In the list below, it is assumed that the eye is inside a Black group.
This 1x2 point eye space is worth 3/2 moves in No Pass Go
This 1x3 point eye space is worth 2^ moves in No Pass Go
This 1x4 point eye space is worth 3 moves in No Pass Go
This 1x5 point eye space is worth 3* moves in No Pass Go
This 1x6 point eye space is worth {4|15/4} moves in No Pass Go
This 1x7 point eye space is worth {9/2|17/4} moves in No Pass Go
This 1x8 point eye space is worth 5* moves in No Pass Go
This 1x9 point eye space is worth {6|11/2} moves in No Pass Go
This 1x10 point eye space is worth 6 moves in No Pass Go
This 1x11 point eye space is worth 27/4 moves in No Pass Go
This 1x12 point eye space is worth 29/4 moves in No Pass Go
This 1x13 point eye space is worth 8 moves in No Pass Go
This 2x2 point eye space is worth 2* moves in No Pass Go
This 2x3 point eye space is worth 3 moves in No Pass Go
This 2x4 point eye space is worth 4 moves in No Pass Go
This 2x5 point eye space is worth 5+Tiny(1) moves in No Pass Go
This 2x6 point eye space is worth {47/8|||23/4v,{6^|11/2,{6^||6^|5^|||{11/2|5^},{6^|5^||5^}}}||5^,{6^|5^||5^}|{5^|5vv},{5,{6v|5v}|5vv}} moves in No Pass Go
(Mean 23/4, temperature 1/8)
So far, the best move for black in all of the 2xN eye spaces is the (1,2) position (or its reflections).