Messy Solutions For Messy Problems

We spend|and waste|too much time discussing the pros and cons of diierent programming paradigms and too little time discussing the problems we want to solve. The rst section of this note introduces a problem; the remaining sections discuss approaches to solving it. 1 A problem The problem is to design a computer program that plays good snooker. (You can substitute \pool" or \billiards" for snooker if you prefer. For the discussion, we need a game in which balls roll on a horizontal surface bounded by rubber cushions and, perhaps, pockets. Players take turns to strike a particular ball|the \cue ball"|with a cue.) To simulate the game, we can set up diierential equations for sliding, rolling, and colliding spheres, and solve the equations numerically. This isn't interesting, although it is a nice exercise in elementary physics. To simulate a player, we could use the simulation code to predict the eeect of various shots. This isn't interesting either, because it's not how people play. Our goal is a program that provides a plausible model of how people play snooker. To see why this might be an interesting problem, we contrast our hypothetical program that plays snooker with existing programs that play chess or other combinatorial games. A snooker player has to know both what shot to play and how to play it (Chomsky's \competence/performance" dichotomy). Since even the best players sometimes miss shots, strategy and skill are interwoven. This distinguishes snooker from chess, in which even beginners can get their pawn to K4. Snooker is chaotic in the sense that a small change in a shot leads quickly to a completely diierent game. Even in a deterministic snooker simulation, tiny random variations in the opening shot lead to an apparently innnite variety of diierent games. The chess programming approach, in which deep search compensates for the limitations of the position evaluator, does not work for snooker. There are situations in which the result of a shot is necessarily uncertain. The outcome of a shot that involves more than two or three balls, for example, is essentially unpredictable. Chess provides no correspondence to uncertainty of this kind. Generalizing, we are interested in situations in which there are many possible actions and the result of any particular action is uncertain.