Can anyone help me figure out the what the largest number of possible moves for a given turn would be in Othello/Reversi? On the first turn, there are 4 possible legal moves, the next player has 3 possible, and depending on that move, the next turn there are 4 or 5 possible moves. I'm not sure how to go about figuring out the best-case case scenario for a player to gain the most possible moves that turn, and I'd like to find out what this maximum is. I searched around, but only saw information on maximum number of games possible, which is not what I'm looking for.
It is very hard to say it without browsing all possible combinations. Another question is are you asking about moves in game that make sense or any random game. I was playing this game many years and usually one consider move choosing out of 3 maximally 5 possibilities for good move. However in mid-game there are 10-20 legal moves frequently.
You can try some maths to estimate max number of legal moves. Board is 64 fields. You can move only on adjacent. So in my opinion max number possible moves is when you have filled center 6x6, lets say white are on boarder of 6x6 and black are in center. Black have a move so he can move on any field left on board. It gives 28 possibilities. I would say it is maximal estimate.
If you still need to analyse that you should have a look on that program. It is used by most good players. There is also big openings book.