AiS Challenge 2003 STI :: Craps Simulation

Real Problem: To determine, by experimental means, our chances of winning at the game of "craps".
- Area of Science: Mathematics/Probability
- Background: A player rolls two dice. Each die has six faces. These faces contain one, two, three, four, five, and six spots respectively. After the dice have come to rest, the sum of the spots on the two upward faces is calculated. If the sum is 7 or 11 on the first throw, the player wins. If the sum is 2, 3, or 12 on the first throw (called "craps"), the player loses (i.e. the "house" wins). If the sum is 4, 5, 6, 8, 9, or 10 on the first throw, that sum becomes the player's "point". To win, you must continue rolling the die until you "make your point" (i.e., roll your point value). The player loses by rolling a 7 before making the point.
  From "Java : how to program" / H.M. Deitel, P.J. Deitel -- 4th ed.
- Why is this a Computational Science Project? To experimentally obtain our probabilities, with a high degree of accuracy, we would have to play millions of games! This would take much too long in the real world, but only seconds in our "virtual" world.
Working Problem: We will not make any simplifications to our simulation. The working problem will be identical to the real problem.
Math Model: A pair of random numbers between 1 and 6 will be generated to simulate rolling the dice. Simple arithmetic, a sequence of logical comparisons, and possibly additional "rolls of the dice" will be needed to determine whether or not we win the game.
Computational Model: There are, of course, MANY ways to program this problem. It may benefit you, however, to incorporate the following programming constructs; conditional statements, for loops, and a while loop. A boolean variable may be useful as well.
Results/Conclusions: Verifying our results will be quite easy, as the exact probabilities are known from purely mathematical techniques.
- Question: How many games are needed to obtain an "acceptable" level of accuracy?