If Randyll Tarly and Willas Tyrell are both in the same challenge together (on the same side), would Randyll count his strength?

Assuming you are talking about dual house Randyll, he would not count his strength.

Generally speaking, cards with multiple House affiliations are considered to belong to all of those affiliations. They gain the strengths and weaknesses of all their affiliations, no matter what House they are being played out of. You can't pick and choose the affiliation most advantageous to you at a given time.

So Randyll is always considered both a Lannister character and a Baratheon character, no matter what your House card says. He is hit by Willas' effect as a Lanni character, although he could benefit from something like Andal Charger (Lanni character only). Similarly, he is vulnerable to Fury of the Dragon as a Bara character, but can benefit from Heart of the Stag ("choose a participating Bara character").

Similarly, he is vulnerable to Fury of the Dragon as a Bara character, but can benefit from Heart of the Stag ("choose a participating Bara character").

I thought the fury's looked at the house card and not the affilitition.

Similarly, he is vulnerable to Fury of the Dragon as a Bara character, but can benefit from Heart of the Stag ("choose a participating Bara character").

I thought the fury's looked at the house card and not the affilitition.

So they do. Shows you how long it's been since I've looked at one!

Thanks for the correction.

Thanks! As I thought!