Honors Integrated Math II Third Quarter Project ClaireMarie Clark ('00) and Honey Quirit ('00)

Craps

Craps is a very simple game relying heavily on luck and probability. In this game you are given two dice to throw. The objective of the game is to get a sum of seven or eleven. Only if you get either of these sums do you win.

Probabilities:

Theoretical Probability:

There are 36 different possibilities and out of these 8 are favorable for the player. The rest are favorable for the casino. The favorable outcomes are highlighted in the chart below.

calculations: 8/36 = 2/9 = 22%

Theoretically there is 2/9 chance, about 22% chance of winning the game. This experiment is independent. If you roll the dice a second time you still have the same probability of winning.

e.g. 2/9 2/9 = 4/81 which is about 5%

Experimental Probability: To find the experimental probability of this game we used a simulation. Since we didn’t have dice we used a spinner divided into six equal parts so it would have the same probability for each number as would a die. Next we span the spinner twice for each try and added both numbers. We did this twenty times. Results: As you can see from the charts and calculations the theoretical and experimental probability are very close. The experimental probability is 20% and the theoretical probability is 22%. So we can see how the casino would be winning all the time and therefore they would get all the money and the state profits allot from this. As you can see you loose for often than you win. In fact theoretically you should lose 7/9 of the time, about 77.8% since winning and not winning are complementary.

In a casino when playing when playing these games you bet money on whether or not you will win. If you win you get to keep your money and get some of the casinos money too, but if you lose then the casino keeps its money and it gets some of yours as well. With people loosing 7/9 of the time the casino would make allot of money.

When someone who gambles wins money he usually feels lucky and continues playing. Of course winning two times in a row is a lot less likely( 2/9 * 2/9 = 4/81 = 5% ) and the casino will most likely gain more money.

Following are some examples of players playing CRAPS in a casino. In this example they stop playing if they don’t win within two throws. However if they win they keep on playing.

Conclusion:

In this report we have proved that in the game CRAPS the casino always has a chance of gaining more money than the people playing against it. Both the theoretical and the experimental probabilities calculated in here prove this. In this small example of four players the casino gained a total of four dollars of the players’ money. This in turn helps the state because the casino pays big amounts of taxes to the state and the more money it wins the more money the state wins. This is why in some areas gambling is legalized. By doing this project we have learnt that there are many useful ways to use the calculation of probabilities to our own advantage. Calculating the probability of winning a game is only one of the few things it is useful for.