After getting stuck with a damaged tire last year on Mt. Hamilton, 12 miles from my car (thank you, Good Samaritan, for picking me up), I determined to not get stuck in the same situation. Fool me once -- you know the rest.
I added the following items to my saddle roll:
Well, on yesterday's descent, my rear tire blew from striking a rock, at almost exactly the same place on the road. The cut in the sidewall was substantial -- I could push my pinkie finger through it. I got my tire repair materials from the saddle roll, cut off a piece of ripstop nylon about 1" larger than the hole (rounding off the corners), dabbed some super glue on the inside of the tire, and pressed the patch in place. Time to repair, including hand-pumping with
silly small mini pump: 20 minutes.
The fix worked like a charm. I was expecting to see a bulge in the sidewall when inflated, but the combination of nylon and super glue was enough to keep the hole from opening up at all. I can hardly tell where the tire was damaged. I was able to complete the descent at normal (fast) speed.
Any way, if your travels take you to places where a tire failure means a multi-hour walk in bike shoes, I recommend adding something similar to your repair kit.