Impolite to capture the deadstones?

This is true, but I think it misses the point. In a real game, if there’s no response then that means the opponent tenuki’s to make gains elsewhere, and that’s a practical penalty much greater than one point. Even in the tail end of the yose, the opponent in Chinese rules (or for that matter, European rules) can still tenuki to fill a dame and get a point.

As has already been mentioned, this discussion is about speculative invasions that occur at the end of the game. Obviously if there are still valuable moves to be played, wasting a move loses the opportunity to play one of them.

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Sorry for responding a day late, but real life interfered, as it often does.

Yes, you are all right, and I am eating humble pie. I am happy to be corrected, however, rather than walking around with a misapprehension. The accumulated comments made me revisit the issue on my long commute yesterday, and I realized my mistake—not sure how I got off track originally, but I guess it’s moot. Thank you @speedchase for your ingeniously simple illustrations. And I apologize to all of you for wasting your time on this.

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Uh…no. The best you can get is 1 free point per move your opponent plays that you ignore. Perhaps you mean worst the defender can get? Still not worst though, if you mess up you might lose 1 or 2 points having to remove the enemy’s stone

Again…NO. While the statement about Japanese rules might just be a mistake, you clearly do not understand Chinese rules. The defender neither loses nor gains any territory for either his or his opponent’s stones (assuming they all die). What you are describing is Japanese rules which is where the “break even” even comes from from the previous paragraph. In Chinese territory, under no circumstances will you gain extra points even if you opponent invades your territory and plays a hundred moves that you ignored.

Edit: Ah I see you were already corrected. Well just ignore this then.

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