Which easy-to-acquire clear liquid would be best for testing whether or not a twenty-sided die is balanced?

Question

In another question on another stack, I asked if the Saltwater float present in a specific youtube video was capable of determining any differences in mass between the faces of a die in determining the balance of a group of dice, and was met with very good results and a positive affirmation that yes, it was very possible to do so.

Which led me to believe that there was a possibility that denser liquids might have the possibility of testing the balance of the dice even better, with much less mess. This led me to go through and search the densities of many liquids to determine which would be best for the job.

• Water came in at ~1g/mL at room temperature, which was the medium for the test initially.
• Saltwater was at about ~1.028g/mL. Dice were able to float in this.
• H2O2 (Hydrogen peroxide) clocks in at ~1.44g/ML, but I tested this one myself with a commercially available H2O2 and was unable to float dice in it just on its own. It isn't dense enough to float a die on its own.
• Originally I thought Galium might be a good choice since it has a high density and is very easy to melt, but it isn't transparent.

So the question is this:

Is there a liquid, that is easy to acquire, that has a higher density than H2O + MgSO4 (Epsom Salt), that it would be easier to test a dies balance in and at what density does a d20 float?

Generally when referring to dice, the most well known manufacturer is probably Chessex. The dice are made out of some kind of plastic polymer of some sort. I don't really know any specifics about their chemical composition, but they could just be injection molded plastic dice.

As for the approximate mass of said dice.. This site states that the dice themselves are ~5mg (That doesn't sound right. I learned in school that a Paper clip is a gram, Dice weigh much more than a paper clip..)

Answer 1

You don't want a denser liquid. You want a liquid with just the right density so the dice would barely float, almost fully submerged. To this end, you mix the solutions of different concentration and so fine-tune the density, as is beautifully described in the accepted answer to your rpg.SE question.

A denser liquid is worse for your purpose. Ultimately, with a very dense liquid (like mercury) the dice would just sit on one face, much like they do on a tabletop.

In the relatively rare case your dice might be made of different kind of plastic and wouldn't float at all. That's when you genuinely do need a denser solution. Chemistry knows a lot of salts; which of these are available to you is another question. Saturated solution of $\ce{MgSO4}$ has the density of 1.3 or so; $\ce{CaCl2}$ will get you to ~1.4, and other salts farther yet, but they are also more difficult to come by.

As for the reference books with some density values, you have to read those really, really careful to see what they actually refer to, and then read again, just in case. 1.028 looks like the density of seawater; it is salty all right, but that's pretty far from saturation. The solution you use is a lot more dense. 1.44 for hydrogen peroxide looks like the density of the pure compound, which you surely can't acquire (which in turn is probably good for your survival); what you had is probably the 30% solution which is a lot less dense.

As for the density at which your d20 will float... well, how are we supposed to guess that? For all we know, your die may be carved out of wood; also, chances are it is cast in bronze. The resulting figures may vary pretty widely. Upd. So it is plastic, after all. Well, that still leaves a pretty wide room for wiggling. You can't tell the density until you measure it. Chemistry is an experimental science, they say.

So it goes.

Answer 2

Near impossible to say at what density of solution some unknown die will float. I've seen hollow plastic dice and metal dice.

I'm also not sure how reliable some float test would be. I'd guess that the various gaming commissions have standard tests for dice. Using such a standard test would be preferable to trying to invent some test of your own.