You're more of an optimist than I.
But that might, as much as anything else, be due to where you (have) live(d) and the people you mix with.
I’ve lived in various European countries and travelled a bit further afield as well. And, in my experience, no matter where I go, most people don’t really think much below the surface of things in general anyway but, most specifically, when it comes to matters mathematical/logical, they are hopelessly out of their depth in a puddle. They take at face value what they are presented with and, if you’re lucky, they comprehend it but don’t question it — far too many don’t even comprehend it to begin with (people’s reading comprehension is all too often alarmingly poor).
In the UK in particular (and, in my experience, the US as well), people’s grasp of logic in general … and their ability to separate concerns in particular … are frankly appalling. I’ve had an hour long argument with people about how to follow the instructions on the back of a pizza box! They refused to acknowledge that, whilst they were following the correct procedure to bake the pizza by removing the packaging and then placing it in the oven, they weren’t following the instructions — according to which, if you followed them to the letter, the pizza needed to be placed in the oven and the packaging then removed (without removing it from the oven). If people can’t even see what’s staring them in the face, but deny reality, what hope is there of their grasping something as abstract as probability? (It’s like trying to persuade someone with blindsight that they walked around the table they didn’t see when crossing the room).
I’ve had interminable arguments with people about the whole car behind one of three doors (but one door is eliminated before you have to pick one) scenario. Probabilistically speaking, the likelihood of the vehicle being behind the door you are not in front of is 67% and you should, therefore, select that door. But … there being only two doors to choose from … you still only have a 50% chance to choose the correct one. And people get upset because, no, there’s a 67% chance that it’s behind the other door, so you have a 67% chance of picking the right door, if you pick that one — they cannot wrap their heads around the difference between the 67% chance of your having picked the right one versus the 50% chance of your actually picking it.
So, no, I’m not convinced most people are aware of the fact that the ‘6' needn’t necessarily occur on the next roll. In fact, a lot of them truly believe that, the longer it doesn’t appear, the more it must do so in the Future — suggest to them that there’s as much chance of it never turning up at all as of it turning up as the result of any particular roll and their minds are blown. And that principle is the one that ‘the House’ relies upon: people continuing to place their bet on that next roll of the dice, spin of the wheel, turn of the card, because this time, it has to turn up — the laws of probability dictate it (they’re sure that’s what they half remember learning in school that day they were paying zero attention in class).
As for taking things literally, that is a danger, yes … one I rely upon in fact for a lot of the humourous things I say/write:
But, personally, I err on the side of being overly cautious by going into matters in depth, in order to ensure that I understand you and have made my own thinking equally clear; far more so than most people have the patience for (because it requires them to think about things rather than tossing out a predigested response without any thought behind it). Of course, the British public is particularly prone to throwing out tabloid ‘soundbites’, as it were rather than thinking for themselves, so my own thinking may be affected as a result; who we are depends as much upon where we are as any inherent qualities — for all that he was a benighted, tree-hugging hippy and only did so by complete accident, Jung did get that much right about the collective unconscious (it was an accident, however, so, morally speaking, he was still wrong and there is, therefore, no collective unconscious that I acknowledge — it’s the principle of the thing, you understand).
