Remember: the tiger doesn't need to climb a tree well. It only needs to be better at it than I am. I am confident that a hungry tiger in hot pursuit will be better at it than I am, no matter how terrified I am (which will be quite a lot). And no, we're not going to settle it by experiment.

Remember, you don't need to be better than it is. Just better than whatever other prey item it could be considering.

Does the adult tiger realize that sooner or later you have to come down, and rather than risking injury, can just wait for you to come down?

Even though a tiger may be biologically more suited than I to stand starvation, if I'm sure of certain death on the ground I'll take very long to come down. And, who knows, I might just find a few eggs.