Double Up Star
In combinatorial game theory, a double up star, notated as “``"↑↑"ast``”, is a game that is worth the sum of a star and two ups. In go, that sum can arise as the combination of these or equivalent positions, plus or minus some integer score.
We can show this by subtracting this position from the other three and showing that the result will be the same no matter who plays first.
To subtract this position from the others we simply change the colors of the stones and add it to them. The negative of double up star is double down star.
Black plays first.
White plays first
White's best play, as the reader may verify, is to enter one of the UP corridors. After , makes miai for 2 points for Black.
The result is the same, no matter who plays first. QED.