Math 4713—Project

Part Four—EC Majors

Should you use the weird dice?

What are weird dice?  Weird dice consist of one die that has the numbers 1, 2, 2, 3, 3, and 4 and a second die that has the numbers 1, 3, 4, 5, 6, and 8.

Game:  One player has a pair of standard dice and the other has a pair of weird dice.  Each player rolls his/her dice and sums the face values of the dice.  The player with the higher sum wins that round.  However, if a player rolls a pair of doubles, he/she automatically loses that round.  After playing 30 rounds, the player who has won the greatest number of rounds is the winner.

Question:  If you are playing this game, should you use the weird dice?  Or does it matter?

To address this question, you should begin by playing the game.  As you play, record whether the person who has the regular dice or the person who has the weird dice wins.  Include this data with your project.  While playing, make a note of how many times doubles were rolled by either player.

Once you have played the game, respond to the following:

• Based on having played the game, do you believe you should use the weird dice or the standard dice, or does it matter?  Explain your reasoning.
• Are the chances of rolling any particular total the same with either pair of dice?  Explain.  (Hint: To answer this question, you may find it helpful to represent the sample space for each set of dice and compare the outcomes.)
• Are the chances of rolling a double the same for either pair of dice?  Explain.  (Hint: You may find it helpful to look back at your sample space from the previous question.)
• What is the theoretical probability of rolling a double using the standard dice?  Using the weird dice?

Provide a thorough response with explanation and justification to the original question, “If you are playing this game, should you use the weird dice?  Or does it matter?”