1. Probability and
Chance: A Ping Pong
Ball Game
Team EE

2. How to Play:
In this game, the player is given a bucket of twelve white ping
pong balls. Each ball has one number from 1-6 written on it. In
total, the numbers 1, 2, 3, 4, 5, and 6 each appear two times. After
paying the game fee of $4, the player reaches in and grabs two
ping pong balls. He is to set the first one down before picking out
the next. The absolute value of difference between the two
numbers is calculated and used. A difference of 5 earns the player
$15. A difference of 4 earns the player $10. A difference of 0, 1,
2, and/or 3 yields no monetary win.

3. Theoretical Results
Difference
0
1
2
3
4
5
Winnings
-$4
-$4
-$4
-$4
$6
$11
Probability
1/6
5/18
2/9
1/6
1/9
1/18
• Theoretical Expected Value (Mean):
(1/6)(-4)+(5/18)(-4)+(2/9)(-4)+(1/6)(-4)+ (1/9)(6)+(1/18)(11)
= -2.06
• Theoretical Standard Deviation:
√[(1/6)(-4-(-2.06))²+(5/18)(-4-(-2.06))²+(2/9)(-4-(-2.06))²+(1/6)(4-(-2.06))²+ (1/9)(6-(-2.06))² + (1/18)(11-(-2.06))²]
= 4.45

4. http://youtu.be/ftmCz7OlaEw
Experimental Results
Difference
0
1
2
3
4
5
Winnings
-$4
-$4
-$4
-$4
$6
$11
Probability
1/25
7/50
2/25
2/25
11/50 11/25
• Experimental Expected Value (Mean):
(1/25)(-4)+(11/50)(-4)+(11/25)(-4)+(7/50)(-4)+
(2/25)(6)+(2/25)(11)
= -2.00
• Experimental Standard Deviation:
√[(1/25)(-4-(-2))²+(11/50)(-4-(-2))²+(11/25)(-4-(-2))²+(7/50)(-4(-2))²+ (2/25)(6-(-2))² + (2/25)(11-(-2))²]
= 4.69

5. Conclusion
By comparing my theoretical and experimental results, I can see
that my actual results were pretty close to the theoretical results. From
the theoretical data, I expected a mean or house advantage of about
$2.06 on average per game. After my 50-trial simulation, I observed
that the house advantage was extremely similar at about $2.00 on
average per game, which is only a 6 cent difference. Both theoretical
and experimental standard deviation values were also close to each
other; there was only a difference of 0.24 (4.69-4.45) with my actual
standard deviation being the larger one. This shows that the overall
values’ range I got did not deviate that far away from the expected
results’ range. A way I could improve upon this game is by increasing
the number of ping pong balls used. Rather than twelve, which is the
bare minimum required for the game to work, I could use, for example,
60 or even 120 ping pong balls. Also, I could increase the amount of
trials to improve my closeness to my expected values.