What to take into account?
I look for a sequence of visits that will allow me to play for a big win (2 or more places), then the pause at the next visit farther away so I can withdraw early and conserve cards.
Depending on the sequence layout, the face-up cards available, and the number of players, I might withdraw early on Visit #1 to get the two cards I want plus the third from the face-down deck. Then I can concentrate on Visit #2.
Avoid lengthy showdowns unless the big win is absolutely essential. Normally, 1-2 palaces is enough of win to sustain momentum.