The quote in your post title "God does not play dice." is an often repeated simplified paraphrase of Einstein.

The context is quantum mechanics. Einstein made references to dice a number of times.

For example:

Letter to Max Born in 1926, "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."

Letter to Cornel Lanczos in 1942, "It seems hard to sneak a look at God's cards. But that He plays dice and uses "telepathic" methods... is something that I cannot believe for a single moment."

Conversation with biographer William Hermann in 1943, "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."

Few people understood the context of Einstein's thought. This lack of understanding resulted in people projecting their own ideas (such as the idea of a personal god) into the dice reference. Einstein did not believe in a personal god as seen in the quote below:

A letter from 1954 as found in Albert Einstein the Human Side, "It was, of course, a lie what you read about my religious convictions, a lie which is being systematically repeated. I do not believe in a personal God and I have never denied this but have expressed it clearly. If something is in me which can be called religious then it is the unbounded admiration for the structure of the world so far as our science can reveal it."