On a quiet Wednesday evening at home I tossed two dice 216 times. I added the die face values and tabulated my results. The smallest sum of two was the result of "snake eyes," a pair of ones. The largest sum of twelve was the result of "box cars," a pair of sixes. In the game of Craps gamblers bet based on a complex series of rules. The results for the first roll are shown in the second to last column, a term for that roll is in the last column. What happens for subsequent rolls after a first roll of 4, 5, 6, 8, 9, and 10 is more complicated.

Roll (Bins x) | Frequency f | RF p(x) | x*p(x) | Result | Term |
---|---|---|---|---|---|

2 | 6 | __________ | __________ | Lose | Craps, snake eyes |

3 | 12 | __________ | __________ | Lose | Craps, ace deuce |

4 | 16 | __________ | __________ | Point | Little Joe (2-2), ace-trey (1-3) |

5 | 25 | __________ | __________ | Point | Thirty-two juice roll |

6 | 33 | __________ | __________ | Point | Big Red |

7 | 32 | __________ | __________ | Win | Seven's a bruiser, the front line is a loser¹ |

8 | 34 | __________ | __________ | Point | A square pair (4-4) |

9 | 22 | __________ | __________ | Point | Ocean liner niner |

10 | 19 | __________ | __________ | Point | Puppy paws (5-5) |

11 | 12 | __________ | __________ | Win | Yo leven |

12 | 5 | __________ | __________ | Lose | Craps, box cars |

Sums: | __________ | __________ | __________ |

- Fill in the table above. Calculate the sums row and relative frequency column.
- _______________ What is the sample size (the total number of tosses)?
- _______________ Based on my data, what is the probability of rolling an 8?
- _______________ Use the x*P(x) column to calculate the mean roll. This is also sometimes refered to as the "expected outcome."
- Toughie: _______________ What are the odds of rolling "craps" (losing) on the first roll?

¹ After the first roll, a roll of a seven is a losing roll.

Sources:

http://faculty.weber.edu/brague/CS1220/Assignments/CrapsAsgnt2Sp05.htm

http://web.stat.ucla.edu/~vlew/stat11/lectures/sp041111.pdf