Yes, you can solve them mathematically. The main difference is that instead of a strategy picking a move for each possible state of the game, it picks a probabi

Yes, you can solve them mathematically. The main difference is that instead of a strategy picking a move for each possible state of the game, it picks a probability distribution over moves for each possible state of the game (including history). Given two strategies, you can determine which one is expected to win and by how much. That allows you to find the strategy that's hardest to take advantage of. In the case of non-transitive dice, the hardest strategy to take advantage of is likely to be "pick each die with equal chance". That being said, solving these games is extremely expensive. Super-exponential in the size of the game, if I remember correctly. Way worse than games like chess. See this paper: http://www.sciencedirect.com/science/article/pii/0022000084900345 http://www.sciencedirect.com/science/article/pii/00220000849...