I was white in this game with "John's Connect Four Playground," a "perfect playing connect-4 program" Its "12Kbyte database of all 8 ply positions" did not stop it from making a losing mistake on its second move.

1) d1 - a1
2) f1 - b1??
3) e1 - g1
4) c1*

No human expert would let me win in four moves, regardless of who started. What constitutes perfect play as black is subjective, of course, but that is exactly why humans are better at it.