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That would depend a lot on what and how often you feed. I pesonally would change quite often in a tank that small, at least half 2 or 3 times a week, using temp matched, dechlorinated water...especially if offering a variety of foods..which I recommend.
Opinions vary, but in mine, a 1g hex is to small for even a single betta.
The smallest I'd try is more like 3.5 gallons, but even then I think keeping consistently stable water quality and maintaining a cycle with that little water volume can be a little tricky.
Were I to have another betta, I'd personally go with 5 gallons at least, but again, opinions differ.