Depends a lot on what size of plant you like. Bigger pots=bigger plants.
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A couple of good illustrations:
https://www.youtube.com/watch?v=0FWOjX89psI
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Last year I had a plant in a 2 liter pot (0.5 gallon) inside in a windowsill, it remained relatively small, and produced about 25 or so peppers during the season.
Outside I had plants in 5 liter pots which produced better, and had bigger, more sturdy plants.
Also had a plant in 20 liter pot, which produced a whole lot more of peppers.
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Also worth to note, as others have stated, I experienced that the larger the container, the less often I had to water the plants.
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So if you grow for yield, outside with plenty space, go >15 liter pots (4-5 gallon), for low effort, high yield growing.
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For more variety or houseplants, smaller pots will do fine, though your effort per yielded pepper increases drastically.