Two Dice Problem

Today in class we used Excel to solve the two dice problem.

Here are the parameters:

Each Player is given a Game Board consisting of 12 boxes numbered 1 to 12 as seen below.

2. Each Player is given 20 tiles to distribute among the boxes numbered 1 to 12.

3. Two die are rolled.  With each roll, each player can remove one tile that is in the numbered box that equals the sum of the die rolled.

4. How would you best distribute your tiles to be the first player with no tiles remaining on your game board?

With the help of my classmate Alexandra, I was able to decifier this spread sheet to determine the best distribution.

Note: Although Alexandra’s spreadsheet did help me ALOT, I was able to pair up with my partners to explain to them how to solve the problem.  And John and I discussed our plans for distribution and had some deep conversation.  There was a lot of collaboration in class today.

According to my calculations in FerrisTwoDice, my tiles would be laid out as follows:

1 – 0 tiles- there is no possible way to get a one

2 – 0 tiles – the probability of getting a total of 2 is 3% , I would not put any tiles here.

3 – 0 tiles – the probability of getting a total of 3 is 6% , I would not put any tiles here.

4- 1 tile – the probability of getting a total of 4 is 8% , I would take a small risk

5- 2 tiles – the probability of getting a total of 5 is 11% , I would take a little bigger of a risk

6- 4 tiles – the probability of getting a total of 6 is 14% , I would place more of my tiles in the 6,7,8 tiles.

7 – 6 tiles – the probability of getting a total of 7 is 17% , I would place more of my tiles in the 6,7,8 tiles.

8 – 4 tiles – the probability of getting a total of 8 is 14% , I would place more of my tiles in the 6,7,8 tiles.

9-  2 tiles – the probability of getting a total of 9 is 11% , I would take a smaller risk then the middle tiles.

10 – 1 tile – the probability of getting a total of 10 is 8% , I would take a small risk

11- 0 tiles – the probability of getting a total of 11 is 6% , I would not put any tiles here.

12 – 0 tiles – the probability of getting a total of 12 is 0% , I would not put any tiles here.

This would be an ok question for class to have students use probability to explain why they chose to place their tiles that way.  Having students play against each other to test their hypothesis would help them to understand better why or why not their choices were correct.

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