I thought that red X was blood...way to kill it for me, guys.
Anyway, there is absolutely no-random in non-random. Even in the case of ties, the lowest star-value card wins, and if that's a tie, then it's the card that went first in the round.
@Zhen_Huo - was this in the DT rooms? Because they can switch from random to non-random and vice-versa without warning.
Daily tournaments switch between random and non-random every event; for example, if you're hanging out in the Type 1 room and playing at GMT 19:00-20:00, for example, is non-random; the next tournament at GMT 21:00-22:00 is random, continuing like this would give you whether the tournament you're in is random or non-random. This means that even rooms that say they are non-random, can be random during half of all daily tournaments, I hope that helps.