Just a note on chess programs: Until very recently (months) the best chess programs consisted of both neural network based ones, and search based ones similar to deep blue. They would go back and forth for supremacy, and both are way better than any human.

Recently, one of the top search based engines (stockfish) added neural networks on top of it, and it got significantly better still. This was a couple months back, maybe the pure neural nets have caught up again!