Game nn
- 1. The Real Die is Cast By: John O’Malley & Jeff Panara
- 2. Instructions • The entry fee to the game is $6. Start the game by rolling the first die. If the number face-up is an odd number (1,3,5) then you’re out. If the number is even, then you have the chance to roll the second die. After you roll the second die, you will flip a coin. The coin flip will decide whether you get to keep the difference of the two dice or the sum of the two dice. If you roll double 6s and get heads-up on the coin, you win $20.
- 3. Expected Value/Standard Deviation (Theoretical) • Theoretical Expected Winnings : $2.49 • Theoretical Standard Deviation : $3.37 • Experimental Expected Winnings : $ 2.56 • Experimental Standard Deviation : $3.14
- 5. Results • The experimental winnings of the game were very close to the theoretical winnings. The predicted mean value was $2.49 and we experimentally had a mean of $2.56. We came up with the $6.00 fee based on the sum of the predicted winnings and predicted standard deviation. The experimental standard deviation of $3.14 from a mean of $2.56 proves that $6.00 is an adequate entry fee. • The game could be improved by adding more opportunites for greater amounts of winnings per game. However, by adding these opportunities we would need to either raise the price of the game or raise the probability of winning $0.00.