You needed to finish the game, after which, assuming optimal play, White would have won by a very large margin (if it was their turn next) or a large margin (if it was Black’s turn).
The rules of go do vary a little, but it very rarely makes any difference to who wins, and certainly not in this case.
Your final position (diagram)
Finishing the game
If Black plays first
Your final position
You can enter diagrams on this site (though a photo is sometimes easier); I have made one of your position.
$$Bcm1 Your final position
Finishing the game
You pass at the end of the game when you do not think you can increase your score (explained below), and stop when both of you pass one after the other.
Your set should include enough stones for you to be able to get this far, but you may occasionally have to swap prisoners.
The winner is then the player with the higher score.
Since you did not finish the game, I have added the marked stones.
To keep things simple1 I assume White plays first at F45, which forces Black to capture at B12!2 After that I assume moderately good play from both players:
$$Wcm1 Final moves 1-10
and then (I fear this site only supports 10 moves/diagram):
$$Wcm11 Final moves 11-13
These result in this final position:
$$Bcm1 After reasonable endgame
Black territory (surrounded points) is marked b or a red O for a captured white stone, white territory as w or a red X for a captured black stone3.
Counting the score
There are two (nearly) equivalent ways to score the game:
- The simplest rule is that you score a point for every point on the board you control, i.e. occupy or surround4.
- It is usually easier to just count up the area you surround and subtract one for every one of your stones your opponent has captured. If you have played the same number of stones, this gives the same difference in scores and hence the same winner.
I counted 39 black stones and 72 white stones in your original picture, a difference of 33. For simplicity I assume White has captured 33 stones and Black none.
- For White, I count 41 points of territory and 5 extra captives (at A13 and around F4). With the 33 previous captives that makes a score of 41 + 33 + 5 = 79.
- For Black, I count 12 points of territory and 3 captives (B13, N4, N3). That makes a score of 12 + 3 = 15.
- That means White has won by 79 - 15 = 64 points, quite a large margin.
To avoid subtraction and make counting easier, people usually put their captives into their opponent’s territory and rearrange the stones to make the territory into rectangles. Neither of these changes the score (difference), if done right. In your game, however, this would have completely filled Black’s territory, another way of seeing that White had won heavily.
If Black plays first
If Black plays first after your final position, we have, as noted in footnote 1, a somewhat more complicated sequence:
$$Bcm1 Black first 1-10: 4 retakes ko (J4), 6 connects (at ❶)
$$Bcm11 Black first 11-17
In this case I count:
- For White, 34 points of territory and 2 extra captives (at A13 and J5). With the 33 previous captives that makes a score of 34 + 33 + 2 = 69.
- For Black, I count 12 points of territory and 4 captives (B13, J4, N4, N3). That makes a score of 12 + 4 = 16.
- That means White has won by 69 - 16 = 53 points, still a large margin.
In fact I now believe that White would have done 1 point better by making their threat at E3 instead of G12, but I am afraid I do not have the time to redo the diagrams. In any case, Black is 10 or 11 points better off than when it was White’s turn first.
1 If Black plays first, they can capture at ⬤ J5, creating a ko, which makes the game a lot more complicated. White is not allowed to recapture at ◯ J4 because that would recreate the situation after their previous move, so they first have to make a threat, such as ◯ G12, after which ◯ C12 would capture 7 black stones.
2 This is probably not clear to you, but if White gets to play at ◯ B12, Black will be unable to get to separate eyes, and will be captured in the long run.
3 Although ⬤ A1 has not been fully captured, White could do so. This would not make any difference to the areas White and Black control. If Black tried and failed to defend it, territory scoring would give the same answer, because they would give White (almost) as many extra captives as White made extra moves. If Black just passed, some versions of the rules would require Black to give White an extra prisoner every time, to make territory scoring give the same answer.
4 Surround in the sense that (it is unoccupied and) there is not way from that point to one of your opponent’s stones (except perhaps one that they agree is lost, such as ⬤ A1 – see also3).
5 Actually, ◯ has a better but trickier play at B12, which (as per note2 forces ⬤ J4 to try to connect his stones, then ◯ E3 threatens to disconnect, but if ⬤ answers, ◯ retakes, ⬤ has no threat, so loses the ko and all his stones except those in the bottom right 5×5. So ⬤ cannot save his stones on the left, and should not answer the threat but rather finish the ko by capturing with ⬤ K6, then ◯ F4 captures – ⬤ is all but wiped out! In fact the score is roughly ⬤ 25 : 144 ◯ (i.e. 5×5 : 13×13 - 5×5).