In chess, attacking the centre and using major pieces to support minor pieces to support pawns are common tactics. In three-player chess the game is more complex. Should I be taking the centre, knowing I will be attacked from both sides, or should I try to flank opponents? If two players team up against one for a couple turns, how can I prevent my teammate from launching a surprise attack against me? There is little research into the mechanics of three-player chess and I find it very interesting.
Well, since an exchange between A and B is in the sole benefit of player C, your primary objective should be: avoid exchanges. How do you avoid exchanges in a normal chess game? Play an opening with a closed center (e.g. King's Indian, Ruy Lopez), or choose a modest setup (like the Hedgehog system). The less you're exposed, the better.