How often do Tigers even run into another tiger?

All the time. While tigers lead solitary lifestyles, they’re not devoid of socialization. Territories overlap and lead to peaceful interactions and conflicts over borders. Sometimes they even cooperate in hunting or live together, though that’s less frequent. The nature of their interactions is mostly dictated by sexual relations and the ratio of tigers to prey.

This is not meant to contribute to the tiger vs lion issue.

I also think it’s interesting to note that while the mane serves a practical purpose, it’s also wildly oversized as a result of sexual selection.