Depends on the subject. If it's over something factual, then the answer for both parties is whatever the science says, to whatever confidence level it says it. The mind must be open to new data.
Subjective topics is where it gets more interesting. Assuming the other person wasn't just lobbing a bunch of sophistry my way, and holds their own in the argument, I usually can't avoid acknowledging a kernel of truth in their argument. That doesn't mean that I have changed my mind, necessarily, but my position has become slightly more nuanced.
In my life, the times I've been the most open to change hasn't been from argumentation, though. But rather when someone shares the experiences that shaped their opinions, in a low-stakes, ulterior-motive-free way. I believe this is called invitational rhetoric. If there is a strong enough parallel to my own experiences, it has caused a wild shift in my thinking at least once before.