1. Fifteen
Team MM

2. How to Play
• The first step is easy. Pay the house $5 to play.
• Roll three die (the individual dice do not matter)
simultaneously and add up the three outcomes.
• If your rolls add up to a multiple of 5, excluding 15 (5, 10), you
win $2 that round.
• If your rolls add up to a multiple of 3, excluding 15 (3, 6, 9, 12,
18) you win $0.25 that round.
• If your rolls add up to exactly 15, you win $10 that round.
• Roll all three dice again for another round.

3. Theoretical Probabilities
• X is the sum of the three die.
• Expected Value: (.19)($0.25)+(.16)($2)+(.005)($10)-5
• Player loses $4.58 per round
• Standard Deviation
• SDx^2= (.645)(5-4.58)^2+(.19)(4.75-4.58)^2+(.16)(34.58)^2+(.005)(-5)^2
• SDx=$0.72

4. Stimulation Probabilities
• Link for the fifteen video https://www.youtube.com/watch?v=25Ux3GG1Ntw
• Roll outcomes: 13, 12, 8, 15, 9, 10, 14, 16, 8, 14, 13, 11, 11, 9,
12, 12, 7, 12, 13, 11, 13, 10, 11, 13, 7, 9, 15, 13, 8, 7, 10, 11, 9,
12, 10, 11, 6, 11, 9, 13, 12, 16, 11, 12, 5, 9, 7, 6, 17, 6
• Total money lost: (4.75)(16)+(3)(5)+(-5)(2)+(5)(27)= $216
• Mean money lost per round: 216/50= $4.32
• Standard Deviation: (.645)(5-4.32)^2+(.19)(4.75-4.32)^2…
• SDx=0.75

5. Results
• The theoretical mean of the money lost is similar to the
experimental mean. This means that enough trials were
carried out to be somewhat accurate. In order to be more
accurate, one could carry out more trials and, by the Law of
Large Numbers, the experimental mean will come closer and
closer to the theoretical mean. The standard deviations are
also similar and could be more accurate by carrying out more
trials as well. To improve this game, we could lower the ante
and raise the winnings so the player does not lose so much
money!