Spin-OH-rama is a simple game that costs $3 to play and involves choosing a color and body part combination. Players can win $5 for correctly guessing the color or body part, or $15 for getting both correct. Based on 50 simulations of the game, the average payout was $2.40 per game, with a standard deviation of $2.523. Theoretical odds and payoff calculations predict an average payout of $2.81 per game with a standard deviation of $3.94. The simulation results had more variability than the theoretical predictions.

1. Spin-OH-rama
Team B

2. How To Play
Spin-OH-rama is a game for all ages! It’s a simple game of chances
including 4 colors and 4 body parts. Before you make any predictions, it is
a 3 dollar fee to play the game. The participant chooses between red,
green, yellow and blue combined with right hand, left hand, right foot, and
left foot.. The payout for only choosing a correct color or number is five
dollars. If you get both correct, you get 15 dollars. If you get none correct,
you get zero dollars.

3. Simulation Data
Tria
ls
1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
19
20
21
22
23
Payout
0
5
0
0
5
0
0
0
0
5
5
5
0
0
0
0
5
5
5
0
0
5
0
0
5
Trials
26
27
28
29
30
31
32
33
34
35
36
37
38
39
40
41
42
43
44
45
46
47
48
49
50
Payout
0
5
5
5
0
5
0
5
0
5
5
5
0
0
5
5
5
0
0
5
5
0
0
5
0
Mean
The total profit made was 120.
120/50=2.4
μx=$2.4
Standard Deviation
Standard Deviation was found using a Ti-83 Plus.
σx=2.523

4. Theoretical Data
Odds:
Getting both a color and body part
wrong
-56.25%
Getting a color right and a body part
wrong
-18.75%
Getting a color wrong and a body
part right
-18.75%
Getting a color and body part right
-6.25%
Mean:
0(9/16)+5(6/16)+15(1/16)
0+1.875+.9375=2.8125
μx= 2.81
Standard Deviation:
9/16(0-2.81)²+6/16(5-2.81)²+1/16(15-2.81)²
4.442+1.799+9.287=15.528
σ²x=15.528
σx= 3.94

5. Conclusion
Differences Between Means and Standard Deviation
In our theoretical data, the average payout is $2.81 and the game cost $3.50
so we make a 69 cent profit on every game. In our actual fifty simulations,
the average payout was $2.40, so we made $1.10 on every game. That means
that we made $55 in 50 simulations. The standard deviation in our
theoretical data was $2.52. The standard deviation throughout our 50
simulations was $3.94. This means that our simulated data was, on average,
$1.24 further away from the mean than the theoretical data said it should
be. This means that the simulated data had more variability than what it
was supposed to have.