Randomness and Doomsday for Weak agents

Most things that we model as random, are in fact deterministic. The outcome of a dice roll is determined by the initial momentum and angular momentum of the die, computer generated random numbers are chosen in a deterministic way by hard-to-predict programs. Sometimes, the extent of the non-randomness is very clear. As a child I enjoyed the "Lone Wolf" choose-your-own adventure books. In these books, you sometimes had to resolve fights with monsters, which were determined using random numbers between 0 and 9. To generate these numbers the book provided this table: You close your eyes, get a pencil, wave it around and stab it down into the book to get a number. This system is frustrating and terrible. You very quickly learn how to aim at the numbers you want. You don't want to cheat, its just that not-aiming is harder than aiming. You come up with some new system, where you rotate the book to some skew angle to throw yourself off, you wave your arm dramatically, as if that would help, and you hit a 3. A 3! That is a bad result, so you must have succeeded at not aiming. This technique is good, lets keep using it. You then hit the same 3, or the 2 next to it, for each of your next 5 goes. In the, very likely, event you have not played Lone Wolf you may have encountered a similar experience in certain card games, which require you to shuffle a deck of cards that can get quite small (Dominion for example). If you get down to shuffling about 5 cards, then doing a "shuffle" motion doesn't randomise them at all. Not because the physical motion looses its power, but because the number is small enough that you can easily track where the most important card or two is. At this point a different randomisation procedure is needed, usually one where another player helps you randomise the cards works fine. Sticking to cards, a well-shuffled deck of cards looks, to me, a pathetic human, like its random. To Superman with X-ray vision the top card is clear as day. Perhaps to a very perceptive being without X-ray vision trying a shuffle motion on 52 cards would find it just as futile as I find it on 5 cards. This hypothetical being might also find rolling dice to have all the problems I have with the Lone Wolf stabby number grid. It knows that a little more torque will flip it from a 5 to a 6, it can't pretend to itself that it doesn't know. So, things that we model as random, because they look random to us, might be better modelled as non-random to "stronger agents", for example ones whose grasp of mechanics means that they cannot actually get unexpected dice rolls even if they try. This post is about the opposite, weaker agents. Imagined agents who have less information than we typically do. Something we would never model as random, they do. As an extreme illustrative example, lets imagine that some poor person suffers from a brain injury or stroke. They remember the names of the days of the week, and they remember that these days form a cycle. But, the brain injury means that they completely forget the order of the days. They know that today is Monday.  They tell you that it "just like a dice roll", there are six possible days it could be tomorrow: Tuesday, Wednesday etc., and its equally likely to be any of them. You would, I suspect, find this jarring. Its so obvious to you that tomorrow is Tuesday that describing it as random feels viscerally wrong. Even leaving that aside, the fact that it is cyclical,  means that even in ignorance calling it "random" feels off somehow.  Why would we even think about weak agents? Its because they make very good examples for learning or teaching some concept in probability. A weak agent who knows only that an election had 3 candidates, candidates A, B and C, can be imagined to give a 1/3rd chance of each candidate winning, and this example could teach us something very basic about probability. Further, we know that the 1/3rd answer is, given this weak agent's state of knowledge, the right answer. If we go for a more "real world" example where the agent has a much bigger knowledge space its very hard to see what the right answer, given that bigger knowledge base, actually is. (What is the correct probability to give for Count Binface winning the Clackton by-election based on everything I know? Or for your preferred candidate in the next election you care about given everything you know?)[1] When we do basic probability problems, guessing the top card of a deck etc, we are always implicitly (or explicitly) thinking about clean situations where you have nothing else to go on. You don't know that the deck used to be in state X and was badly shuffled, you can't read the body language of your opponent or whatever. We can imagine an annoying student in a maths class derailing our nice probability examples with questions like "But what if I am really good at reading my opponents microexpressions?". I think that this is a part of why various anthropic type discussions are so confusing. Whenever