I don't mean to sound anal or anything, but there's a scene in the first 3 minutes of this episode I want to talk about, Columbo-style. Alan and Charlie are in the living room talking when their mother calls and they do odd/even to figure out who will talk to her. Charlie loses, and just then someone is at the door so Alan goes to answer it. It's his ex-wife and their son Jake. Question: why doesn't Jake have a key of his own, since he's there all the time (he's the "half" in the title)? And don't give me that "he's too young" argument. He's old enough to have a key or simply walk in the door (doors are always unlocked on sitcoms anyway). It's probably a minor detail (probably?), but it just seemed like a sitcom set-up to get Alan out of the room so the Charlie/mom scene didn't go on too long and seem even less labored than it was (too late). I like this show though; it's actually funny when it doesn't go for the easy joke (and the laugh track seems to be in hyperdrive sometimes).  This ep had the brothers arguing about...well, everything, and it gets cruel. The insults really fly, and it's great the show doesn't get overly sentimental. Charlie to Alan, about his ex-wife's spending habits: "You're like an Alzheimer's victim in a whorehouse. Constantly surprised you're being screwed, and then you forget that you have to pay for it."