Split screen players put on opposite teams

This one has been driving the lady and I nuts. We play together, split screen. Playing on the same TV, it’s often assumed we’re going to be playing on the same team. This is not the case, but I’ve narrowed it down to a pattern:

Upon first loading any given playlist, we’ll typically (high percentage) be put on the same team once the game starts. Once we play a game, if we stay in the lobby then it’s about a 50/50 chance that we’ll be on opposite teams for any subsequent games.

It does NOT happen for Halo 3 very often, but has. It happens quite a bit on Halo 1, and again about 50/50 on Halo 2.

Same. It will happen for splitscreen online and others online, it disregards party entirely.

I wish there was actually an option for this when playing split screen.