How exactly do casinos come up with their probabilities?

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Recently I was diving into the world that is casinos and while looking at all the games, I seemed to focus on the slot-machine side of things. (Primarily due to the technology side of it.)

While reading up about the odds, different types of slots, how they work, etc... I noticed one common thing. While the game itself tells you; "You will win x amount with these combinations." Casinos seem to be very quiet when it comes to discussing actual percentages. I assume they do this since when someone sees that their chance to win a large amount is 0.000001%, it could deter them from using the machine?

Presumably, I assume they take a range of numbers like; 12,000. Take their number of payouts, then assign the payouts to a sub-range of that first range. For example; Payout 1 = 5, 24, 2356, 8000, etc... Then they just use a RNG to determine the outcome?

Anyway, with that in mind I started to brainstorm and try and make my own "odds/probabilities" for a classic three-reel slot-machine. Something that has given me some trouble is sourcing some actual information. As said above, casinos are pretty hush, hush about actual numbers.

So, my question is; "How do casinos come up with their probabilities?" For example; Let's say a casino wants to start a new machine, and they start allocating percentages to their payouts.

Is it as simple as them just picking a random super low percentage? Or are they actually basing it off some kind of formula?

Another follow up question I had, do they play the same odds/percentages on all reels or would they dynamically change the odds on the 2nd and 3rd reel based on the outcome of the 1st reel? (If so that seems a little dodgy???)

Any help/information is greatly appreciated! :)