Aiming strategy error analysis and verification of a billiard training system

Abstract

A low cost training system is proposed for regular billiard game tutoring. We describe the elements to construct an interactive computer system which helps train billiard players in enhancing their skills. Most research on computer billiard has focused on creating highly competitive billiard playing programs, based on various search algorithms. Game playing strategies are embedded into these programs to beat the toughest human players. None of them is designed to reveal these information and help increase the public players’ skills. This lack of interactivity foundations makes most billiard playing programs inadequate as billiard tutors too. Our computer system is designed to combine with a visual guide interface to instruct users for a reliable strike. The system makes use of a vision system for cue ball, object ball locations and cue stick tracking. A least square error calibration process correlates the real world and the virtual world pool ball coordinates for a precise guidance line calculation. Users are able to adjust the cue stick on the pool table according to the visual guidance line instruction displayed on a PC monitor. Analysis found that a tolerance angle around the ideal visual line for the object ball to slide into a pocket decide the difficulties of a strike. This value further depends on the distance from pocket to the object, the distance from object to the cue ball, and the angle between these two vectors. Simulation results of tolerance angles as function of the angle variation between cue, object ball and pocket and distance variation between pocket and object ball are conducted. Players with different proficiency level were selected for the experiment. The result indicates that all players benefit from our proposed visual guide system in enhancing their skills. All exhibit enhanced hit-in rate both in maximum values and average values, while the low skill player shows the maximum enhancement in skill with the help of our system. The maximum hit in rate increases about 20.45% while average hit in rate increases about 38.76%. The experiment result as evaluated in hit-in rate has shown a consistent pattern with that of the analysis. The hit-in rate is thus tightly connected with the analyzed tolerance angles to sink object balls into a target pocket. These prove the efficiency of our system, and the analysis results can be used for an efficient game playing strategy.