Nice work and some thoughs
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It assumes ganks in the middle of a battle weakens "pure melee" strategies somewhat. Although not in the same way as in twin duel.
With 3 teams, I believe "shooting the team with lowest energy" 2x1 strategy will dominate. One team is eliminated almost on luck, and the battle is decided between the remaining 2. It happens in most 3 player games.
There is a catch though, since the API doesn´t tell you which bots from the opponents belong to the same team. Which is not a problem in either meleerumble or teamrumble. But estimating it in team melee might be worth. This alone may change the game significantly... or not.
A bigger battlefield or 4 teams seems nice. I thought of 5 teams of 2 bots each to keep the 10 bots total from meleerumble/teamrumble, and 2 bots per team from twin duel. And see strategies from all 3 divisions clashing against each other.