Recapping to make sure i understand
Chance makes more sense from a scientific view point is what you are saying?
Chance is an approximation method that is used when you don't fully understand how something works in a natural logical way.
When you buy a lottery ticket is that based on an intelligent choice? Or is that based on imagination, emotions and a hunch? Why would science depart from the riggers of logic in favor of faith in the lottery, and call that a solid basis for science? The science casino is designed, so the house can appear to win with nothing more than luck.
Gambling goes back to the ancient times. Dice were used in Ancient Greece as far back as 500BC; whims of the gods. Gambling was also in China about the same time. Dice are manmade inventions. They are not natural to the earth or the universe. Dice do not grow on trees, but are manufactured. I can see how the theory behind the behavior of manufactured things like dice, may be preferred when discussing new manmade objects made in factories, since neither are natural, so do not have to obey natural laws.
When one is learning about statistics and probability, the lessons for the theory uses manmade objects like coins, dice and cards as teaching aids. I can see how this manmade foundation may be useful in factories. But when discussing nature, one should not be allowed to base natural theory on the behavior of manmade objects, like dice. Does anyone see a potential problem? It is like saying we should model the behavior of animals on robots, and not the other way around; cart before the horse.
The hydrogen atom has energy levels. It does not randomly move between these energy levels, since each side of this natural dice, is loaded differently by nature. Based on an energy context, one side will be favored. Dice are designed by man, not to have any differences between the sides. If a dice did have differences, like the hydrogen atom dice, that would be called cheating in a casino, since it would default closer to the natural logic of the hydrogen atom. This will take away the fantasy reinforcements of manufactured dice.
If you go to a casino and play cards, card counting is illegal and one will be black balled. What does card counting do? It tells us which cards are left, making the new final result more logical and less based on manufactured rules; all is still in play allowing the house to win. I would send Science to Gamblers Anonymous to help ween them away so we can get back to the world of science outside the casinos.
What I think happened is what had been and understood to be an approximation method, lost its original common sense. Later generations of scientists, who had to learn the technique apart from its inception, began to assume that the approximation was real and not just a method. It was was easier, since it did not require as much rational thinking. Here we are.
When I was a grad student in engineering, if if tried to mathematical model a chemical process, setting up the equations was easy, compared to solving all the equations. Approximation methods were developed by mathematicians that allowed one to solve all the equation using computers. The math models did not reflect reality, but were tools to help simplify the math solution. This appears to be the case with statistics, with the approximation now assumed to be more that it ever was intended to be. It was not designed to replace logic but to help logic get through math bottlenecks.