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Out of my little training experience in Thailand, I would say as long as you're doing something they most probably will appreciate the effort. I trained at Lamnammoon Muay Thai (in Ubon Ratchatani) for about two months and during that time I saw that most people (foreigners) weren't always doing the full 10k in the morning, and some had to walk or skip altogether because of injuries or exhaustion, etc. Even the Thai fighters didn't always run non-stop. Sometimes they walked, especially in the afternoon run. Also their running pace were usually quite slow. Not that they can't run fast but most often they couldn't be bothered. That said, the more you run (and the harder) the more the coaches will be content and take you seriously. My coaches basically told me I could fight when they saw how much I ran. Not when they saw how hard I hit or how slick my techniques were (Lol I would still not be ready then). Running is really essential. You say you're an awful runner, but how many days per week do you run usually? Unless you're a rare exception, your running endurance should definitely improve if you run everyday. It sucks for a while but that's okay. It should stop being awful once you're used to it. Unless you personally want to keep improving your pace for whatever reasons, then running will suck forever haha.