Craps Simulation

Write a program to simulate the game of craps. The rules are as follows:

Roll a pair of dice. If the sum of the spots is 7 or 11, you win immediately. If the sum of the spots is two (snake-eyes), three (craps) or 12 (boxcars), you lose immediately. Otherwise, the number you rolled is called your “point”. You keep rolling until you get either (1) your point, in which case you win, or (2) a seven, in which case you lose.

Run the program 3 times simulating 100, 1000 and 10000 games of craps and calculate the following statistics for each case:

1. The probability of winning on the first roll

2. The probability of losing on the first roll

3. The probability of winning a game (first or subsequent rolls)

4. The probability of losing a game (first or subsequent rolls)

Print all probabilities to the nearest thousandth (3 places to the right of the decimal). Print the actual mathematical probabilities (given below), the calculated or simulated probabilities and the percentage difference between them. In general, the more games included in the simulation, the closer the simulated probabilities will be to the actual probabilities which means the percentage differences will be less. However, this pattern will not be true in every case. If the percentage difference is too small, it may show as all zeros since you are printing only 3 decimal places.

The percentage difference should be calculated by taking the absolute value of the difference of the Actual and Simulated probabilities divided by the Actual and multiplied by 100.0.

Percent Difference = ( abs ( Actual - Simulated) / Actual ) * 100.0

Use the random number functions named srand ( ) and rand ( ) which are available in C++. At the beginning of your program, you must input a seed value which is used to initialize the random number generator. The seed value should be an odd number of your choice, usually at least 5 digits long:

srand ( Seed ) ; // Seed should be an odd integer value

To generate a dice value of one through six, use the rand ( ) function which generates a positive random integer in the valid integer range for the local machine. To map the value onto a one to six range, use the modulus operator to divide by 6 (which returns a remainder of zero to five) and add one:

Dice1 = rand ( ) % 6 + 1 ;

Calculate Dice2 in the same manner and the sum yields your total for a roll of a pair of dice.

The report format should be:

Craps Simulation

Number of games in simulation: xxxxx

Actual Simulated % Difference

Win on first roll .223 .xxx xxx.xxx

Lose on first roll .112 .xxx xxx.xxx

Total Win .497 .xxx xxx.xxx

Total Lose .503 .xxx xxx.xxx

All numeric values should be right justified with the decimal point aligned.