Lawfuldice.com is my latest endeavor and I am excited to announce it is operational! Lawfuldice.com offers a variety of d20 dice for sale that have all been tested for statistical validity (“fairness”).
Our methodology is simple; we roll each die 1000 times and then apply a “Goodness of Fit” statistical analysis to check if the die is behaving as expected.
Finding a “Fair” D20
Let me explain our methodology. Here are the results of a die that passed our testing process.
Each column represents the number of each die face rolled (41 “ones” for example). The dark blue line represents a perfect distribution of rolls; 50 for each die face. It is extremely unlikely to get a perfect 50 rolls per face, which is where “Goodness of Fit” calculations are valuable. Though the graph above has a “saw-tooth” appearance, you use “Goodness of Fit” to determine if it is within an acceptable tolerance versus the expected outcome.
(A quick note for the statistics nerds, I use a .05 P value as my break point for a bad die. Further information is available at the lawfuldice.com FAQ as to my methodology.)
If the die meets the threshold for a “good” die, it goes up for sale. The dice that fail are destroyed, never to curse a table again. Some of them fail badly, as you can see below.
Why does a die fail?
I found some with clear external defects such as sides being wider than others, making the d20 slightly oblong. Others I could not find anything external, which implies there is an issue within the die itself. Perhaps an air bubble or a bit of heavier metal or plastic mixed into the die’s interior, throwing off the balance. Regardless of the reason, I am ruthless with my testing. Pass or die.
As to your next question, no I am not rolling the die by hand 1000 times. I built a robot to roll the dice consistently. Exactly the same force is applied to every roll and then the robot ( I call her “Fortuna” after the Roman goddess of fate) captures an image of each roll.
This image is then fed into a machine learning system that I trained using 30,000 d20 dice images that can read the result on the face of the die. Fortuna is 99.56% accurate at reading the faces and I validate the results manually.
For the skeptics out there that think I may not be actually rolling the dice, I provide images of every roll upon request.
What percentage of dice are biased?
I have no idea what percentage of dice in the wide world are biased, but I can tell you that around 30% of the dice I test fail.
Why bother finding a “fair” D20?
Tabletop RPG games are played for fun, with no money on the line. So why would anyone care about d20 dice that are unfair? My answer is simple; biased dice suck the fun out of any game. Though experienced players have multiple dice sets,beginners often have a single, cherished dice set. If they get a bad d20 either they will experience an amazing run of luck that lets them roll through the adventure with minimal effort or actual strategy. Great for the player, but annoying for his fellow players. Even worse, a bad d20 biased towards low numbers might drive the player away with ongoing, soul-crushing failure after failure. Neither is “fun.”
Dice are agents of chaos in games and they should remain as such. Every time a player throws his d20 that is the difference between failure and success they should have an good chance at both. Not biased for one or the other because a manufacturer skimped on manufacturing consistency for his dice.
If you have any questions about Lawfuldice.com drop me a line. I am always happy to talk about dice!
Trask, The Last Tyromancer