Can I make a CnR with no winning criteria for Cops?

Question

I've had two challenge ideas floating around in my head for a while. I'll spare the details but as a general overview:

The first is a challenge that should, in principle, be fun but in practice it is so easy for cops to make solutions that are virtually impossible to crack that it couldn't be fun in practice. Similar to how it is quite easy to make a riddle that no one can crack, but hard riddles are not good.

The other is not really even a cops and robbers question, but would involve collecting OEIS sequences (and some other information) submitted by users and then having a competition based on the submitted sequences. There can't rally be a winning criterion for OEIS sequences.

Here there seems to be a common thread. I would like to post a two thread (cops and robbers style) question that is competitive and does have a winning criterion but only for one thread. In the second case the goal of the non-scored thread would be to maximize your own score on the scored thread, but the first is in even murkier water where the ostensibly the only goal of one thread is to make the other thread "fun" (whatever that means).¹

Now perhaps each scenario should be treated separately, but they are similar so I thought I'd put them as one meta question.

Can a two thread challenge have one thread without a winning criterion? If so what restrictions should we put in place on such challenge types?

^{I have thought of making it a pop-con and robbers but I really, really don't like pop-cons for a number of reasons, and I'd rather not ask the question than ruin it by making it a pop-con.}

Answer 1

Tailoring the incentives

Not a direct answer to the title question, but a potential solution for your first example case.

If you want cops to have an incentive to produce difficult problems, but also an incentive to avoid problems that will never be solved, you could design the scoring mechanism with this in mind, rather than not scoring at all. This would avoid the grey area problem with banning cryptographic hash functions (what counts as one...?). The scoring mechanism itself will give cops an incentive to avoid things that can't be cracked.

There may be many ways of including this incentive in the scoring mechanism, that suit different types of challenge.

Example

A cop's score is the length of time between posting the cop answer and having a valid robber answer posted.

Now if a cop misjudges this and posts something that never gets cracked, they score zero.

---

This might even apply to in a similar way to your second example case. If the cops thread is effectively a list of golf challenges, you could score in a way that gives an incentive to find sequences that are harder to compress. For example: A cop's score is the length of the shortest corresponding robber answer. So robbers try to win by posting the shortest code for each cop, and cops try to win by posting sequences that require more bytes of code than other cops' sequences.

There isn't a concept of "uncrackable" in this case (you can phrase the challenge spec to ensure all sequences are well defined and can be described in code), but you could still put an upper limit on code length if you wish. For example: A cop scores zero until the shortest corresponding robber answer is less than 100 bytes (or 1000 bytes, or whatever suits your challenge). This gives cops an incentive to be difficult but not too impractical.

Loopholes

The scoring mechanisms may need some refinement to avoid unwanted incentives and the possibility of loopholes. It might take a few test challenges to iron these out.

For example: a cop might be able to inflate their score by looking at the timezones/frequently active charts for the users in the robbers thread, and posting when fewer of them will be online. This might be mitigated by making the score the floor of the number of whole 24 hour periods, starting at the cop posting time. There's a similar potential problem with weekends too.