Reading about random shuffle algorithms, I sometimes see the "randomness" of the method being discussed, and described as "less random" than a different algorithm.
For example, if I take a random process like a dice roll and modify it so that no number can appear twice (or more) in a row, one would say this process is "less random". Is this so because the probability of each outcome depends on the previous result? Moreover, if I have a perfectly shuffled deck of cards, does it mean taking a card from the deck is less and less random (since I cannot take a card I already got)? If so, how much less is it random?
Still, if I sum two numbers from two independent dice rolls, the result tends to be around the middle of the interval, but should still be totally random (i.e. independent on previous results). Still, one would describe the outcome as being not so random, since it prefers certain results over others.
Is the amount of randomness described only in terms of uniformity of the distribution and dependency on previous values, or is it something else? How can we measure how much "random" something is?