Computational Pool: A New Challenge for Game Theory Pragmatics

Abstract

C ue sports have been captivating humankind for thousands of years, with written references dating to the first century CE. They evolved as a branch of modern croquet and golf, as a kind of indoor table version, and much of the modern nomenclature can be traced back to that common root. Cue sports today are vastly popular, and comprise variations such as pool, billiards, carom, snooker, and many other local flavors. In a 2005 U.S. survey, pool ranked as the eighth most popular participation sport in that country, with more than 35 million people playing that year. Leagues and tournaments exist in nearly every country worldwide, with strong appeal to both experienced and casual players alike.A number of robotic cue-players have been developed over the years. The first such system was the Snooker Machine from University of Bristol, United Kingdom, in the late 1980s (Chang 1994). This system comprised an articulated manipulator inverted over a 1/4-sized snooker table. A single monochrome camera was used to analyze the ball positions, and custom control and strategy software was developed to plan and execute shots. The system was reported to perform moderately well, and could pot simple shots. Since then, there have been a number of other attempts at automating pool, including Alian et al. (2004) and Lin, Yang, and Yang (2004).Developing a complete robotic system that can be competitive against an accomplished human player is a significant challenge. The most recent, and likely most complete system to date, is Deep Green from Queen's University, Canada (Greenspan et al. 2008), shown in figure 1. This system uses an industrial gantry robot ceiling-mounted over a full-sized pool table. High-resolution FireWire cameras are mounted on both the ceiling to identify and localize the balls, and on the robotic wrist to correct for accumulated error and fine-tune the cue position prior to a shot. This system has been integrated with the physics simulator used in the computational pool tournaments and the strategy software developed to plan shots. Complex

The SP Theory of Intelligence: Benefits and Applications

“…Consider, for example, how top-ranking players learn to play games like pool, billiards, or snooker. This is quite different from how some existing robots play pool (see, for example, [22]), where the situation is simplified compared with what a human player faces, and where the robot is provided with a knowledge of geometry and associated mathematics.…”

Augmented reality system to assist inexperienced pool players

“…[2,4,22] work with video (or video streams) taken from pool or snooker championships, with very stable and controlled conditions (lighting, player positions, etc. ), or expect a controlled environment because of the use of robots [5][6][7].…”

“…Other research uses a robot capable of choosing and executing shots on a real table, although these robotic systems have been tested under laboratory conditions [5][6][7].…”

Phy-Q: A Testbed for Physical Reasoning

“…We consider PHYRE [16], Virtual Tools game [18], and OGRE [17], which are game based benchmarks, IntPhys [25], CLEVERER [1], CATER [28], and Physion [27] which are video based benchmarks, COPHY [26] which is an image based benchmark, CausalWorld [19] and RLBench [29] which are robotic benchmarks. The AI game competitions we consider are Computational Pool [30], Geometry Friends [31], and AIBIRDS [32]. Table 1 summarises the comparison.…”