Let’s play snooker

1. Group 2 Yannick Thimister Frans van den Heuvel Enno Ruijters Esther Verhoef Ali B. Ozmen Achim Leydecker Let’s play snooker

2. Overview Task description - Yannick Physics and noise – Ali Simple method – Frans Complex method - Enno Product demonstration - Esther Experiments and results - Achim Conclusion - Yannick

3. Task description Design and implement an artificial intelligence for a Snooker simulation with a realistic physics model, including noise. Then determine the effects of this noise on the artificial intelligence.

4. Physics Spin & Cue Ball Impulse Noise Model

5. Spin and Cue ball

6. J = J = Impulse • Collisions between balls are handled by adding a certain amount of impulsive force to both balls in opposite directions. • The magnitude of this impulse is given by the equation ;

7. Impulse • When we used to calculate the change in velocity in the collision, previous equation can be simplified into this equation: • By assuming the two balls have the same mass, since the masses are factored out again when converting the change in momentum into the corresponding change in velocity.

8. Noise Model A set of standard deviations • Five parameters specified (4 Input parameter & Coefficient of friction ) • Error is modeled by perturbing these 5 parameters by zero – means Gaussian noise.

9. Simple method • Repeated random sampling • All directions / variation of force / No spin • Two versions • Iterate through the 50 best shots • Highest average amount of points • Easy implementation & good results 

10. Tactical method Extended version of Simple AI Multithreaded(4000 shots, 4 threads) Adds heuristics to shot evaluation Avoid complex shots Use tactics to improve future shots Naturally more resistant to noise

11. Tactical method(complexity avoidance) Minimize number of collisions Ignore irrelevant collisions Collisions between two moving balls strongly avoided Minimize distance traveled Again, ignore irrelevant paths

12. Tactical method (snooker tactic) Snooker if no potting possible Avoid snookering yourself Considers only direct snookers

13. Tactical method(easy ball tactic) Try to leave easy balls for later shots Avoid impossible shots later Problem: helping opponent?

14. Tactical method(shot evaluation) Initial score based on actual points gained Add points for snookering opponent Scale by penalty for every collision Exponential reduction Scale linearly by distance Add/subtract points for easy balls

15. Program demonstration

16. Experiments • Basic setup • 100 full games per experiment • No player change • Foul points are subtracted from the total points • Average and standard deviation are recorded

17. Experiments • Noise • All four types of noise are tested separately with five different degrees of intensity • Fixed maximum number of random samples

18. Experiments

19. Experiments • Number of random samples • Fixed noise level (2) • Effects of heuristics for tactical method • Fixed noise level (2) • Each tactic is tested separately • Collision-avoidance & distance-minimization only • Snookering is tested by playing against the simple method with 500 random samples

20. Results

21. Results

22. Conclusion Both methods decrease in performance when noise is added. The simple method performs better in general than the tactical method. In the tactical method, collision avoidance is less effective than distance minimization. Snookering is less effective than leaving easy balls.

23. Questions