TEAM G

Risk it or Go home!

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.

Theoretical Expected Value and Standard Deviation

Expected value = μx = X1P1 + X2P2 + X3P3 + … X is the value and P is its probabil-ity Standard Deviation = σ^2 = P1(X1-μx)^2 + P2(X2- μx)^2 + … + Pn(Xn – μx)^2

Expected value = ($2)(1/13) + ($5)(1/13) + ($10)(1/13) + ($15)(1/13) + ($0)(9/13) = $2.46This means that the player is expected to win $2.46 each game. This means that the player will lose $0.54 for each game because he or she paid $3 to play the game.Standard Deviation

Money Earned/Card

$2 (Jack) $5 (Queen) $10 (King) $15 (Ace) $0 (Other)

Probability 1/13 1/13 1/13 1/13 9/13

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 (K-ing)

$15 (Ace)

$0 (Other)

Probabil-ity

2/25 1/10 2/25 3/50 17/25

Mean value = Standard Deviation =

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 advan-tage. 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 stan-dard deviation was 4.3, so they were fairly close. Based on the law of large numbers, the expected value and standard devia-tion will get closer to the theoretical values as the number of trials in-creases. 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.