I don't think that there is any mathematical training needed to gain insight from running repeated simulations.

The only intuition you need is that you can become better at the game by practicing. This is a good (if optimistic) belief to have as a default. Then it's just a matter of playing over and over again and keeping score. It doesn't even have to occur to you that the strategy can be automated, you can play yourself. Just doing this you could build intuition for the best strategy the same way that most people can learn to play poker or dice.

You can say that the brain or learning process or whatever is obeying mathematical laws, or has learned a mathematical fact, but that's not the same thing as doing math or thinking mathematically.