Give tire cuts the boot!
I carry a pump, a tube and patches. I also carry these Park Tool emergency tire boots just in case I ever run over something big enough that just addressing the tube puncture isn't going to solve it. A tear in a tire my compromise your new tube and will require something to cover the hole long enough to get you home. I carry them for my road bike and my mountain bike. My mtb tires are tubeless, but if I ever get a hole bad enough that the Stan's sealant seal it, I may need to cover the hole to put a tube in. The package includes three boots, each slightly smaller in size than a credit card. Three of the take up virtually no room in my saddle bag and weigh a few grams. At only a few dollars, I can't think of any reason not to carry them.