Play to draw?

As I was watching Star Trek: the Next Generation today, an interesting point came up. How do you win against something better than you? How do you turn the "playing to win" attitude against its user? The answer may surprise you, unless of course you actually read the title.
In this episode, Data (an android, for those who may not be familiar with the series) quickly loses a game against Sirna Kolrami, a character with a reputation for being a great strategist. Data, being one supposedly of no emotion and purely analysis, felt that he made no mistakes whatsoever during the game. As result, he starts making a thorough diagnostic of his systems. His premise: he lost, therefore mistakes were made that his system could not detect. Obviously to me (partially because I had seen the episode before), his program did not incorporate game theory.
Most of the above movie is irrelevant to my point, so you can freely move on to 6:39. Data has a rematch with Sirna, and comes with a different strategy. This time, he does not play with the objective of winning, nor to have fun (a concept he does not recognize). This time, he plays purely to create a stalemate. He passes up obvious advantages solely so that he can keep up the stalemate. Obviously, Sirna gets upset and leaves the game.
There is a huge point the show missed here. Data does not wear down, at least not to the degree that organic humanoids do. Multiple times, the scene shows Sirna becoming agitated while Data is calmly performing. There would naturally become a point when Sirna would become too fatigued to put up a reasonable resistance, at which point Data simply claims the victory. Although strictly theory, there is little way anyone could conclude anything other than Data's eventual victory if Sirna continued to play indefinitely. Data would keep up the "play to draw" objective for a long time sure, but there would be a clear point when Data notices that Sirna is no longer able to compete. In effect, this would be a "war of attrition," a concept based on the idea that one side will merely work for small material advantages until there's nothing left to oppose them. Of course, the loss would be in fatigue rather than anything material, but it creates the ultimate turtle defense. Even if Data did continue to just maintain a draw at all times, this concept would become clear to him at some point after the game.
At this point in writing my entry, I basically said the same thing in many different ways. The key thing to keep in mind here is that Data played for an entirely different goal than his opponent anticipated. I illustrated this principle in an earlier post about Chaos in the Old World, in which I managed to gain a win through means completely alien to my character. I think the bigger point here though, is patience. It's one thing to go for the apparently obvious "winning strategy." It's another to simply grind the opponent's mental faculties to a halt.