They got stuck for me as well. It reminds me a bit of the card game War, which has a similar zero-sum (and zero-choice) competition for a single resource that can take an extremely long time to complete, but without an equivalent for the mechanic for how to handle when the players play the same card. Maybe some sort of RNG is needed to break out of those stalemates, unless there's some sort of metaphorical lesson intended (like War Games, which despite the naming doesn't have much to do with the card game, but it does feature Tic Tac Toe prominently).