Aye, that's what I meant.

I ran another experiment with 30 trials, and I've come to the conclusion that I need to ramp up the difficulty. Out of 70 battles with this same methodology, I've won 56 of them; the chance of that happening if it doesn't matter which side I play is 1 in 16,369,000 -- patently ridiculous. The symmetry we find between one unit and another might be an artifact of my playing each side an equal number of times on Medium difficulty.