We have added a second, shared ko-shape in the centre (= ). We first assumed that this liberty had to be added to Black's liberties, resulting in the case EX = 1 (five ko-fight liberties for White vs. four ko-fight liberties for Black). But we soon had to learn that we were mistaken.

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As known to be preferable for EX = 1, White occupies Black's liberties.

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White captures the ko "late".

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However, Black wins the ko by investing two ko-threats (and not only one, as expected with EX = 1). This result is typical for EX = 2, so we counted one of Black's liberties too many, to get the number of ko-fight liberties.

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Let us try a cross-check by White's capturing the ko "early".

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Black wins after using five ko-threats; t = ( + ) - 1. Again, the known formula for EX = 2 applies. So, for the relationship discussed here, we cannot count the liberty in the central ko as a ko-fight liberty for Black.

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EX = 1
White has an outside liberty less than before, so we can expect that Black wins after using one ko-threat.

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White captures the ko "late".

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Black's one ko-threat.

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Black wins. We have t = 1 = EX.