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At default random tick speed, each nether wart grows one age step approximately every 13653 game ticks (11.3775 minutes) on average, and fully grows from planting to harvest every 40960 game ticks (34.133333333333 minutes) on average. The growth rate is not affected by light or any other environmental factors.
Breaking a fully grown nether wart drops 2 to 4 nether wart, while an immature one drops a single nether wart. Using a tool enchanted with fortune increases the maximum number of nether wart dropped by 1 per level, for a maximum of 7 for a tool enchanted with Fortune III.
Before making a nether wart farm, it is necessary to have one soul sand per nether wart which can be grown. At least one nether wart is also needed to begin producing. It is recommended to have more than one, however, to decrease the initial amount of time spent waiting for it to grow.
Nether wart does not need light to grow, but the farm should be built in a lit and enclosed area to prevent creepers from damaging growth. Additionally, putting the farm in a place where it will be often loaded will help the farm to continuously grow.
Probability of Full Growth (2 levels) Time (min.) Probability; 10: 8.66%: 20: 25.55%: 30: 43.02%: 40: 58.10%: 50: 70.03%: 60: 79.00%: 70
You can have a single wart insta-grow upon planting or it can be ten minutes (or more) for a full 16x16 farm to see any growth at all. It'll average out to something not fast, but reasonable, play mechanics wise.
So with the addition of potions you know that any alchemist must have nether warts unless they only wanted to make 1-2 different types of potions, so a proper nether wart farm must be in place. Here is some info that i know about starting these farms.
