Here are all the cards in Elements that require randomization, and the smallest dice needed:
Quantum Tower (3d12)
Fog Shield (d5)
Shard of Freedom (d4)
Ice Shield (d10)
Ice Bolt (d20)
Pest (d12)
Dusk Mantle (d2)
Spine Carapace (d4)
Skull Shield (complicated)
Skeleton (complicated)
Fate Egg (complicated)
Dissipation Field (d12)
Chaos Seed (d12)
Chaos Power (2d5)
Singularity (d7)
Mutation (complicated)
Fallen Druid (complicated)
Pandemonium (d12)
Discord (18d12)
SoSe (complicated)
So yeah, entropy has a lot of cards that require randomization, but over half of them are simple. This makes a total of only 6 cards that go beyond a simple dice roll.
Skull Shield has variable percentages. If we remove rounding to a whole percent, because dice can circumvent it, it potentially needs everything from d2, d4, d6, d8, d10...d996, d998. Obviously this doesn't work, so it would have to be simplified to be done without a device.
Skeleton, Fate Egg, Mutation, and Improved Mutation require a d(X-9), where X is the number of creatures in the game. There are nine creatures in the game Fate Egg cannot become, as well as flying weapons, and as far as I know these are also the exceptions for Skeleton, Mutation, and Improved Mutation. I'd prefer removing some of these exceptions, but I'm going by the current game for this purpose.
In this case, X isn't terribly big, hovering somewhere considerably less than 100. There's actually ways to make this work depending on the number.
Mutation and Improved Mutation, after generating a creature, also require 2(d5-1) for stat changes, a d23 for the ability, and a d2 for the ability cost. Furthermore, before even getting to this point, Mutation requires a d10 to determine whether it becomes an abomination, mutant, or dead.
Personally, I don't think a RL CCG should have two versions of a card in the way Elements does, so I'd be for merging them into 60% mutant, 30% abom, and 10% death. But that's just my opinion.
SoSe simply requires a dX, where X is every card in the game that's legally obtainable, except marks, shards, and nymphs. In this case, X is somewhere above 150, and there's probably not a usable die that big.