When devising the payouts for a gambling game, there are two things you have to balance: you want to make sure that players have enough chance to win that they want to keep playing, but you also want to make sure that they lose enough so that you make enough money for it to be worth your effort. In this game, players will roll two regular 6-sided dice. You will design the entire game and be using probability and expected value to decide how much to charge to play and how much to pay out for certain events.

Before we get to your game itself, we have a few items to attend to:

1. a. (3 points) Calculate the number of outcomes for rolling two 6-sided dice: 36

b. (2 points) Choose the amount that you want to charge to play the game once. Cost to roll: $2

Events

A. Roll 2 of a kind and win $10

B. Roll snake eyes and win $10 (on top of the other $10 for getting doubles, so $20 in total)

3. Explain if a single roll could win according to both winning events. If it could, give an example and explain how your game would payout

A single roll can win both events but rolling a snake eyes would double the prize from a normal double prize of $10 to getting $20 in total.

4. A. Compute the probability of rolling that event and compute the probability of winning by rolling that event. The probabilities of rolling the event and winning on that event could be different depending on how you chose to handle rolls that win on more than one event (from question 3). ________

Event 1

Roll the following event: (copy this from question 2)

Win this much:____

Probability of rolling this event: ______

Probability of winning on this event: ________ (This may be different depending on if one roll can win more than one event and how you chose to pay out in question 3):

Event 2

Roll the following event: (copy this from question 2)

Win this much:_____

Probability of rolling this event: ______

Probability of winning on this event: _____ (This may be different depending on if one roll can win more than one event and how you chose to pay out in question 3):

5. (5 points) Find the probability of losing the game. Be careful if a single roll can win more than one event! You are welcome to use the sample space above to help you visualize which rolls win/lose. ________

6. Expected value.

A. (15 points) Find the expected value of your game. You must show your expected value equation and work for credit for this question. Remember that the player paid to play. If I pay $10 to play and won $25, I am only up $15. If I pay $10 to play and won $2, then I really lost $8 on that roll. _______

B. (5 points) What does your expected value mean for the player? Should the player expect to win or lose money if they played for awhile? _____

C. (5 points) Compute the expected value of playing your game 100 times:______

7. A. (5 points) In order for the game owner to make money, the expected value should be negative for the players. In order for players to want to play, the expected value should be no more than 20% of the amount it costs to play the game. The goal for this game is for the player to lose 15-20% of the cost to play.

Calculate -15% of the cost to play your game: cost to play your game once (from 1b) x- 0.15=_______

Calculate -20% of the cost to play your game: cost to play your game once (from 1b) x- 0.20=________

The two above values should be negative.

8. If the expected value of your current game does not fall within this range (between these two negative numbers) at the moment, you will need to change your game! The easiest way is to adjust your payouts.

Adjust your game if needed:

A. Roll _________________________________________ and win ___________

B. Roll _________________________________________ and win ___________

(10 points) Show that the expected value now means that the player is expected to lose 15-20% of the cost to play. If your original game already had that, please write that here: _____

Is your Expected value now in the range of -15% to -20% of the cost to play? Circle one: Yes/Yes

(If it is not, go back and adjust your game until the expected value is in that range!)

9. (5 points) Compute the expected value of playing this new and improved game 100 times:______

10. (10 points) "Play" your game 100 times by completing the attached random roll sheet. How much did the player end up winning/losing after the 100 games? ______

11. (10 points) Does the total amount "won" or "lost" after the 100 games fit your expectations for your game based on the expected value of playing the game 100 times (question 7)? Explain why it does or does not and any possible reasons. _____

12. (5 points) Now that you have finished, what have you learned? How would you build a game like this if you were to start all over from the beginning? Is there a way that you would have made the game "Easier" for either you or the player? Would you have chosen different events that were easier to identify as winning events? ______