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Testing d6′s

After seeing this article about d6's being biased to roll ones, I thought it was time to do some more dice testing of my own. Here's what I came up with.

What is being tested?
Are some types of six-sided dice biased? If so, what kind of dice are the best ones to roll up your character with?

Test Conditions-
Three d6's of the same type are rolled together in a dice cup onto a hard wood table- 48 times. Perfect results would be that each face on the dice would appear 24 times. For this test, the Sum Squared Error (SSE) must be 264 or less for the dice to be considered to be fair. (All I know about testing dice is from this great article at Delta's D&D Hotspot.) The closer the SSE is to 0, the more fair the dice are.

The Dice Tested-
10mm d6's - square edges with pips. I got these from some game maybe from Awful Green Things from Outer Space. 12mm d6's - rounded edges with pips. The most popular kind of d6's used by gamers. 14mm d6's - rounded edges with numbers. The kind of dice that usually come with D&D boxed sets. 16mm d6's - square edges with pips. The big d6's of the kind you see in Walmart. GameScience d6's- square edges with numbers.

Results-
3d6 Average Rolls (best to worst):
11.02 - 10mm
10.81 - 16mm
10.69 - 14mm
10.58 - 12mm
10.19 - gs

Fairness (SSE, best to worst):
28 - 14mm
82 - 16mm
144 - 12mm
152 - 10mm
210 - gs

Summary-
The results were surprising as the GameScience dice finished last in both fairness and high rolling. The 12mm dice that are so impugned in the article mentioned above are shown to be reasonably fair and I now suspect that article to be complete bs. Also surprising is that the lame dice that came in basic sets are actually the fairest rollers. But the most important thing learned here is that I'm going to start using those 10mm dice to roll up my characters from now on. :)

And now some graphs-

Posted in Games.


5 Responses

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  1. Andy says

    Even if some professor somewhere could get the time and hardware to do all that testing, this fails the smell test:

    “I sent a copy of the study to Chessex and their official response was to inform me that the amount of plastic saved from rounding the corners and hollowing out the pips of 2 dice actually gave them enough left over plastic to make a 3rd die. Economics wins.”

    In order to save enough plastic on two dice to make a third, almost half the die would need to be gone. There’s no way the math adds up there, although perhaps he was actually told that, but it’s just inaccurate.

    • Mike says

      Yeah, I thought that sounded very wrong as well.

  2. Rory says

    You say some dice are fairer than others, but is that really accurate? It’s a little hard to tell from the article you linked to, but the sense I got is that if a die meets the minimum requirement it’s X percent likely to be fair (a type 2 error)? So really all you can say is that the other dice are more likely to be fair, but probably all the dice are fair since they were under the threshold, right? And then if you rolled the dice like a million times, and they were still under that threshold, then you’d feel pretty good about saying all the dice were fair. Is that right, or am I missing something?

    • Mike says

      That’s my understanding too. As long as they test under the threshold, they are considered to be reasonably fair, ie- they aren’t cheaters dice. But fair and perfectly balanced are two different things. Otherwise casinos wouldn’t worry about having precision dice. Outside of those, all dice will probably have some slight bias to certain results. The trick is to find the dice that are biased in your favor. ;)

  3. Mike says

    PS- I took the 10mm d6′s from this test to GenCon and rolled up an awesome character (Str- 17 Dex-18) for my HackMaster game there. Testing your dice pays off!



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