Walter Montego: It depends on what you mean by "using a computer" and "advantage".

If you mean having the computer choose the moves then there's a perfect example in the top three of the backgammon rankings. That is, there's enough of an advantage that you'll get to the top of the rankings, beatable only by a very strong human player who plays the longest matches possible to take advantage of his cube skills relative to the much weaker playing pool.