The "Open" crease has been around since the very first Stetson cowboy Hat invented by John B Stetson in 1865.
The first "Open" crown hat was called the "Boss of the Plains".The “Boss of the Plains” was a big, natural-colored hat, with four-inch brim and four-inch crown, and a strap for a hatband
The crown of an open cowboy hat can be 5"- 6" tall and the brim 4.5" - 5" wide.
History records crowns of a cowboy hat to be as tall as 9" and 6" for the brim.
Many cowboys like the open crease so that they can shape and mold their new cowboy hat to their style and personality.
John Wayne would take his hand and grab the "Open" crown (Boss of the Plains) of his cowboy hat to crease it.