I hope someone else can answer that question.

Here's a great series of pictures from the UNLV collection: http://gaming.unlv.edu/WSOP/outside_photo.html

The Shoe (Eldorado) was originally purchased by Binion in 1950 and became the Horseshoe in 1951. So I'd bet right around there. Brown took over for a while (while Benny cooled his heels in Leavenworth) and then the family got part ownership of it (Benny could not ever hold a license again after prision). They didnt get 100% ownership back until '64. Becky got partial ownership after Benny's death in 89 and then full ownership in 96.