Tyler Cowen has a good post on the forthcoming chess match between Gary Kasparov and computers. He concludes,

I know it is not as simple as Moore's Law, but hey, don't these machines improve their game more rapidly than the human players do?

In the case of Othello, this was clearly the case. Back in the late 1980's, computers running the Intel 286 chip and the best Othello programs were a joke. In 1993, I bought a 486, and the same program killed me. The programs have since gotten better.

In Othello, the humans had to adapt to the computers. Top Othello players spend a huge amount of time studying computer openings. It turns out that a lot of openings that humans think are unplayable are in fact decent openings if you know how to handle them.

Tyler Cowen's description of chess games in which the computer falls behind and then grinds out a win sounds familiar. But the same thing happens between two human players. In Othello, I was ahead in games against David Shaman or Brian Rose (two top U.S. players) much more often at move 30 than at the end. My estimate is that the best players make optimal moves about 75 percent of the time. If you make optimal moves only 65 percent of the time, you may get lucky for a while, but over the course of an entire game your chances of winning are slim.

In chess, I imagine that it's a similar story. The reason that you are more likely to be ahead of a superior player (computer or human) in the middle than at the end is that you have a better chance of playing over your head for a short stretch than over the long haul.