Ye Olde

In Old English, the "th" sound was represented by the letters thorn, þ, (voiceless) and  ð  (voiced).  They were written similarly to the letter y.  So whereas the written word "ðe"  was "the," the letter ð, when handwritten, looks like a y to modern readers. So, there is no Ye Olde, anything.  It's a corruption of "the old."