1. Risk it or Go home!
TEAM G

2. Description of Risk it or Go Home!
The cost to play this Risk it or Go Home! is $3. In
the game, the player will draw a random card from
a deck. If the card is a jack, the player will receive
$2. If it is a queen, $5. If it is a King, $10. If it is an
Ace, $15. The player will receive $0 for any other
cards. The player can play as much as he or she
wants to.

3. Theoretical Expected Value and Standard Deviation
Money Earne
d/Card
$2 (Jack)
$5 (Queen)
$10 (King)
$15 (Ace)
$0 (Other)
Probability
1/13
1/13
1/13
1/13
9/13


4. Expected Value and Standard Deviation of Simulation Data
Simulation Data:
Card
Frequency
Jack
4
Queen
5
King
4
Ace
3
Other
34
Money
Earned
$2 (Jack) $5
(Queen)
$10
(King)
$15 (Ace)
$0
(Other)
Probability
2/25
2/25
3/50
17/25
1/10

5. Explanation of Results
The theoretical expected value for the player was $2.46. This means that the
player would lose $0.54 each game since he or she paid $3 to play the game.
Since the player is losing $0.54 each game, there is a house advantage. The
expected value for the simulation of 50 trials was $2.36. This was fairly close
to the predicted expected value. In the simulation, the house ended up gaining
more money than predicted by the theoretical data.
The theoretical standard deviation was 4.6 while the simulation data standard
deviation was 4.3, so they were fairly close.
Based on the law of large numbers, the expected value and standard deviation
will get closer to the theoretical values as the number of trials increases.
To make the game more appealing, we could increase the amount of money
earned by jack, queen, king, and ace by a small amount. This means that the
house would win less money for each game, but it would make it seem as if the
game is in favor of the player. With this change, more people would play the
game, and the house could possibly end up earning more money.