View: Aces full of 9s is a better hand than than Aces full of Kings

Hear me out.

The game is 5 card stud. Which is a better hand, AAA99 or AAAKK?

If it were a community card game we'd just say that aces full of kings is better, but there's no sharing cards, so AAA99 is the same strength of hand as AAAKK; however, AAA99 blocks more straight flushes than AAAKK (I think independent of suits?). So we are beat less frequently. That our absolute hand rank is higher with the AAAKK doesn't translate to 'better' - which is really just 'how likely we are to have the best hand'.

(with apologies to Alex Bellos)