You’re missing the bigger point that both 50/50 and 80/20 are valid probability assignments as far as the mathematical theory of probability is concerned.
If we were talking about a deck of cards there would be no causal connection between the probability you assign to the next card in the deck and the next card in the deck.
Note that for the deck of cards different people can also have different probability assignments! Maybe you saw the first 26 cards as they were dealt face up, I saw them plus the card at the bottom of the deck, someone else has just arrived and has seen only the latest card dealt. Each of us will calculate different probabilities for the next card but all of them are unrelated to reality where the next card in the deck is fixed but unknown to us. Can any of us “explain the outcome”?
Mathematical theory has no causal effect on reality either. So no I am not missing some bigger point. I might as well make a metaphysical claim like. Thor will make x happen.
Ok, so probability doesn't exist at all for you [1] and the deck of cards discussion is just a red herring.
If your argument is that probability can't exist because if can't have a causal effect on reality maybe you should try to define and use probability as it's usually done - with the understanding that 'having a causal effect on reality' has nothing to do with it.
Probability can be used to say things about reality. 'Things' like 'what we know or expect'. Probability is about uncertainty. Statistical mechanics will say things like 'the average energy in that system is whatever' - this is something about reality. Particle physics will say 'the half-life of that muon is whatever'. That's physics as far as my defition of physics goes.
Can physics - in your view - explain that if you put together a glass of hot water and a glass of cold ethanol you end up with a warm mixture of water and ethanol? That "causality" only exists in a probabilistic sense after all...
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[1] You are in good company. Bruno de Finetti wrote:
“My thesis, paradoxically, and a little provocatively, but nonetheless genuinely, is simply this:
PROBABILITY DOES NOT EXIST
The abandonment of superstitious beliefs about the existence of the Phlogiston, the Cosmic Ether, Absolute Space and Time, . . . or Fairies and Witches was an essential step along the road to scientific thinking. Probability, too, if regarded as something endowed with some kind of objective existence, is no less a mis- leading misconception, an illusory attempt to exteriorize or materialize our true probabilistic beliefs.”
Probability exist as a concept in our heads just like god and math does.
Probability can be used to say something about closed systems like a game of poker using a deck of cards.
If 4 aces have been used I know that there will be no more aces dealt. I can explain why there won't be another ace. And even if magically there was one, we can explain that someone cheated or an extra card was accidentally in the deck.
If 3 aces have been dealt and there are 10 cards left there is statistically a 10% chance of me getting an ace, however I have no way of knowing. The card has already been dealt and I will either get it or I wont.
If I play 10 games will I be getting it 1 time? if I play 100 will i be getting i 10 times? I have no way of knowing.
Now if I learn how to read you and know that you blink more often if you get an ace then I have found an explanation for why I might fold. Not based on statistics but because I can read you. I might still be wrong but I have an explanatory model not based on statistics to play against you, one which I might have to adjust if it turned out to be wrong (ex. you know I know so you change behavior) but at least it's providing me with something more tangible (you give clues I might be able to learn how to interpret)
With the probability it's purely based on blind belief, not substantiated by reality.
Now a deck of card is isolated and not really consequential to society.
But now apply this to open systems economics, weather, climate, elections etc. and you will start to see the problems with assuming there is casual connection when you end up turning that into policy.
The thing is that I'm not sure of what you are saying.
Can physics explain that if you put together a glass of water and a glass of ethanol you end up with a mixture of water and ethanol?
Do you agree that it's possible - but unlikely - that they don't mix?
For other comments of yours it seems that your conclusion would be "I have no way of knowing. It depends on the positions and velocities of each of the molecules and they will either mix or they won't."
I really would appreciate having a clear answer to the question "Can physics explain that if you put together a glass of water and a glass of ethanol you end up with a mixture of water and ethanol?". Don't be shy to answer "no" if that's your idea of physics!
I don't understand the answer. (Assuming it's "yes".)
What is the explanation of why they will mix? Does it involve probabilities?
Why didn't you say "I have no way of knowing. It depends on the positions and velocities of each of the molecules and they will either mix or they won't."
(By the way, if I had asked about a container of neon and a container of helium would you have also claimed that asking whether they will mix is a chemistry question?)
The explanation of how different molecules combine when mixed.
Has nothing to do with probability.
If you can predict that it happens exactly 10% of the time (ex. every 10th time) then you have an explanatory model that can explain why that is and you don't need statistics.
I don't think you are asking what you think you are asking.
What I'm asking is a quite simple physics question. I know what I'm asking - what I don't know is why you don't at least try to give a definite answer. I'm trying to make it clearer (let me know if it's not clear enough):
I have a container with two compartments, separated by a moving wall. In each side there is an equal volume of gas at normal temperature and pressure (helium and neon). What happens when the moving wall is removed?
A) The gases will mix.
B) The gases will not mix.
C) I have no way of knowing. It depends on the positions and velocities of each of the particles and they will either mix or they won't.
The usual (wrong?) answer is A. But it seems that you could (should?) answer C. Because you cannot rule out the possibility that they don't mix - you would be guessing.
If we were talking about a deck of cards there would be no causal connection between the probability you assign to the next card in the deck and the next card in the deck.
Note that for the deck of cards different people can also have different probability assignments! Maybe you saw the first 26 cards as they were dealt face up, I saw them plus the card at the bottom of the deck, someone else has just arrived and has seen only the latest card dealt. Each of us will calculate different probabilities for the next card but all of them are unrelated to reality where the next card in the deck is fixed but unknown to us. Can any of us “explain the outcome”?