I don’t think the average person actually has any mental tells for when something is rigged. They just assume everything’s gaussian or uniform distribution until… someone they trust tells them otherwise.
Or in other words – everything they are told is gaussian or uniform, they will defend as such, until the moment they are told otherwise.
Some of them may know of statistics and the “correct” way to determine what a distribution is, but even if they use it, which they generally won’t, I don’t think they will believe it.
Test: Suppose you give the average person a loaded die and they lack access to complicated equipment to measure directly, the only way they can test it is by rolling it. Suppose one face is loaded to 1/4 instead of the true 1/6, meaning that it’s almost a 10% chance more likely roll than it should be – significant if you think about it, but not completely noticeable if you don’t. How many times does the average person need to roll it before they believe that it is loaded?
Test: Additionally supposing you were trustworthy or otherwise held authority with them, what is the chance that the number of required rolls is infinite?