Question

For this project:

Create a game with at least 3 outcomes

Develop a probability table with the outcomes for X and the probability p(X)

Find the expected value and standard deviation

Determine if your game is fair

How could be changed to make it fair or favor the player or "house"?

Run the game 50 times and record each outcome

Compute the empirical probability and compare it against the theoretical probability in #2. Find the average outcome of the 50 trials, and compare against the expected value

Please help ! I am confused with this project.

Answer 1

You can create a game of rolling a die of six faces for example if the outcome is 6 player wins $5 and if the outcome is 4, 3 player wins $5 and otherwise loose $5.

The distribution of outcomes are,

Face value	X	P(X)
6	10	1/6
5,4	5	1/3
1,2,3	-5	1/2

The expected value and variance of X,

This game is fair because the probability of landing each face of die is equal. However the game can be biased or can be make in favour of player if the probability of landing 6, 5 and 4 increases.

Let the game is fair and played 50 times and the outcomes are listed in table below. The 50 random numbers for face value are generated in excel using the function =RANDBETWEEN(1,6)

Number	Face Value	Outcome($)
1	1	-5
2	6	10
3	5	5
4	1	-5
5	1	-5
6	3	-5
7	2	-5
8	6	10
9	6	10
10	5	5
11	3	-5
12	5	5
13	6	10
14	2	-5
15	6	10
16	3	-5
17	2	-5
18	1	-5
19	4	5
20	5	5
21	6	10
22	2	-5
23	1	-5
24	6	10
25	6	10
26	3	-5
27	2	-5
28	2	-5
29	2	-5
30	5	5
31	4	5
32	2	-5
33	2	-5
34	6	10
35	4	5
36	2	-5
37	2	-5
38	1	-5
39	3	-5
40	6	10
41	2	-5
42	2	-5
43	4	5
44	2	-5
45	4	5
46	3	-5
47	5	5
48	1	-5
49	4	5
50	6	10

The average value of outcome = $0.7 which is near to expected value of $0.8333