Sorry for this rather late contribution. But I wanted to sort my thoughts before writing.
Brian Sheppard wrote: > Speaking of laziness, I have been intending to post a study > concerning capturing races, but I haven't gotten around to it. > So is it surprising that MC is lazy, given that MC programmers > are lazy? :-) That is completely common in human learning or human performance: we work much better when there are competitors of similar strength. Pupils in general do not learn well when they are severely "overtaxed" or "undertaxed", independently of the existence of competitors. > Ingo's Double Step Race is a simplified model of capturing race. > My model was more complex, and I solved it recursively rather > than via simulations. > ... > Please consider "race" here in a general sense: you must reach > your goal before the opponent reaches his goal, where the goals > are incompatible. Semeai is a special case. My group at Jena University is analysing different types of races (here described for the case of two players, with alternating moves): (1a) Each player has a lane with a target. Winner is the player who first reaches his target. (1b) Each player has a lane of infinite length. T rounds are played. Winner is the player who is ahead after the T rounds. (T is a fixed parameter, known to all players.) (2) Each player has a lane of infinite length. Infinitely many rounds are player. Winner is the player who first is k steps or more ahead of the opponent. (k is a fixed parameter, known to all players.) (1-mix-2): Each player has a lane of infinite length. There are two parameters k, T, known to all players. At most T rounds are played. The game is stopped when one player is ahead at least k steps at some moment (he is winner immediately). If this does not happen within the T rounds, the game is stopped after T rounds, and the player in the lead is winner. (1a) and (1b) both show the phenomenon of "classical laziness": Monte Carlo players play best when "in their eyes" the players are head to head. "in their eyes" depends on the heuristics they are using in their Monte Carlo runs. (2) is different. Here a player is most concentrated when he is either almost k steps ahead or almost k steps behind. Laziness occurs mainly when players are near to each other. In (1-mix-2) the form of laziness depends on the pair (k,T). When T is very large (much larger than k*k) players behave like in (2). When T is small compared to k*k, behavior is like in (1b). For intermediate values of T (like 0.25*k*k), the performance is described by a W-shape: strongest play, when either almost k steps behind or ahead or when very near to the opponent. In general, Monte Carlo procedures are better in type-(1) games than in type-(2) games. ****************************************************** Putting this in perspective to classical board games, it seems that games of territory (go, amazons) and connection games (hex, conhex. havannah, twixt) are related to races of type (1a) or (1b). (A game ends when the board is full. Go is a bit atypical because sometimes occupied parts of the board may be cleared again.) On the other hand games like chess, shogi, 9-men-morris are like races of type (2). Having done the abstract experiments with Monte carlo races, it is no surprise for me that Monte Carlo (and UCT) are (very) weak in chess and similar games. > To this I would add that laziness is not just a problem in > handicap games. Agreed. > We need to elevate the discussion about laziness > beyond the question of how to win when given 7 stones. Agreed. But different people in this discussion (not only in this mailing list) have different horizons. For some it is important to have a topic made as concrete as possible. Therefore I threw up the (high)-handicap problem, which really is one in Monte Carlo go. ******************************************************* By the way, Don Dailey wrote that he would prefer heuristics with artificial (random) passes to the approach of dynamic komi. I agree with him that "random passing" is a more general tool because it is applicable not only to games of territory but also to connection games (where MC bots exist for instance for hex, conhex, havannah). Ingo. -- GRATIS für alle GMX-Mitglieder: Die maxdome Movie-FLAT! Jetzt freischalten unter http://portal.gmx.net/de/go/maxdome01 _______________________________________________ computer-go mailing list computer-go@computer-go.org http://www.computer-go.org/mailman/listinfo/computer-go/
