Comment by antonb2011

Well, viva human brain versions of Monte Carlo Search Tree algorithms. Your game was at least solvable deductively in practice. If you were talking about solving something like the game of Go, i.e. high branching factor and deep tree, then Monte Carlo algorithms would be your first guess instead of trying to do deductive reasoning. Upper Confidence bound on Trees (UCT) algorithm is a good one to read about and understand if you have a spare evening.