Welcome to our Casino Game on the World Wide Web. The picture on the right shows the playing field of a slot machine featuring three concentric, independently rotating disks, each with 7 positions marked with the 6 standard dice values plus a special blank die which has the value 0. In practice, you would insert a dollar, click on a button that says Play and watch the disks spin. The disks come to rest with the dice lined up. Each triple of lined-up dice is added and the value of the sum in each position is displayed.  What makes this slot machine different and interesting is that you get to position the dice yourself before playing! Two ways to win:  You can win two dollars if at least one of these sums equals 7 and at least one of the sums equals 11.  You can win the fifty dollar SuperJackpot if all  seven  positions add up to 9.  What's required: The only requirement is that you must use all six different dice values plus one blank die in each of the three disks. But how you distribute them is entirely up to you. You're going to see that the method of distribution makes a great deal of difference to your gambling success.  For instance, don't use this arrangement:         (0,1,2,3,4,5,6) (0,1,2,3,4,5,6) (0,6,4,2,5,3,1)  because it cannot produce any 7/11 winners or SuperJackpots. With this arrangement, the expected value of the game is minus \$1 - you lose a dollar every time. However, other arrangements can produce games with a positive expected value. That means you can make unlimited amounts of money if you stay at it long enough!
 Try the game!  See how well you can do. Explore the mathematics! This document is available in Adobe Acrobat's PDF format. You need to download the free Acrobat Reader to view it.

Original mathematical design © 2002 by Dean Clark and Charles Smith
University of Rhode Island