I just started a new game and while playing Marco's game in Rockland, I noticed a pattern. This applies to the first turn when you play his game. In order to get this to refresh you need to win, exit the game and start a new game effectively making each session just a single turn.
You aren't actually looking for which cup the coin is left under for this, but instead the pattern is in the moves he makes in order for the coin to end up there. When you watch his moves is surprising easy to predict which cup the coin will be in. I just tested this and won 20 10,000 bit games in a row. Granted I know this has only been tested on my game, 30 or so total times, and only in Rockland, but it's a start and I thought I would point it out.
What you're looking for is the very LAST move he makes before you get to decide which cup the coin is under. What ever this move is will tell you which cup it is. I'll call the cups 1, 2, and 3 in order from left to right. As an example if he switches the position of cups 2 and 3 as his last move the coin will be under cup 1. Below are the patterns for each of the cups.
Coin under cup #1: Switch position of cups 2 and 3
Coin under cup #2: He will rotate cups 1 and 3 in a circle motion but not actually switch them.
Coin under cup #3: Switch position of cups 1 and 2
Again, this pattern is only relevant for the first round of each session and as far as I have tested, only in Rockland. It does not hold up for any additional turn of the game and there is no distinct pattern for if the coin starts in cup 1 or so on for the additional turns.
If anyone else tries this and fails or succeeds, reply and let me know.