Craps–Construct and perform a Monte Carlo simulation of the popular casino game of craps. The rules are as follows: There are two basic bets in craps, pass and don't pass. In the pass bet, you wager that the shooter (the person throwing the dice) will win; in the don't pass bet, you wager that the shooter will lose. We will play by the rule that on an initial roll of 12 (``box cars''), both pass and don't pass bets are losers. Both are even-money bets. Conduct of the game:
Roll a 7 or 11 on the first roll: Shooter wins (pass bets win and don't pass bets lose). Roll a 12 on the first roll: Shooter loses (boxcars; pass and don't pass bets lose). Roll a 2 or 3 on the first roll: Shooter loses (pass bets lose, don't pass bets win). Roll 4, 5, 6, 8, 9, 10 on the first roll: This becomes the point. The object then becomes to roll the point again before rolling a 7.
The shooter continues to roll the dice until the point or a 7 appears. Pass bettors win if the shooter rolls the point again before rolling a 7. Don't pass bettors win if the shooter rolls a 7 before rolling the point again. Write an algorithm and code it in the computer language of your choice. Run the simulation to estimate the probability of winning a pass bet and the probability of winning a don't pass bet. Which is the better bet? As the number of trials increases, to what do the probabilities converge?