A bag is provided having a first end and a second end. The bag has a generally tubular shape, with the first end configured to remain sealed and the second end configured to be opened. The second end defines a recess, and the bag is configured to receive one or more objects in the recess defined within the second end. The bag has a first cross section at a location between the first end and the second end. The bag is folded in the first cross-section so that the bag material forms at least three plies. At least one inner ply is formed, at least two outer plies are formed, and a first portion of the at least one inner plies is left exposed. One or more bags may be provided as a sheet. Methods for making the bags and for opening the bags are also provided.