When playing games, sometimes it’s just a little thing, or a player perception that causes things to go awry. I have had people refer to Euro games, as dice chuckers because it had dice in it. Looking for randomization ideas, I asked on the web, and 3 came out on top:
3. Bag Pull
Each of these has a perception and can be manipulated.
With Cards if everyone shares the random deck, card counters will know when it is better or worse to draw. If each person has their own deck, ala Gloomhaven, then it becomes more of a choice than a result to many players.
With Dice a players luck can make people perceive randomness where none is intended. Even when people reduce dice to 2-3 positions only that are evenly distributed, some people perceive this as a bad randomness. Some people love throwing dice, but it can be perceived as random, so be aware.
With Bag Pull if everyone shares the bag, bag counters will know when it is better or worse to draw. With each person having their own drawbag, the game and perception becomes quite interesting. An excellent implementation of this style is Orleans. Items are being added and taken from the bag so often that someone would need to be a fantastic counter and constantly watching the pulls to make this even somewhat predictable.