Exploring the concepts of European Roulette Wheel. Pascal code for generation of Random number.

1. Exploring Game of
Roulette
By: Aditya Chimbalkar
Under the guidance of Prof. Lucas Vespa
Graduate Research Seminar
CSC 540
December 1st 2016

2. About Roulette
• What is Roulette?
• General Overview
• Objective

3. Algorithm and Code Implementation
Group A
• Identifying Data types
• Use of Functions and Procedures
Group B
• Breakdown of various challenges
• Actual coding
Group C
• Comparing Results

4. Implementation
• Calculating average frequency of occurrence of a number.
– Occurred Twice and Thrice
• Frequency of occurring twice in a row
• Longest run of Evens and Odds in row.

5. Challenges faced
• Pascal Language
• Size of the Array
• No Object Oriented support
• Similar to C language
• Good for small programs

6. Average frequency of occurrences of a
number
0
200
400
600
800
1000
1200
1400
1600
n=100 n=1000 n=10,000 n=100,000 n=1,000,000 n=10,000,000
20 40.63 35.79 38.34 37.18 37.0152
676
805.27
1262.3
1426.53
1362.09
Average Frequnecy of occurrences of a number - Twice in a row Average Frequnecy of occurrences of a number - Thrice in a row

7. Frequency of number generated twice
in a row.
0
1000000
2000000
3000000
4000000
5000000
6000000
7000000
8000000
9000000
10000000
n=100 n=1000 n=10,000 n=100,000 n=1,000,000 n=10,000,000 n=100,000,000
2 119 8762 98310
998873
9989916 9992605
Frequnecy of number generated - Twice in a row
Frequnecy of number generated - Twice in a row

8. Longest number of Evens and Odds in
a row
0
0.5
1
1.5
2
2.5
3
3.5
4
n=100 n=1000 n=10,000 n=1,00,000 n=10,00,000 n=10,000,000 n=100,000,000
2
3
2
3
1 1 1
3
1
2 2 2 2
4
Longest number of evens in a row Longest number of odds in a row

9. Table of Comparison.
Number of Spins
(n)
Average
frequency of
occurrences
of a number
twice in a row
Average
frequency of
occurrences of a
number thrice in
a row
Frequency of
number
generated twice
in a row
Longest
number of
Evens in a row
Longest
number of
Odds in a row
Execution
Time
(seconds)
100 20 52 2 2 3 0.1
1000 40.63 676.00 119 3 1 0.1
10000 35.79 805.27 8762 2 2 0.1
100000 38.34 1262.30 98310 3 2 0.1
1000000 37.18 1426.53 998873 1 2 0.3
10000000 37.03 1345.44 9989916 1 2 0.7
100000000 37.01 1362.09 99926605 1 4 5

10. Conclusion
• Data Types in Pascal
• Size of an Array
• Input Value increase execution time
• Repetitive occurrences can be predicted

11. Future Work
• Implementation of different data-structures
• Solving problem of size of an Array
• Implement in Turbo Pascal
Thank you!