This is more of a physics question, but I’ve heard that in the 1950s and 1970s, scientists developed microcontrollers to calculate how the speeds of the ball and roulette wheel determine where the ball lands. I haven’t found much on math or programming. I only know it had one button to time the speeds. Does anyone have code or sources on how it worked?
Sounds like a tale to me, what you described would not be reliable at all. BUT I am old so maybe I am wrong.
There were no microcontrollers in the 1950s!
First microcontroller was developed in early 1970s I think.
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My understanding that the "roulette computer" was not a digital computer, but an analog computer built from transistors. You can read Thorp's brief description at https://www.cs.virginia.edu/~evans/thorp.pdf but it does not contain a circuit diagram.
I imagine anyone publishing such a diagram would have the casino's legal teams hounding them!
I found a video on how to program a roulette computer, but they never finished it, but they did leave a link to all the math that is involved.
https://youtu.be/79-AqolLdQs?si=KsPTWHGB0wLLIYB_
https://www.dewtronics.com/tutorials/roulette/documents/Roulette_Physik.pdf
I seems impossible in the real world... Randomness and The Butterfly Effect.
Or maybe it DID work and they lied!!! 
If they wanted to test it legitimately they could have purchased their own roulette wheel or done the experiment with the cooperation of the casino without really gambling. I'm sure the casino owners would have been happy to participate or observe.
...I saw a story on TV about someone cheating roulette. It was a lot simpler... It was done by the operator cheating if favor of his player-partner. The final ball location was detected electronically and announced automatically-electronically. But there was a short time-gap and strangely no one was watching and apparently there was no camera. The operator would just quickly the move ball to the number he wanted by hand. I don't remember how much they stole before they were caught.
It's like with a perpetual motion machine - there are a lot of videos about it, but the authors are always "a little short" of bringing it to useful use...
If I were to "invent" something to cheat for the purpose of stealing someone's money, rather than getting a respectable job and working for a living like the rest of the tax-paying world, I would find the average number of rotations the wheel takes to come to rest, know the size of the ball track (which can be any of four sizes), and record the pitch/frequency of the rolling pill (the ball, which can be any of four sizes) to get its velocity, also know the number of deflectors and the angle of the bowl. The pill will fall from the ball track at the same accumulative velocity, always, and fall into the bowl, striking a deflector or two reducing the speed further, when the frets give the pill some more life before dropping into the "programmed" pocket.
Sidebar, and true story: While at a well known institution having roulette wheels, I ended my evening with one of their watered-down drinks, to try to drain my last few "tokens" and put my "play" on "00" The Croupier looked at me and asked, "Trying to go home early?" so I said, "Let 'er ride," and received, "Good luck." The wheel was spun, the pill was rolled, and a few clakity-clacks later, the money shot was, "00" I said, "SPLENDID!" (or something like that) which got some attention. I fiddled around until I got another drink, then played another "00" at which the Croupier just chuckled. Wheel spun, ball tossed, and blammo! "00" and I said, "SPLENDID!" which was followed-up by a couple of guys getting close to me for some small talk. I drank some more watery something while I ones-and-twos some tokens and asked for another drink. My new friends said I didn't need any more, so I bet on "00" one more time. The Croupier shook her head, the "friends" smiled, and POW! "00" and I said, "SPLENDID!" ... at which point the two fellas asked me to follow them... past the cashier... to the door... where they took my free, cheap, drink and said, "Do not return." I asked, "Can I get my money?" and they said, "What money?" Understood.
Fast forward a few years to a small bar with friends on both sides of the bar, where they had a roulette wheel (the one with the ticking finger). I was given a chance to call a number for a free refill. I called "00" which hit, and I said "SPLENDID!" along with the bar. A few hours later I got another chance, and called, "00" where the bar tender said, "Don't waste your chance, really guess." Where I said, "00" and hit... and I said "SPLENDID!" along with everyone in the bar. And lastly, a few hours later, I got one last chance, and I called "00"... and the bartender stopped and stared at me, and the waitress said, "If you hit, I will show the bar "something special." so the whole bar was saying "SPLENDID! LET 'ER RIDE!" and the wheel was spun... and the "00" hit, and I did say, "SPLENDID!" and everyone in the bar did say, "SPLENDID!" except for the waitress... who looked defeatedly at the bar tender... who commenced to ripping off his own top, and everyone, including the waitress, in the bar did say, "SPLENDID!" through the night and drinks became rather inexpensive at that time.
Bottom line: Get a job, quit trying to cheat, bet "00," and you will have a splendid life.
I do not want to gamble. I am just amazied on how something that is puerly randome as roulette is, that scince and math shows that it is as perdictable as the phases of the moon. I want to know how it can be.
I told you.
I think that is an interesting question, which has fascinated me for a while. Physical systems show a range of behavior from very predictable to very unpredictable. Possibly nothing is truly completely predictable, nor completely unpredictable. Even chaotic systems have attractors, or regions that are somewhat linear.
Nuclear fission is "random" in the sense that we can't predict when an individual atom splits. However, on aggregate a fissile material has a very predictable half-life.
I guess the classic example is the weather. Weather systems are classically chaotic, in that they are sensitive to small peturbances (aka the butterfly effect). However, there are also macro level effects which can be predicted. By running many models with slightly altered input parameters, it is possible to get a statistical view of which course is most likely.
I suspect roulette is in the same category, if you know the initial conditions, you can make a calculated guess at the most likely outcome.
I would recommend James Gleick book Chaos: Making a New Science - Wikipedia