Fair expectimax

Look a few moves ahead, take the best column on your own turns, and average over every sampled disc the game might deal.

Scores visible board traits, adds them together, and plays the highest-valued column.

Lifetime objective

Judge a move by how much longer the game will still last, rather than by how many points it scores right now.

Oracle and curriculum research

Let a planner cheat (show it the hidden numbers and the discs still to come) then try to teach a player who cannot cheat.