1. Black and White Numbers
Team U

2. 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.

3. How much are you supposed to win?
Probability 20/36
10/36
5/36
1/36
Payout
$5
$15
$25
$0
Mean Payout= (20/36)($0)+(10/36)($5)+(5/36)($15)+(1/36)($25)= $4.17
Standard 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
Mean Payout
Standard Deviation
$4.17 (House wins $0.83)
$6.18

4. Simulation Data
Number or 27/50
Outcomes
16/50
6/50
1/50
Payout
$5
$15
$25
$0
Mean Payout= (27/50)($0)+(16/50)($5)+(6/50)($15)+(1/50)($25)= $3.90
Standard 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
Mean Payout
Standard Deviation
$3.90 (-$1.10)
$5.69

5. 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.