Noob scoring Q

What happens when you play this out (wrt the bottom right corner)? White to move.

Thanks.

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It already is played out. Neither player wants to add a move. This is called seki - mutual life. All stones are alive.

See also: Seki at Sensei's Library

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Oh, thank you. So to be clear, how are H3, F1, and J1 to be split up for scoring between the players?

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F1 and J1 aren’t points for anyone.

In Japanese rules J3 also isn’t a point for anyone. No points in seki in japanese rules.

In Chinese rules J3 should be a point for black, as that intersection is only surrounded by black. (Hope I didn’t get this wrong, because it’s sort of a ‘false eye’, but I don’t think that’s relevant.)

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Chinese rules apply here.

if fake eye is unbeatable, it is point in Chinese rules. It doesn’t matter why its unbeatable.

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Chinese rules
You put away black prisoners in the white territory. No use of them.

Then black has
14 points (emptyness)
and
23 stones.

That’s a final score of 37, less as half the board so loss. (9x9/2). Komi would add a few points (5.5/2) to white, compensation for not starting, so even worse here for black.