In school I worked part time in a service station and patched more tires than I care to remember. There are many "patches." Plugs, patches on the inside, and great big "boots" on the inside. I have seen all types work, and all types fail. The main question is what the injury was. You don't patch the sidewall. You don't plug a large puncture. You don't patch a very large puncture, although a "boot" might be a reliable fix. And it depends on how lucky you feel. I have plugged tires on my own cars and never experienced a problem. However, on my motorcycles, a patch or plug was never anything but temporary.
In considering whether to replace the tire, its age, and the age and condition of the other tires that will be working with the new tire matter. You might get some funny handling if you add one new tire to a set of well worn tires.
Proper preparation and application of the plug, patch or boot is also very critical.
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