Unfortunately, order and random are two ends of a scale. And where you are on that scale is called entropy. If you're asking on a cryptography forum, we have to look at this from an information angle.
Thermodynamic entropy from an information perspective
If all the balls are at rest because the stuff is cold, they are very ordered. It is easy to describe their positions and thus the state of the material.
If the stuff is hot and all the balls are flying around everywhere (randomly), it's very difficult to totally describe the state of the gas molecules. You'd have to write down all of the current 3D positions of them and their respective velocity vectors. That's a lot of writing and thus lots of entropy.
Entropy from a poker and information perspective
Consider the two decks. It's very easy to describe this one:-
It's simply C,S,H,D,1-10,J,Q,K in code I just made up. You might be able to shorten it. This illustrates that an unsorted deck doesn't have a lot of entropy.
Now attempt to describe this shuffled deck:-
You'd have to write down each card individually, there's no other way unless you can find some sort of mathematical relationship between each card. If this is a fully random shuffle, the state contains $ log_2(52!) $ bits, or about 226 bits of binary information. It cannot be completely described with less.
To answer your question of removing cards - not necessarily. You could just slightly order the cards, forming relationships between them. Say all Diamonds are ordered as new. That would reduce the entropy whilst keeping the same number of cards.
Entropy = information necessary to describe a system or state.
In cryptography, if you know the information, entropy = 0. So cryptographic entropy is the enumerated amount of uncertainty. And we measure that in bits.