We show that generic infinite group extensions of geodesic flows on square
tiled translation surfaces are ergodic in almost every direction, subject to
certain natural constraints. Recently K. Fr\c{a}czek and C. Ulcigrai have shown
that certain concrete staircases, covers of square-tiled surfaces, are not
ergodic in almost every direction. In contrast we show the almost sure
ergodicity of other concrete staircases. An appendix provides a combinatorial
approach for the study of square-tiled surfaces
