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I have some actual numbers for the Golden Caldron (GC). In 100 rolls I got:
0 stars* – 1 roll
1 star – 13 rolls
2 stars – 57 rolls
3 stars – 29 rolls
*There is a bug with the GC that it will sometimes give 0 instead of 3 stars.
This would seem to imply that the actual ratios are 1:4:2 for 1-3 stars. Thus the average stars would be 2.14, or 3.14 items per brew.
Also, in evaluating the ingredients based on their price in snouts, it seems to me that the main thing you’ve shown is that it’s more economical to buy potions than to buy the ingredients (which is a very worthwhile analysis). In order to determine if you should spend your time farming snouts or ingredients, you need to reduce both methods to TIME spent, not snouts spent.
In Western Cobalt Plateau (WCP), I can farm 100 snouts and 21.4 seeds (based on 10.5 snouts and 2.25 seeds per battle) in about 5 minutes. The average loot roll from a dungeon is 234. If we figure you get an average of 50 snouts from the pigs directly (which I think is about right if you let Piggy McCool knock the snoutlings out of them), then the dungeons and WCP are break even on snouts when it takes 14 minutes per dungeon run. I haven’t timed it, but that seems a little slow to me. I timed it once at about 11 minutes, so 14 is a little slow. However, WCP also gives you the seeds (and forging items), so it may be overall best.
Since your analysis shows that buying water is not as economical as buying potions, but since I already have the seeds, I prefer to farm South Beach 4 for water and Golden Fields 2 for sand, and spend my snouts at the dojo.
EDIT: Corrected some of my figures.