Concisely: Randomness exists if and only if there is ignorance. As a DM, if I reach my hand in my bag of unfair chessex dice, make a biased choice of which whi

Concisely: Randomness exists if and only if there is ignorance. As a DM, if I reach my hand in my bag of unfair chessex dice, make a biased choice of which which biased die I unfairly throw... From my perspective, the odds of a 20 are still 5%, because I don't have good enough memory to know what direction any of those biases go. If one of my players, who have much less to do than a DM, rolls their same d20 every session, they will eventually pick up on its tendencies and know their die is more likely on average to crit. If a cheating player understands the velocity of their roll, they can toss in such a way that 20 is much much more likely to appear. The DM I describe can roll the same die as the player I describe but experience different probabilities because of ignorance. A fair player I describe who rolls their die in the same way as the cheating player I describe is experiencing different probabilities because of ignorance. Situations we think of as random are just good at quickly spreading ignorance. A tiny change in velocity for the cheating player will spoil his plans, and the dice numbers are spread nearly equally so that this small ignorance about velocity quickly becomes large ignorance about the probability distribution of the result. Knowing half the bits of the seed of a PRNG quickly decays into nearly zero info about it's probability distribution. Knowing the seed of a PRNG precisely and the number of cycles imprecisely quickly becomes worthless, by design. Dice, PRNGs, other things we think of as random are only different from any other piece of knowledge (future election results, whether the 1000th digit of pi is odd...) in that they are decent at quickly turning what knowledge you have into ignorance.