At first glance, throne is a bit of a weird card to consider if your goal is to play Rudolf. You can't run it with Rudolf.
A thing to remember, however, is the majority of your time playing is prepping your legacies. The strength of your parents is an overlooked factor but its pretty much what makes or breaks your ace once you already have a good deck.
As Rudolf our bread an butter lineage is the typical array of backliner sparks:
- Uma stan
- THH
- Nimble nav
- Scenario spark
Add to that some assortment of other typical skills you buy and situational skills like risky buis. I personally don't have a Falco power at high enough LB to also loop GW but that is also something we would like.
So, our parent runs become a combination of:
- Get the skills we want
- Hit rank SS
- Hit stat breakpoints to get higher chance at 3* blues
My deck as of now for parent runs if I want to have an easy time is something like this

And if I want to torture myself a bit more then

Eventually I would like my parent deck to look something like

And then once GL drops add light hello for gold PTO.