This was originally a comment, but it became too big. It doesn't provide a single answer per se, but more of a collection of ideas.
First of all, I think I disagree with
there’s nothing I can do to try to win
In the two examples, making more answers increases the chance that you will win, and making more answers is what we should be incentivizing. There is nothing you can do to improve an individual answer's chance of winning, which is I think you take issue with, but overall you can increase your chances of winning by producing more answers.
That being said, I don't think this is the best winning criterion for answer-chaining. While it does incentivize more answers, it only does so probabilistically and, like what I think you are getting at, there is nothing you can do to improve an individual answer. I think this winning criterion works best when each answer is harder than the last, which is not the case for one OEIS after another. Even in cases where it does increase in difficulty, it's not the best, as it doesn't really encourage answers to do anything other than to be valid.
As a challenge writer I would suggest doing something along the lines of "each answer counts as n-points towards its poster with the one that breaks the chain counting negative", but that doesn't really help answer the question.
All in all, I don't know what we can or should do about this. I'll let other people sort that out since I don't have a strong opinion. Until then, I'll just downvote any challenge I don't think incentivizes good answers.