A “God playing dice” cartoon, by John C. Holden (Ѻ), showing Niels Bohr and Albert Einstein arguing about whether the universe is deterministic (non-chance based) or indeterministic (chance based), as quantum mechanics sees things.

In hmolscience, God does not play dice is statement made often by German-born American physicist Albert Einstein, originally in 1926, and many times after in respect to quantum mechanics.

Einstein
German-born American physicist Albert Einstein, in the rise of quantum mechanics, often used to talk often about God and dice. Einstein's belief in the existence of god, as he has said, was supposed to have been akin to Benedict Spinoza's "god = nature" model, with slight adjustment.

In 1926, Einstein, in a letter to German physicist Max Born, about quantum mechanics, commented the following: [1]

“Quantum mechanics is certainly imposing. But an inner voice tells me that it is not yet the real thing. The theory says a lot, but does not really bring us any closer to the secret of the "old one." I, at any rate, am convinced that He does not throw dice.”

In 1943, Einstein, in conversation with biographer William Hermann, concerning what is real and exists versus what is but mental constructs, stated the following: [2]

“Nature doesn’t know chance, it operates on mathematical principles. As I have said so many times, God doesn’t play dice with the world.”

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Dirac
In 1927, at the fifth Solvay Conference in Brussels, while sitting around one evening at the hotel’s smoky lounge, some of the younger physicists were sitting around on chairs and sofas, among them English theoretical physicist Paul Dirac, along with Werner Heisenberg, and Wolfgang Pauli, during the course of which, as recalled by Heisenberg, Dirac went off on rant about religion, triggered by a comment about Einstein’s habit of referring to God during discussions of fundamental physics: [3]

“If we are honest — and scientists have to be — we must admit that religion is a jumble of false assertions, with no basis in reality. The very idea of God is a product of the human imagination. It is quite understandable why primitive people, who were so much more exposed to the overpowering forces of nature than we are today, should have personified these forces in fear and trembling. But nowadays, when we understand so many natural processes, we have no need for such solutions. I can't for the life of me see how the postulate of an Almighty God helps us in any way. What I do see is that this assumption leads to such unproductive questions as why God allows so much misery and injustice, the exploitation of the poor by the rich and all the other horrors He might have prevented. If religion is still being taught, it is by no means because its ideas still convince us, but simply because some of us want to keep the lower classes quiet. Quiet people are much easier to govern than clamorous and dissatisfied ones. They are also much easier to exploit. Religion is a kind of opium that allows a nation to lull itself into wishful dreams and so forget the injustices that are being perpetrated against the people. Hence the close alliance between those two great political forces, the State and the Church. Both need the illusion that a kindly God rewards — in heaven if not on earth — all those who have not risen up against injustice, who have done their duty quietly and uncomplainingly. That is precisely why the honest assertion that God is a mere product of the human imagination is branded as the worst of all mortal sins.”

At the end of which Pauli, when asked what he thought, declared: [4]

“Well our friend Dirac, too, has a religion, and its guiding principle: There is no God and Dirac is his prophet.”

after which everyone laughed, including Dirac. The following, likewise, is an unpublished 1933 handwritten note by Dirac: [5]

“Any further assumption implied by belief in a God which one may have in one’s faith is inadmissible from the point of view of modern science, and should not be needed in a well-organized society.”

which, to note, is near verbatim to the famous 1802 "I had no need of that hypothesis" Napoleon Laplace anecdote on Pierre Laplace's god-free celestial mechanics.

A cartoon of Stephen Hawking's god playing dice around a black hole. [7]

Other
In 1975, English physicist Werner Ehrenberg was working on the book Dice of the Gods: Causality, Necessity and Chance, published posthumously (1977), with discussion of soul and indeterminism. [6]

In 1994, Stephen Hawking, during a debate with Roger Penrose, at the Isaac Newton Institute for Mathematical Sciences, University of Cambridge, about whether or not Einstein was wrong in his God does not throw dice statement, gave his opinion that: [6]

“Consideration of black holes suggests, not only that God does play dice, but that he sometimes confuses us by throwing them where they can't be seen.”

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References
1. Einstein, Albert. (1926). “Letter to Max Born”, Dec 4; in: The Born-Einstein Letters (translated by Irene Born) (Walker and Company, New York, 1971).
2. Hermanns, William. (1983). Einstein and the Poet: In Search of the Cosmic Man (pg. 57-58). Branden Books.
3. Heisenberg, Werner. (1971). Physics and Beyond: Encounters and Conversations (pgs. 85-86). Harper.
4. Farmelo, Graham. (2009). The Strangest Man: the Hidden Life of Paul Dirac, Mystic of the Atom (Dirac is his prophet, pg. 138; reductionism, pg. 158). Basic Books.
5. (a) Dirac, Paul. (1933). three page hand-written note, Jan 17; in Private Papers of Mary Dirac.
(b) Farmelo, Graham. (2009). The Strangest Man: the Hidden Life of Paul Dirac (pg. 222). Basic Books.
6. Ehrenberg, Werner. (1977). Dice of the Gods: Causality, Necessity and Chance (indeterminism, 4+ pgs; quote, pg. 13). Birkbeck College.
7. Hawking, Stephen. (2000). The Nature of Space and Time (pg. 26). Princeton University Press.