Up A Blind Alley
Following a course of action that leads to no good outcome.
Alleys are blind if they have no ‘eye’ or through passage – what might now be called a cul-de-sac.
The phrase was first recorded in Richard Stanyhurst’s, Thee first foure bookes of Virgil his Æneis translated, 1583:
“Through crosse blynd allye we iumble.”