I had a hard time trying to find the best-suited stackexchange site to ask this question. I'm still not sure whether this is the right place, so please guide me to the right one if you think this is off-topic.
In turned based games with perfect information without randomness and with end results among win, loss, and draw (such as go, chess, reversi, tic-tac-toe etc.), it is possible to search through the game tree by brute-force and conclude the result of a certain board position.
With a board position P, there are m_0 .. m_n possible moves for the current player, and m_0 appears to be the winning move. Let's say there are two players B and W in this game, and now it's B's turn. B plays m_0 and will win the game unless he makes mistakes in the responses to W's later moves. Let's assume that both player do not make mistakes at all. At this point W really has no reason to play the game further because whatever move she makes, she knows she will lose.
Still, I was wondering whether there exists a 'best losing move' for W. Is there such thing? If so, how can it be determined?
In many games, including Go as it is usually played, there is a score at the end of the game, so you can use that to compare losing moves. You might say a best losing move is one where the difference in score is as small as possible at the end of the game.
More generally, in a game where you lose when you can't make a move, the game will eventually be something like "a number of free moves for the winner", and the best losing moves could be said to be the ones that minimize that number. This is related to the concept of left and right stops in combinatorial game theory. Which are standard material in textbooks like "Lessons in Play: An Introduction to Combinatorial Game Theory", but are also featured in this tidy summary paper: http://www.math.uchicago.edu/~may/VIGRE/VIGRE2009/REUPapers/Ye.pdf