This document describes a simple gambling game where players pay $2.50 per spin of a paper clip on a wheel. The wheel has different colored sections that correspond to potential winnings from $0.25 to $20, or no money and being "out" if it lands on green. Theoretical calculations show the game favors the house with an expected profit of $0.14 per player. A simulation of 50 spins found an average loss of $0.56 for the house, though more simulations could bring results closer to the theoretical expectations.

2. DESCRIPTION OF GAME
The cost of our game is only $2.50!! Your winnings do not depend
on others. You only spin once, but you have the opportunity to win LOTS
of money. You can play multiple times but each spin costs $2.50. Good
luck!
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place the pencil on the center of the circle, inside of the paper clip.
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Then flick the paper clip so that it has a good rotation.
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If the paper clip lands on dark blue, the player receives $0.25
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if the paper clip lands on orange, the player receives $1.00.
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If the paper clip lands on red, the player receives $3.00.
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If the paper clip lands on purple, the player receives $5.
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If the paper clip lands on light blue, the player received $10.
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If the paper clip lands on the blue space labeled with $20, the player
receives $20.
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If the paper clip lands on green, you receive no money and “your out”
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If paper clip does is in between two sections, look closely to see which
section the clip is mostly in. (No re-spins)

3. THEORETICAL EXPECTATIONS
X=the amount of money won
X
$0
$0.25
$1
$3
$5
$10
$20
P(X)
13/50
11/50
9/50
7/50
5/50
4/50
1/50
σx= 3.62
μx= $2.36
Expected value= $2.50– 2.36 = $.14
The player should expect to lose $.14

4. SIMULATION RESULTS
X= amount of money won
X
$0
$.25
$1
$3
$5
$10
$20
P(X)
17/50
7/50
3/50
11/50
5/50
5/50
2/50
μx= $3.06
σx= $4.60
Expected Value= $2.50-$3.06= -$.56
The house lost $.56 cents

5. WHAT DO OUR RESULTS MEAN?
Theoretical
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Our results showed that on average the house will make .14 per player
Simulation
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In our simulation the house lost $.56 on average.
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This does not reflect future simulations
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With enough simulation we would expect our values to form a normal
distribution. Therefore, we would make profits closer to the theoretical
expectations.
Improvements
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If we could improve anything it might be the prices on the wheel. Maybe
we could increase them or decrease them to make it more appealing to
play