, forcing ◯C2 (otherwise you play there and capture), then ⬤B1 gives you an eye in the stomach, and neither group can capture the other. In this case you get another 5 area points and White does not get a point for C1. However, this comes at a cost: White can now capture at J2, and when Black captures at J3 White can recapture a stone at J2 and when Black plays J1 White can connect at J3, forcing Black to connect at G2! This reduces your area in the SE by 2, making the area score 44:1:36, so you win in spite of komi even if you had a 5-stone handicap.

Unfortunately, if White correctly answers ⬤E4 with ◯C2, they capture the SW and still get ◯J4, yielding the same result as above (they win if compensated for the handicap)! Moreover, if you play 58 in the corner before filling J4, the only hope I see is ⬤B1, ◯A2 ⬤A1, ◯C2 ⬤A3, ◯A2 (which White wins) or ⬤A3 (double ko, which White is bound to win) or ⬤A1, ◯C2 (which White also wins).

² _{seki: A stand-off where neither side can capture the other}

With territory scoring

If you use territory scoring (Japanese style), we want to know how many captives there were. Since the last move was White 57, you must have had a handicap, and there must have been 29 white and 28 black stones played. I count 32 black stones and White can have taken at most 1 captive (at H5), so you had a 4-stone handicap and White has no captive or a 5-stone and White has one; both seem consistent with the position. I count 26 white stones, so you must have taken 3 captives (at F2, G2, G1 or C6, D6, E7).

At the end of the game you can expect to capture at J2, giving you a score of 10 territory + 4 captives = ⬤14; while White has 14 territory + 3 or 4 captives + ½ komi + perhaps 4 or 5 handicap compensation = ◯17½ to ◯23½. Again, you lose (by 3½ to 9½ points), unless

White blunders as previously described. In that case, your score is unchanged³ at 14, but White loses 11 points in the SW, which is enough for you to win.

³ _{I am assuming your rules count no points in a seki; otherwise you both get one more point in the SW, which cancel out and make no difference.}

Answer 2

As far as I can tell, the only territory that is still up for grabs is r6c5, and even that only if you are playing with the area scoring system (since otherwise, filled territory doesn't score so no points are gained by playing there). But if you are playing area scoring and white is given no komi (extra points as compensation for going second), then it looks like you do win by playing in r6c5 - after that, white fills r6c9 and then both players pass (or make insignificant moves) and black wins 41-40.