How much liquid is in each bucket?
E.g. each bucket has 1 cup of liquid to start:
1. The wine bucket becomes empty, with 2 cups in the water bucket, 1:1 mix.
2. The water bucket is reduced back to 1 cup, 1:1 mix.
3. The wine bucket once more has 1 cup of the 1:1 mix.
Thus, the buckets are equal.
Or, each bucket has 9 cups to start:
1. 8 cups in the wine bucket; 10 cups in the water bucket (now 90% water).
2. 9 cups in the water bucket, still a 9:1 ratio (== 81:9), favoring water.
3. 9 cups in the wine bucket, 8.1:.9 ratio (8 cups wine plus a cup that's 90% water): also 81:9, favoring wine.
So, it doesn't seem to matter; they are the same. I think I see a relationship with the water:wine ratio being the inverse of what's needed to balance out the other bucket. Since the ratio for the water bucket is calculated with an extra cup of liquid (e.g. 9:1 rather than 8:1, which means a 90% solution rather than an 88.9% solution), the cup being added back to the wine bucket needs to reflect that offset in some way. What did I miss?
// On topic: my teacup came with measurements; I just use those.