## Monday, August 28, 2017

### Testing unbalanced dice in water

I've written about how to use standard statistical procedures to test for unfair dice a few times in the past (one, two, three, four). As noted in the last of those linked articles, for a d20 this probably involves some hundreds of dice-rolls at a minimum to get a test of sufficient power.

Here's a clever and much faster way of doing a check for unbalanced dice. This is from a video sent to me a while back by reader Ro Annis. Get a bowl of water, pour salt in to increase the buoyancy factor, and throw your dice in. If they repeatedly and consistently spin up the same face, then that die is obviously unbalanced. Like the second die in the video here.

I can imagine a few corner-cases where this may not suffice -- like if the die is balanced by weight, but the faces are malformed so as to bias the rolls on a table. But this is a great and fast way to do a first-pass check. Thanks, Ro!

#### 8 comments:

1. So bring a bucket of salt water with you when you go to the game store to buy dice. The proprietors love it when customers do that! ;)

1. Do it in the winter and say you'll de-ice their walk at the same time. :-)

2. I wish there was an upvote button for this comment. That is an awesome pun!

2. You probably already covered this, and I don't mean to be a curmudgeon. But if we're talking about not-huge factors of unbalance, then it's not clear to me that it really matters. You still have epistemological randomness if not metaphysical randomness. And partly since one presumably is using a variety of dice for a variety of purposes, it's epistemological randomness which I would think would be the most important thing. I know I'm not putting it very well. Does that make sense?

That said, the water test is fascinating.

3. I've done this test on dozens of D20s.

All the opaques failed and all the clears passed!

Only one exception: one clear die failed that had a relatively large bubble on the side that was lighter. It turns out, the bubbles matter.

No need to bring salt water to the store. Just avoid the opaques and check the clears for bubbles.

The shape isn't an edge case. I've seen dice pass this test with flying colors while being so deformed some faces were actually convex.

I've read that opaques are cheaper because they rush the production on them, because no one can see the flaws on the inside like they would be able to with clears.

Tell the world.

1. That's a really good interpretation, and it sounds to me like solid advice. Thanks for sharing that!

4. Before summer, a friend and I did a test to see which was better at identifying biased dice. He had 10 d12s, and he got a player to roll each of them 112 times and record the results (not sure why that number, but that's the data he sent me), and then he separately tested them in salt water. I haven't seen him over the summer so I didn't get a chance to find out the results of his test.

The stats method definitely took ages, and I only identified 1 biased d12. However, based on the power of the test, I couldn't say with certainty that any of the other 9 were unbiased (I did some power tests and I think upping the number of rolls to about 200 would have been enough, but I don't have the working in front of me).

So what do you reckon? I don't know if a die that fails the water test would also fail the chi2 test. It seems to me that rolling is the gold standard, but you need to do so many rolls that it takes forever. Also if you've got multiple dice then you'll need to roll them even more to stop the 1 in 20 slipping through with 20 dice.

1. Yeah, I would definitely think that the water method is a great first-pass. If one fails there than I'd just dispose of it and assume it doesn't roll correctly.* After that I'd go with rolling evidence for my top favorite dice.

* Further Research: A paper confirming that dice failing the water method also show as unbalanced in rolling tests.