A simple probability problem is to find a random number between 1 and 4 (inclusive) using a 6-sided fair dice. A simple solution would be to just roll the dice, and discard all 5's and 6's.
However, at a math talk, someone offhandedly mentioned that discarding the 5's and 6's would lead to a "loss in entropy", whatever that means...? By definition, the mentioned solution would still preserve the requirement of randomness; that is, all events are equally distributed. Then, is there any meaning to this "loss of entropy" that was, perhaps jokingly, mentioned?