There are a lot of pages and vids out there suggesting that floating dice allows you to tell if they’re fair or not. How does this work?
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A weighted die is more likely to roll a certain number than others. This refers to literal weight, where one side is heavier and so more likely to land down while the opposite side is lighter and more likely to land up.
Floating dice will let you check to see if one side of the die is heavier as it will preferentially float with that side down. For example if you are suspicious that a 6-sided die is weighted on the 1 side so that it rolls 6 more often, if it will float on the 4 side then you know the 1 side isn’t heavier than the 6.
Buoyant forces pass through the center of volume of a body in water (so, in a die, the geometric center). However, *gravity* passes through the center of *mass* of the body. If those two points aren’t the same point, the object will reorient itself in the water so that the center of mass is directly underneath the center of buoyancy.
This is used as a test entirely because the method for loading a 6-sided die to make it unfair is to shift the center of mass towards a particular face, which makes that die more likely to roll with the opposite face on top.
Denser materials will sink, lighter materials will float. The weighted side will sink, while the unweighted side will float towards the surface.
On your table, whichever side is weighted is more likely to “sink” and be face down on the table. Same thing is happening in the liquid, it’s just that the dice is free to move while floating so the weight is a lot easier to see.
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