Billiard Combat Modeling and Simulation Based on Optimal Cue Placement Control and Strategic Planning

Abstract

The selection of a best sequential shots for a given start cue position is a major challenging task in a billiard game. A new algorithm is proposed as a strategy to apply maximum tolerance angle search sequentially. The strategy considers combinations among all pockets and target object balls during both the pre and post collision shots selection processes. A simulation program is developed to test the strategy in a competition scenario by players with different proficiencies. The level of proficiency of players in the competition is controlled by a threshold value as a criterion to evaluate capability to conduct consecutive shots and when to give out right of play. The winning score of each game (win rate) is used as a performance comparison index among different gaming situations and to verify the effectiveness of the algorithm. The initial results of several simulation games using our strategy show that higher proficiency player can out beat lower proficiency player easily. This is consistent with the gaming situation in the real world, showing the consistency of our simulation program. The simulation also verifies that the play order does decide the final competition outcomes, when the players' proficiencies are close to each other. This work is the first to investigate the effects of consecutive shots and order of play on the billiard gaming results. A low cost training system is proposed to verify the efficiency of the repositioning algorithm in real world settings. The system adapts an augmented reality technology to instruct users for reliable aiming assistance. It makes use of a vision system for cue ball, object ball locations and cue stick velocity tracking. In all, the simulation program can provide an initial proof of the effectiveness of the reposition algorithm in the competition situation. Experiments results of maximum tolerance angle all pocket search strategy using our training facility as tested by users with different skill levels all out performed the results without guidance for the set of users with the same proficiency.