It's here! The argument in Batterton!

Credit to Justice Sotomayor for her perceptive questioning.

It is probably a fool’s game to predict the outcome based on the transcript, at least in this case. It seems likely that it won’t be unanimous, though it might be a little bit of an odd decision: Justice Kagan refers to the Jones Act as a “flashing yellow light,” warning the Supreme Court not to expand remedies for unseaworthiness, which tends to suggest she’s against a more expansive remedy, a little surprisingly. Then again, Miles was unanimous.

We should know the answer before long - June-ish or before.

Edit: It remains a fool’s game to predict the outcome, but fools rush in where angels fear to tread, so here goes: 6-3 ruling that punitive damages are unavailable. Roberts, Kavanaugh, Kagan, Gorsuch, Thomas, Alito for the majority; Sotomayor, Breyer, Ginsburg for the dissent. (Note that this is wild, wild speculation.)