What does the M counter in Solo Mode mean?
Solution 1:
I believe it counts collected minigames on the board, factoring in how many Minigames you've collected over your entire career. So if you win a game you haven't collected, the M counter gets incremented and the game can be stolen by Bowser, and so forth.
Consider the following gameplay footage in which this video plays with most of the games earned prior to starting a new solo game:
Versus this footage where the boards starts with no games earned: