But words have meaning -- you shouldn't neglect that a "die" is a "3-dimensional object with n sides, usually designed such that each has equal probability of ending up when rolled". My objection would vanish if instead of a die it were a "random number generator returning integers from 1 to 4 with an average of 3"

In this case, the generator has an unknown distribution biased in some way toward the higher numbers. This is a problem because it is highly unlikely that my estimate of the probabilities matches the actual probabilities, and furthermore someone else might know the actual probabilities and be able to win bets against me.