The problem in Computer Go is the search of the best move that can be found. First, Since a computer prgram, or a player cannot consider every possible moves, they usually has a move selecting function which select a sub set of the all possible moves. The moves for consideration selected by a computer program, by a player, or by a pro player may not contain the true best move. In general, the move selected is not the true best move even by a pro player. Thus, on average a move selected has a probability associated with it. This probability tells how good the move selection is. Let's call it the move merit probability. It's higher for pro players and lower for lower rank players. The population distribution of moves with different merit probability is not uniform. The lower is the merit probability, the larger is the number of moves. The move selecting function has its own merit probability. Let's call it the function merit probability. The second reason the elected move may not be the true best move is that the evaluation function used by a computer program, a player, or a pro player is not perfect. Otherwise, the Go game is solved. Here, again, the evaluation function has a merit probability, a third one. let's call it the evaluation merit probability. Thus, one starts with an imperfect subset of moves and an imperfect evaluation function and feed them to a search algorithm (alpha-beta, for example). In general, the higher are the merit probabilities, the more effective is the search. Here one faces a question. How much search should be performed? In general, more search means better probability of findng the best move available in this scope. The merit probability function of the selected move is just the move merit probability. Thus, the move merit probablility is a function of three variables: the function merit probability, the evaluation merit probability, and the serach scope (or search time). Postulation: For a given function merit probability and a given evaluation merit probability the move merit probability function approaches a constant value for large enough search scope. That is beyond certain value of the search scope, the move merit probabability function won't improve anymore. Above discussion should be able to be formulated in a complete mathematical form. The exact mathematical form of the move merit probability function can be derived. It's possible that the MC-UCT method is based on this statistical nature of Go game. It's success is due to its suitability for such a statistical process. This last sentence may be wrong. Daniel Liu ________________________________________________________________________ AOL now offers free email to everyone. Find out more about what's free from AOL at AOL.com.
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