I've written a program that can play mini optimally by brute forcing the whole game tree. If anyone is interested I could set up a bot account that would play games if invited. And any human-parseable insights that I get out of it I would share. All I know so far is 2+O is a draw.
From random sampling of the game tree, I estimate the total number of mini games, after picking an opening pair, at 10^12 and the number of penta games between 10^47 and 10^55. Penta would need something more clever than myself armed with a computer crunching through the tree all the way to the end.