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$\begingroup$ Fair point about the tie-breaking - I've edited the question to assume that we always choose $S_i$ with the lowest $i$ first. Even then, it is still not clear to me whether the limit always exists (I conjecture that it does). $\endgroup$
– pi66
Commented Oct 22, 2021 at 11:34
$\begingroup$ Perhaps one can show that the amoount of water in the cups eventually becomes periodic. The outcome still depends on the initial configuration - I wonder what functions can be computed by a cup-bucket-automaton (i.e. input: initial configuration, output: limit ratios) $\endgroup$
– Florian Lehner
Commented Oct 22, 2021 at 13:18
1

$\begingroup$ The amount of water in the cups does not eventually become periodic. See the answer in the link in the question. $\endgroup$
– pi66
Commented Oct 22, 2021 at 13:43

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