Black and White Numbers

Team U

How to Play

The game is played with one black die and one white die. At the beginning of each game, the player guesses which color die will have the greater outcome (black or white). If their chosen die wins outright (no ties), they win $5, if not, they win nothing. However, if the color die that they chose rolls a 6 and wins, they win $10 more ($15 total). In the case of double 6’s, the player automatically wins $25 (disregard other prizes in this case). The fee to play this game is $5.

How much are you supposed to win?

Probability

20/36 10/36 5/36 1/36

Payout $0 $5 $15 $25

Theoretical

Mean Payout Standard Deviation

$4.17 (House wins $0.83) $6.18

Mean Payout= (20/36)($0)+(10/36)($5)+(5/36)($15)+(1/36)($25)= $4.17Standard Deviation= (20/36)($4.17-$0)∧2+(10/36)($4.17-$5)∧2+(5/36)($4.17-$15)∧2+(1/36)($4.17-$25)∧2= 38.19 -> square root of answer -> $6.18

Simulation Data

Number or Outcomes

27/50 16/50 6/50 1/50

Payout $0 $5 $15 $25

Mean Payout Standard Deviation$3.90 (-$1.10) $5.69

Simulation

Mean Payout= (27/50)($0)+(16/50)($5)+(6/50)($15)+(1/50)($25)= $3.90Standard Deviation= (27/50)($4.17-$0)∧2+(16/50)($4.17-$5)∧2+(6/50)($4.17-$15)∧2+(1/50)($4.17-$25)∧2= 32.36 -> square root of answer -> $5.69

In Conclusion…

The expected payout is theoretically $4.17 where the house made $0.83 per game on average with a standard deviation of $6.18. In the simulation, however, the average payout was $3.90 where the house made $1.10 per game on average with a standard deviation of $5.69. The established $5 game cost theoretically gave the house a 19.9% profit while the simulation yielded 28.2%. A possible improvement could be a larger number of trials in order to get more accurate results.