I just caught up with this series.
Why would Kase even entertain doing this race in the first place? Fukami should have no say at all about where Kase wants to live or who Kase wants to be a roommate with.
That was the first question everyone had, and still has.
After seeing their interactions, I think it basically comes down to Kase being kinda dumb, but also she sort of lied to defuse the situation?
It definitely seems like she has no intent to stay even if she loses the bet. She is moving in with Yamada. Period. She's already told Yamada to commit, and last time she talked to Fukami about it, she used the "If I lose, I'll tell you why I'm moving," which is a clear shifting of the goalposts. The race is no longer about "I'll stay if I lose" And honestly, that's way less egrigious. "I'm going to stay until we resolve this race, but I'm definitely leaving" is way more fair to Yamada than "I'll stay if I lose." It's a little unfair to Fukami that she agreed to the race under false pretenses, but Fukami wasn't being remotely fair to Kase thorugh this whole thing, so I can't really get too mad about it.
She seems to think that win or lose, she's trying to use the race to give Fukami some kind of closure so they can part amiably. I don't know if this was always the plan, or if it's a pivot after realizing how unfair it would be to Yamada to honor the original bet, but either way, it's less stupid than it was originally.