To win at betting with roulette you only need to bet on a set of numbers, where the probability of the marble landing on that set is pretty good, and the payout of winning over time covers the losses from being wrong.
So say you can accurately guess which 1/4 of the wheel will capture the marble. (and there are no greens... the real math is the same but uglier a bit). You put down equal bets on the 9 numbers represented by that. Each beting round will net you a 4:1 payout.
Now say you can only guess that 1/4 of the wheel, 50% of the time. You will still average a 2:1 payout.
Guessing the 1/4 of the board 50% of the time is not that hard, you just need to calculate the linear drift of the time the marble passes a fixed point, and know the frequency of "loops" that is too slow for the marble to stay on the track. Accounting for the rotation of the board is straight-forward, it is almost constant for a given play. The 50% covers the wierd bounces. Just calculate board position for the time that the marble will get below the threshold, and the marble position as well, and you've won. A person can't do it well, but an arduino is overkill for it.
Edit: further notes on this- casinos will be able to detect this easily. All they have to do is look for people on hot streaks that are "too hot", then compare betting placement with wheel positions. And they generally kick people out who are winning too much anyway, even if they can't prove 'chaeting'.