That's possible, but it's also possible that they believed in supernatural intervention when playing dice games. It seems they did for other parts of their lives, why would this be different?

Because people in general weren't more stupid than us in everyday matters -- and you don't need a theoretical knowledge of combinatorics to know when you've been had.

Is it really just a matter of "being stupid"?

We know that cleromancy (casting of lots) was practiced among Hebrew populations and in ancient Rome [0]. Under a worldview in which the knowledge and will of the divine is made manifest through natural acts, where things aren't just "happenstance" but are inherently infused with meaning, this makes complete sense.

This is also why trial by ordeal was a thing in many ancient societies, and why it was seen to be legitimate enough to have as part of a judicial system. The idea is that divine forces will show their favor based on the outcome of what would seem to us to be chance. Now there were probably some that were more cynical or less so about all this, and that may be part of how such systems actually gained legitimacy, because those in authority could tip the scales occasionally [1].

I don't think we can compartmentalize the beliefs and mindsets of people, especially ancient people, into "secular" and "religious" domains. It was all intertwined in a way that is hard for us to relate to in modern times, even among modern religious people.

[0] https://en.wikipedia.org/wiki/Cleromancy [1] https://aeon.co/ideas/why-the-trial-by-ordeal-was-actually-a...

---

EDIT: I did some more reading and found something interesting -- there is a mention of "loaded dice" in the Mahabharata: [2]

>Shakuni's dice were off course made of his father's thigh bone and is believed to possess that special power of giving the number according to Shakuni's will.

From this the idea that dice could be manipulated or used to cheat in various ways seems to have been known far in the past, but there is still an interesting connection between dice-rolling and supernatural influences, even in the case of loaded dice. One of these days I should learn more about the Mahabharata.

[2] https://www.quora.com/Mahabharata-Hindu-epic-How-did-Shakuni...

Given how bad the modern human is at understanding probability, I see no reason to think the ancients were better.

I agree. And I don't think you need to understand probability to see that a flattened cube will fall on the top and bottom more often than the edges. Another possibility in addition to what you mentioned is that the games the dice were used in took into account that some sides were more probable than others and people trial-and-errored until more-or-less appropriate payoffs/penalties emerged.

These were the points I was about to make.

Also, in modern dice when we want nonequal chance of outcomes we use two dice and sum. This wouldn't be needed if a die had unequal probabilities per face.

"such beliefs didn't play a role in playing other games..."

Source?