In practice, you don’t have to actually award the half-point for each dame for using the half-counting method. Instead, people can just count the unfilled dame and subtract it from (361 + komi) to get the total number of points shared between White and Black.

I’ve never heard this one before. I think that area scoring rules are actually much easier to understand than territory scoring rules. I think the only tricky part, for Chinese rules in particular, is being aware of which cyclical patterns can cause a “no result” vs which are forbidden by superko (other area scoring rules, like AGA, NZ, Tromp-Taylor simplify this to just always applying a superko rule and doing away with “no result” outcomes).

This can’t be right. Dame points are either unoccupied, or occupied randomly by black or white, meaning that the Chinese score would have a random component.

When you cannot put stones like in a seki. then the case is explained in the topic too (1point for eye in a seki or 0.5 for each player for dame between both opponent)

In chinese rule we count all, we maximize the global occupation. So you better play the dame as they are points. Ofc if both players take 1 point each time , it balance and the difference will not change unless the last will give one more point (case of a odd number of dame )

Now if you get confortable with the chinese rules, you can easely explain why it works.

why can i put back the prisoners in the bowls?

why the score is the same as with the Japanese rules (modulo 1 point)?

What do you mean by this? The typical definition of dame points is that they are empty points on the board that are not surrounded by only one players. Do you mean something else by dame?

To clarify, where people have talked about “filling dame”, they mean in the sense that dame would be filled by the players playing additional moves (in the typical alternating fashion) on the board.

Many believe black's area - white's area - komi
is the number we look at at the end of the game, which is mathematically correct, but if you use this formula you have to count both sides.

Right. To be more precise, 3.75 is the komi in the official Chinese rules; 7.5 is the komi that yields an equivalent result when we count in a different manner (comparing black’s points vs white’s points).

Actually I’m not sure what “this” refers to in your question. I’ll explain what I think you are asking.

black's points - 180.5 - komi

If we compare black’s (or white’s) points with roughly half of the board, i.e. using the number above, then the komi should be 3.75, according to the current Chinese or AGA rules. But if we use the following formula,

black's area - white's area - komi

the number we plug in for komi is 7.5 instead.

Not sure about komi for other board sizes. I don’t know if official rulesets (such as Chinese, Japanese, Korean, AGA, EGF, NZ) have anything about komi on other boards, since 19x19 is the mainstream.