Team X analyzed the game "Dirty D's", a dice game where the player rolls two dice and can win $10 for rolling a 2 or 12, $5 for rolling a 3, 4, 10 or 11, and loses their $3 bet on other rolls. The expected value of the game is $1.94 in profit for the house and -$1.06 expected loss for the player. Experimental results from 50 trials matched the theoretical probabilities closely. Improvements could include adjusting the payout amounts to better match the probabilities of each roll and lowering the $3 bet amount since the expected profit is almost $1 for the house.

1. Team X

2. Dirty D’s

3. Rules
• Start with 2 six-sided dice, numbered 1-6.
Subject pays $3 to play the game. Have
subject roll both dice simultaneously and add
results to obtain the total. If the sum totals to
either 2 or 12, $10 is rewarded to the subject.
If the sum totals to 3, 4, 10 or 11, the subject
is rewarded $5. All other sums are not
rewarded. This game is played on a “dirty”
Craps table

4. Expected Value/Standard Deviation
• Expected Value: $1.94
• Expected Profit (for subject): -$1.06
• Expected Profit (for us): +$1.06
• Variance: $8.72
• Standard Deviation: $2.95

5. Game Results
• Theoretical • Experimental (50 trials)
– P(X=2,12)=.056 – P(X=2,12)=.10
– P(X=3,4,10,11)=.167 – P(X=3,4,10,11)=.167
– P(X≠2,3,4,10,11,12)=.777 – P(X≠2,3,4,10,11,12)=.777
The Experimental results are close if not the same as the theoretical
probabilities which means our experiment exemplifies what we would expect
as results. Improvements we could seek is a different wage scale that would
be a better representation of the probabilities. The player earns $5 for rolling
a sum of 3,4,10, or 11 when we should have different totals for the
outcomes since 3 and 11 have the same probability and 4 and 10 have the
same probability. If we improved upon this our game will have better
justified wage values which in essence will improve our game as a whole.
We could also possibly change the amount necessary to play because the
expected profit is almost a $1 which is probably too much for someone to
want to take a chance and pay.