I ended up doing an experiment similar to this here. Though I realized even shallow thinking is an advantage when playing board games (no matter how good your heuristics, you still have to calculate a few moves ahead using those heuristics), so I looked at the difference in performance between simple vs. complex games to try to get at deep thinking.
All models were not equally terrible, but all models were more equally terrible on complex games than on simple games.
I ended up doing an experiment similar to this here. Though I realized even shallow thinking is an advantage when playing board games (no matter how good your heuristics, you still have to calculate a few moves ahead using those heuristics), so I looked at the difference in performance between simple vs. complex games to try to get at deep thinking.
All models were not equally terrible, but all models were more equally terrible on complex games than on simple games.