Object Library > Applets > Craps Experiment

Craps Experiment

Description and Use

In the game of craps, the shooter rolls a pair of fair die. The rules are as follows:

  1. If the shooter rolls a sum of 7 or 11 on the first roll, she wins.
  2. If the shooter rolls a sum of 2, 3, or 12 on the first roll, she loses.
  3. If the shooter rolls a sum of 4, 5, 6, 8, 9, or 10, this number becomes the shooter's point. The shooter continues to roll the dice until the sum is either the point (in which case she wins) or 7 (in which case she loses).

Any of the following bets can be selected from the list box:

  1. Pass. This is the bet that the shooter will win, and pays 1:1.
  2. Don't Pass. This is the bet that the shooter will lose, except that an initial roll of 12 is excluded (that is, the shooter loses, but the don't pass bettor neither wins nor loses). The bet pays 1:1.
  3. Field. This. is a bet on a single throw. It pays 1:1 if 3, 4, 9, 10, or 11 is thrown, 2:1 if 2 or 12 is thrown, and loses otherwise.
  4. Craps. This is a bet that 2, 3, or 12 will come up on a single throw, and pays 7:1.
  5. Craps 2. This is a bet that 2 will come up on a single throw, and pays 30:1.
  6. Craps 3. This is a bet that 3 will come up on a single throw, and pays 15:1.
  7. Craps 12. This is a bet that 12 will come up on a single throw, and pays 30:1.
  8. Seven. This is a bet that 7 will come up on a single throw, and pays 4:1.
  9. Eleven. This is a bet that 11 will come up on a single throw, and pays 15:1.
  10. Big 6. This is a bet that 6 will be thrown before 7, and pays 1:1.
  11. Big 8. This is a bet that 8 will be thrown before 7, and pays 1:1.
  12. Hardway 4. This is a bet that (2, 2) will be thrown before 7 or any other 4, and pays 7:1.
  13. Hardway 6. This is a bet that (3, 3) will be thrown before 7 or any other 7, and pays 9:1.
  14. Hardway 8. This is a bet that (4, 4) will be thrown before 7 or any other 8, and pays 9:1.
  15. Hardway 10. This is a bet that (5, 5) will be thrown before 7 or any other 10, and pays 7:1.

On each update, the outcome (X, Y) of the first roll is shown graphically in the first panel and recorded numerically in the first table. In case additional rolls are required, the outcome of the last roll (U, V) is also shown in the first panel and recorded in the first table. Random variable W gives the net winnings for the chosen bet; this variable is recorded in the first table on each update. The density function and moments of W are shown in blue in the graph and are recorded in the second table. On each update, the empirical density and moments of W are shown in red in the graph and recorded in the second table. Finally, the number of rolls N is recorded in the first table on each update.

This experiment involves a familiar casino game with a myriad of bets, and is useful for illustrating the difference in expected value for different strategies. For a more detailed mathematical analysis, see

Instructions for Downloading and Installing

Click on the link below to download the Java archive file:

To add the applet to your web page, insert the following in the html file, at the point where you want the applet to appear:

<applet code="edu.uah.math.experiments.CrapsExperiment.class" archive="CrapsExperiment.jar" width="550" height="350"></applet>

The jar file and the html file must be in the same folder.

This width and height dimensions are simply suggestions and can be varied. Generally, components such as graphs and tables expand and contract proportionally, while components such as buttons, scrollbars, dice, and coins are fixed in size.

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Copyright

Copyright © 2001-2003 Kyle Siegrist, Dawn Duehring

This program is free software; you can redistribute it and/or modify it under the terms of the GNU General Public License as published by the Free Software Foundation; either version 2 of the License, or (at your option) any later version.

This program is distributed in the hope that it will be useful, but without any warranty; without even the implied warranty of merchantability or fitness for a particular purpose. See the GNU General Public License for more details.

Related Resources

If you are interested in the Java source code or the Java documentation and object model for this applet, please visit CrapsExperiment in the Object section of the Library.

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