2. How to play
The player will receive two fair dice each
numbered 1 through 6 on each side of the dice.
After rolling both of the dice at the same time,
if the player rolls two sixes they will win $6, but
if they roll one six, they will win $3. If they roll
any other numbers, they will not gain any
money. The cost of the game is $2. Would you
play?
3. Theoretical Data
Number of 6s (n)
0
1
2
Money earned
-$2
$1
$4
Probability of n
.694
.278
.028
Expected Payout Value: 2(.694)+1(.278)+4(.028)=-.998
Standard Deviation: √[.694(-2--.998)²+.278(1-.998)²+.028(4--.998)²]=1.58
4. Experimental Data
Number of 6s (n)
0
1
2
Number of times rolled
32
17
1
Amount earned
-$2
$1
$4
Probability of n
.64
.34
.02
Expected Value: -2(.64)+1(.34)+4(.02)=-.86
Standard Deviation: √[.64(-2--.86)²+.34(1-.86)²+.02(4--.86)²]=1.57
6. Results
After we rolled both of the dice 50 times, we found our
simulation results to be very similar to our theoretical
results. We expected that there would be a house
advantage of $0.998 and after our simulation, we
observed that our house advantage was similar to this
but was off by $0.138. To improve this game, we could
add more trials to see if the simulation information gets
closer to the theoretical values.
