Some interesting things happen here, the queens almost always seem to go first in my games (perhaps because of their freedom of movement they tend to end up in dangerous territory quickly). Also lots of pawn promotions make the mid-end games a lot more fun, although as the promotion is also random I've ended up with unwinnable endgames (e.g. two knights). I don't play chess beyond knowing the rules, but this is a lot…
I guess the next thing to do is instead of random: if you can capture a piece of equal or higher value: do so. This is, of course, not a particularly good chess strategy, but would probably be less painful to watch.