Capture in Atari
Basically, if you change the capture rule to kill even stones with one liberty, by putting them into Atari, you have this rule. This isn't as counter-intuitive as it may at first seem; many groups in Atari in ordinary Go are dead, they are just never captured. Now they are captured. One consequence is that you need at least two eyes to live but at least three points in them. Life and death would be significantly changed, especially if using the simultaneous kill rule at the same time. Simple Ko would no longer occur, though super-ko could. Seki could still happen.
This rule can be combined with SimultaneousCapture. This can make the game pass by faster in Alter Igo or in games with multiple players (e.g. multi-color go), especially on alternative boards such as the triangular board (6 liberties per single stone in the middle). The rule can of course be extended to 2 or 3 liberties on the triangular grid, though this would likely no longer resemble the traditional game.
The main inspiration was the discussion in "Mathematical Go" for the new term "seeing". The main benefit of this rule is in being able to express connecting and capturing in terms of just one rule or condition :
One color stone fills one empty intersection but connects the adjacent empty intersections by virtue of the connecting lines. Every empty intersection must be able to connect by one color to another empty intersection. Therefore stones of like color connect at least two empty intersection; if they don't they must be removed from the board at the end of the turn.
Alternatively this can phrased in terms of the lines of the board:
Lines normally connect two empty spaces. Every empty space must be connected to at least one other empty space. Filling a space with a stone connects four lines and so these four spaces are connected. Filling more spaces connects more lines but must maintain connected spaces, i.e. the relationship that a line embodies. If a line does not connect at least two empty spaces those stones must be rejected from the board.
Note: if playing with this rule in Alter Igo auto-Atari means immediate loss.
Whoever's turn it is to play will win. Neither eye is safe. Note: in Alter Igo all pieces, including those played in an eye will be ejected from the board.
Whoever's turn it is to play would lose, if moving was compulsory (as it is in Alter Igo.) The odd number of spaces in the middle means that the player to go first will see one eye get filled and their group captured.
Black's eyes are false eyes. Note black cannot play inside white because that would be auto-Atari. Whoever's turn it is, white wins.