I'm trying to learn Go and I'm very confused by how end of game scoring works. I've played a game against an AI player, and I don't understand the scoring that the computer came up with once the game was over. In the screenshot I've included, I don't understand why the points marked 1 and 2 are counted for white and not black. Can someone help me understand this?
@TimK and @KMR are correct -- the game is not quite finished yet, because the stone in atari (that you labeled "2") needs to be resolved.
Having said that, it's worth mentioning that many computer programs are not good at figuring out ambiguous positions (like an unresolved ko that remains after a player has passed prematurely, for example). Some computer programs are very good at figuring that out; some are not.
From the screenshot, I don't recognize the software you're using; but what should have happened was (assuming you were playing as Black and the computer was playing as White), after you passed, the computer should have played at 2 (thereby capturing the stone you labeled "1") and waited for you to move. You don't have any significant ko threats, so you would pass again (or play a ko threat that doesn't work); and the computer next should have filled the ko by playing at "1".
This game isn't really finished. The stone at 2 is in Atari, so black needs to connect at 1. Then there won't be any points in those two locations.
The spaces at 1 and 2 will be counted for white if white was to make the next play, and area scoring is in use.
This is due to Ko. White is able to capture the black stone at by playing into space 1, but black may not respond by playing space 2, as it would return the board to its previous state.
Once white has played space 1 they can follow up on their next turn playing space 2, to take their stone in space 1 out of Atari.
This is not due to the rules of go, but to the fact that an AI is scoring the game all on its own, and tasked with the responsibility of deciding which stones are dead and which stones are alive. The situation you've shown is somewhat unresolved, so the AI is struggling.
The AI is scoring the game and does something not done in real-life, which is to automatically decide which groups are "dead". For instance, the AI found that the two black stones on the southwest are dead.
But the AI got confused by the black stone left in atari, which can either live, if black plays first and connects it, or die, if white plays first and captures it. The AI somewhat arbitrarily marked it as dead (because white could capture it).
Even if the black stone dies, the extra point of territory marked for white doesn't make sense. I am guessing this game was played on BadukPop, so the game should be scored according to Korean rules, and there is no reason why the point marked "1" should be counted as White's territory. This is most likely a bug of the AI and scoring algorithms not really being designed to score properly a game where a stone is left in atari like that.
If the game had been played by two humans, rather than a human against an AI, the game would end in either of these two ways:
The second possibility is the most likely.
