As I have said before, the late 60s actually took place in the early 1970s, and it was an interesting time, with a lot of ideas in the wind. One of the ideas in the wind was probabilistic decision making.
I suspect that the I Ching had something to do with it. All those college kids taking a hit off the bong, tossing the coins, then reading poorly translated Confucian texts in an attempt at fortune telling. It sounds very hippy dippy woo woo, but some of us knurds looked at it and said, "Aha! A probabilistic response to a non-full knowledge game." Then we'd take another bong hit.
Then you had Dungeons and Dragons, with all those weird polygonal dice. Given the degree of emotional investment in D&D characters, it was probably inevitable that someone would try something similar in real life.
D&D came out in 1974, but The Dice Man, by George Cockcroft (writing as "Luke Rhinehart," the ostensible protagonist of the novel) was published in 1971. The story is of a psychiatrist who, suffering from boredom and midlife crisis, decides to start making decisions based on the random toss of dice. Then, as zest, he begins adding some "forbidden" possibilities, including raping the wife of his next door neighbor. This being the sort of fantasy that it is, the dice pop up with that order, he complies, and she enjoys it (I know, I know).
He introduces his patients to "dice therapy" and things get out of hand in the sort of way that novels described as "funny, bawdy, [and] outrageous," get out of hand. A cult forms around him. The government gets involved. All very counter-culture in its way.
So, was it D&D or The Dice Man that was responsible for the following scene at a science fiction convention in the mid-1970s? Elevator stops, doors open. Outside is a woman looking into the elevator. She shakes her hands together, looks at the dice, then looks back at the elevator and waves goodbye.
Anyway, plays have been written, songs sung, lifestyles devised and documented. It struck a chord. I saw no reason not to use it as part of the basis for a religion several centuries from now. It's not as if randomness is going to go away.