I wondered whether dwarves used male-preference primogeniture, absolute primogeniture or something else, so I loaded up the world I've just generated (you can find the worldgen stuff in the cookbook thread) and took a look at the civilisation I'm planning on allying myself with, Ùshrir Ebal.
The first king was Edzul Ilralevost, who had nineteen children, nine of whom survived him. I was surprised to note that the crown passed neither to his eldest surviving son, his sixth eldest son Medtob Nercog nor to his eldest surviving offspring, his third eldest daughter Zasit Ducimzefon. Instead it passed to his eighth eldest daughter Dumed Kelrithlut, his fifth eldest surviving offspring and fourth eldest daughter.
It gets weirder: Dumed Kelrithlut dies without issue (she didn't even marry) so when she dies in 206 the crown passes to... Moldath Kosothegast, who has no ties whatsoever to the royal lineage and isn't even a noble - his wife became baroness of Azothalåth after he died.
As of 250 the crown is held by Tobul Lòrumstiz, Moldath's second eldest son; he inherited it on Moldath's death in 247, over the head of his older brother Mûthkat Kälánatír (who died in 249 with no surviving heirs). From this I conclude dwarven primogeniture is "one of the monarch's surviving offspring is chosen at random; if the monarch died without issue, the crown passes to another dwarf at random".
I'd still like a more deterministic algorithm, preferably one which takes immortal creatures into consideration. What interesting things have happened in the royal families of your world?