Modeling a dice game provides a nice simulation. Nearly everyone is familiar with the game and it is easily described. The models can be very simplistic or extremely complex, as can be the simulation approach.

This game is based on the dice game called "Craps". In a real game, betting may be involved. We, of course, will not gamble but will talk about betting in the context of the model. (If this model is offensive to you for religious or other reasons, please contact the instructor so the game can be modified.) While there are limitless types and combinations of bets that can be placed on a standard dice table, we will restrict ourselves to the most basic bet, the "pass line" bet. Here is the way the "pass line" works:

1. A player puts money on the "pass line" and rolls a pair of 6-sided dice; this is called the "come out" roll.

2. If, on this first roll, the upper faces on the dice total 7 or 11, that turn is over and the player wins an amount equal to the amount bet.

3. If the total is 2, 3, or 12, the player is said to have "crapped out", the "house" takes the amount bet on the "pass line", and the turn is over.

4. If any other number, 4,5,6,8,9, or 10 is rolled on the first roll, that become the players "point". The player continues to roll until he/she matches that number, i.e. "make his point", in which case he/she wins an amount equal to the amount bet, and ends that turn. If, however, the player rolls a 7 before making his/her point, the players loses the amount bet, and the turn ends. For the "pass line" bet, nothing happens if any number except the "point" or 7 is rolled; the player simply rolls again.

Mathematical Analysis - It is not too difficult to determine that the probability of winning a pass line bet is 0.4929293. This gives the house a 1.41% advantage.

Model - In this model you will

You may progress from a basic "brute force" model (using only Excel formulas and functions) to one limited only by your ability, time, and interest.