Use techniques from computer game playing to search for Ramsey numbers, trying to increase the lower bounds. I suspect UCT (Monte Carlo tree search) from go 囲碁 might be useful, along with data mining for heuristics. If there exists a drawn coloring, two good players playing the game of Sim will find it (I'm not sure this is true).
We could also have human tournaments, but graphs tend to look like spaghetti. Maybe humans with computer assistance, like Advanced chess.
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