I've realized something—something that I should have realized earlier than now, for sure, given my love of gaming. But here it is.
All other things equal, the most fun people to play games with are those who are precisely as intent on winning as you. You don't want someone who cares less about winning than you do, because they'll screw things up. You don't want someone who cares more about winning, because they'll kick your ass and not be willing to engage in useless side conversations. For a tiebreaker, play games with people who are as skilled as you.
Now, of course, it won't be fun to play with someone who's just a jerk, for example. But that falls under the "all other things equal" restriction.