How about trying not to fill in a false eye unless one of the surrounding chains has less than 3 liberties? I'm sure it's not perfect, but may be a fairly good rule anyway.
Interesting idea, Mark. But how about black's E4 in the attached example? If E4 is not allowed, then in the endgame, the probability to save the F7 stone is getting lower (even 1/3 lower, if E4 has the same probability with E7 and F6). Then it will cause problem when the game is close, espeically if F7 is a bigger string.
Aja
fill_false_eye.sgf
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