Loaded Dice
Construction Plans and Statistical Results
by Kevin Wilson
Abstract
Dice were constructed from wood using holes or nickels to shift the center of mass to one side. The die was rolled 100 times and the die number was recorded. Simple statistical analysis showed the die landed on the number 6 at a frequency 222% more often than expected.
Introduction
I wanted to investigate the possibility of building weighted dice that would land on the number 6 approximately twice as often as expected. The dice should not land on a specific number every roll - what fun would that be?
The dice would be given as gifts to my niece nephew in an effort to reduce the time required to complete board games. After 15 minutes of Candy Land I beg for the merciful hand of the reaper. Generally, rolling a high number will cause the game to progress faster.
I wanted to keep the cost of the project as low as possible. The first prototype used holes to remove wood and shift the center of mass. This was the lowest cost option available. The second prototype used nickels to add mass. Nickels were the cheapest option that was readily available.
Materials and Methods
The dice were constructed using 1"x2" (actual 0.75"x1.5") poplar board. The final die dimensions were 2.9"x2.9"x2.9". I cut 8 boards to a length of 6.5". Two boards were glued on edge to create a 0.75"x3"x6.5" board. In the first prototype I drilled eight 1" holes in the board (four holes for each die) using a spade bit and drill press. In the second prototype I drilled eighteen 7/8" diameter holes to a depth of 0.08". I placed two nickels in each hole with a small amount of caulk to prevent the nickels from rattling. The total weight of the nickels was 3.2 ounces per die. The boards were glued to create a block 3"x3"x6.5". The block was cut in half resulting in a pair of dice. Each side was trimmed and sanded. The edges were rounded with a 1/2" roundover bit.
Figure 1 shows the 18 holes drilled to accept the nickels.
Figure 1. Holes to accept nickels. (click to enlarge)
Figure 2 shows the eight boards after glue-up that will be cut in half to create a pair of dice.
Figure 2. Boards after glue-up. (click to enlarge)
The dot locations were determined by measuring the dot location on a standard size die (0.62"x0.62"x0.62"), then scaling up to relative positions on my 2.9"x2.9"x2.9" die. The dot positions are coordinates with a corner of the face as the origin. The following locations were used:
| Side | Dot | X | Y |
|---|---|---|---|
| 1 | 1 | 1.5" | 1.5" |
| 2 | 1 | 0.87" | 0.87" |
| 2 | 2 | 2.13" | 2.13" |
| 3 | 1 | 0.87" | 0.87" |
| 3 | 2 | 1.5" | 1.5" |
| 3 | 3 | 2.13" | 2.13" |
| 4 | 1 | 0.87" | 0.87" |
| 4 | 2 | 0.87" | 2.13" |
| 4 | 3 | 2.13" | 0.87" |
| 4 | 4 | 2.13" | 2.13" |
| 5 | 1 | 0.87" | 0.87" |
| 5 | 2 | ||
| 5 | 3 | 1.5" | 1.5" |
| 5 | 4 | ||
| 5 | 5 | ||
| 6 | 1 | ||
| 6 | 2 | ||
| 6 | 3 | 0.87" | 1.5" |
| 6 | 4 | 0.75" | |
| 6 | 5 | ||
| 6 | 6 |
Figure 3 shows the dot locations for the number 2 side of the die.
Figure 3. Dot locations. (click to enlarge)
The dot locations were marked and 6mm holes were drilled to a depth of 0.15" using a brad point drill bit resulting in a flat bottom. The dice were painted and a 6mm rhinestone was glued in each hole.
The dice were tested by rolling 100 times on carpet and recording which side the die landed on.
Results
The prototype dice using holes was unsuccessful. After casual testing it was determined the center of mass was not sufficiently shifted to significantly increase the frequency of rolling any particular number.
The prototype dice using nickels was successful. The dice landed on the weighted side (side 6) 222% more often than would normally be expected. The number 1 side (opposite from the 6 side) was rolled 76% less than would normally be expected. The other sides landed at approximately the expected rate.
Figure 3 shows the occurrence of each side after 100 rolls.
Figure 3 (click to enlarge)
The cost to build a pair of dice was about $5 of poplar board, a few dollars each for spray paint, glue and rhinestones.
Acknowledgments
I want to thank my awesome wife Cindy who paid for this project and puts up with me.