Can't remember the source, but I remember seeing somewhere to wrap 8 times around the arm. Be'ezrat HaShem Beli Neder source coming soon.
As Msh210 wrote up there it is really 7 with an extra half (see Siah Yitzhak Siman 5): ועל הזרוע שמונה כריכות, כי כריכה ראשונה אינה במילואה ואינה נחשבת
The first one doesn't count because it is complete.