Ban generally, not specifically
I'm very much opposed to the idea that "OP has final say" (I.e. if the post author dislikes an answer, or doesn't think it's ok, they get to disqualify it)\${}^*\$. Answers should be objectively valid or invalid by anyone who has read the challenge rules.
Therefore, I suggest that bans be more general than specific. You can ban random bots in king-of-the-hill by requiring them to be deterministic. Beyond that, you can ban specific, objective behaviour (e.g. may only use uniform random distributions), but not specific answers, unless they break the rules.
Unfortunately, this is an all-too-common reality of challenge writing on CGCC. There are very often answers which completely screw up the challenge, but which are perfectly valid. Typically, they are hyper optimised solutions, or clever tricks found in the mathematics. Here, however, the randomness has affected it in unexpected ways. Really, the only advice I can give is that randomness is often compensated for by running a lot of rounds. Try running a sample competition and see whether 1000 rounds "fixes" the extremes produced by Rude Random.
\${}^*\$ And I have, and do, vote to close challenges as "opinion-based" if the OP tries to claim that they have final say