Dice (unloaded) seem a paradigm of chance: when rolling a die, one cannot know the outcome in advance because it is random. For example, if you roll a twenty-sided die, then there is supposed to be an equal chance to get any number. If you roll it 20 times, it would not be surprising if you didn’t roll every number. If you rolled the die 100 times, chance says you would probably roll each number 5 times. But it would not be shocking if this did not occur. But if you rolled a thousand or a million times, then you would expect the results to match the predicted probability  closely because you would expect the law of large numbers to be in effect. 

While dice provide a simple example, the world seems full of chance.  For example, diseases are presented in terms of chance: a person has X% chance of catching the disease and, if it can be fatal, they have a Y% chance of dying. While the method of calculating chance in the context of disease is complicated, the rough process involves determining the number of people in a category who become infected and the number in that group who die. To use a made-up example, if 1 person out of every 100 dies, then the chance of dying from infection would be 1%.

This estimate can be off for many reasons, but one obvious concern is that probability is being estimated based on the outcome. Why this is a problem is illustrated by considering a scenario in which you are given the results of repeated rolling of a die, and you are trying to figure out the type of die being rolled and whether it is weighted. You can, obviously, make some reasonable inferences. For example, if the highest number you are given is a 30, you know the die has at least 30 sides. Matters become more complicated if you are not sure that a die is really being rolled. Perhaps you have been given numbers generated by some other means. They might, for example, be selected to give the impression of chance. One could, for example, create the impression that they are rolling a 20-sided die by picking the appropriate numbers. A similar sort of thing could occur in the world, and this can be illustrated with the disease example.

Let us imagine two universes. Universe A is a random universe that has random chance and probability (whatever that means). In that world, there would be a metaphysical and metaphorical roll of the dice to determine outcomes arising from chance. For example, a disease that had a 1% fatality rate would work metaphorically like this: each infected person would get a roll with a 100 sided die (a d100 for tabletop gamers) and if they roll a 01, then they die. Thanks to the law of large numbers, if enough people got infected then this would work out to 1 in 100 people dying in this random universe.  Naturally, smaller numbers will not match the 1 in 100 perfectly, but with a large enough number of infections the 1 in 100 will be achieved (oversimplifying things a bit). Now to universe B.

Universe B is not random. It could be a deterministic or pre-determined universe or whatever non-random reality you want. In this universe the disease kills 1 in 100 people, but this is not the result of chance. Out of every 100 infected people, there will be one who will die (this oversimplifies things a bit for the sake of the example). This is not due to chance since this is not (by hypothesis) a random universe. In terms of why it occurs, this will depend on the sort of non-random universe one has picked. For example, perhaps the universe is run by a god who created the 1 in 100 death disease and has sorted out humans into groups of 100 using whatever standard the god has chosen and then selects one to kill with the disease.

From the standpoint of humans, this universe will (probably) appear identical to random universe A. After all, the samples people use will be imperfect and will create the impression that it is not a perfect 1 in 100 every time.  As such, it will seem random. Unless, of course, humans can figure out how the 100 person groups work. One could imagine a short story based on this idea in which scientists find that a disease is always fatal to 1 person out of a group of 100 people and the 100 person groups are divided up by the X factor they find. But if humans do not sort out the grouping, then the non-random universe would seem random because of human ignorance.

We do not, of course, know what sort of universe we live in. Roughly put, this might be a random universe and a 1 in 100 chance is “rolled” with metaphysical metaphorical dice. Or it might be a non-random universe in which a 1 in 100 “chance” means that it is “set” to happen once out of every group of 100. Unless we can identify the groupings and get adequate data, then we will never know what sort of universe we inhabit.