After 1000's of tries, and only once before in my life, I have played a perfect game of hearts on Windows. The odds are obviously stacked against you when the computer is playing three of the four players. However, playing a perfect game can happen. I believe this is the first time I've played a perfect game with more than 5 rounds. Notice that the first two I got all of the points, which happened before as well. The program is probably far from random.
Anyway, there it is. A perfect game. Now I can sleep.