He plays an ineffable game of His own devising, which might be compared, from the perspective of any of the other players, to being involved in an obscure and complex version of poker in a pitch-dark room, with blank cards, for infinite stakes, with a Dealer who won't tell you the rules, and who smiles all the time.

-Good Omens

This is really a quote attributed to Einstein in reference to the randomness inherent in quantum mechanics. Einstein believed that quantum theory could not be true, simply because it implied there was a limit to how much a scientist could know about a particle. Everything else, therefore, appeared random to an observer (see Uncertainty Principle, Schrodinger's Cat.)

Einstein struggled through the last half of his life to eliminate this uncertainty, but he never could (no one else could eliminate it either, and since Einstein we have only realized more things that we can't know. see neutrino). Some say (read: Hawking, who is very hung up on comparing himself to Einstein, btw) that never conceding this fact was Einstein's greatest mistake.

All of this is quite ironic considering Einstein never believed in a science that he helped to found.
not only does God play dice with the universe, he throws them where they cannot be seen
Stephen Hawking in reference to quantum mechanics and black holes
On the whole Einstein thing, a better translation form the German would be God is slick but he is no malicious. It is about the physics as hramyaegr says, but it was not due to a lack of knowledge surrounding the subject at the time. It was a statement of Einstein's disagreement with the proababilistic nature of quantum mechanics. He held to his point of view, that the world was determanistic and that we didn't have a good enough theory to realise this, right untill his death. By the time of his death quantum mechanics was quite well understood.
"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."

-Albert Einstein in Albert Einstein: The Human Side, edited by Helen Dukas (Einstein's secretary)
and Banesh Hoffman, and published by Princeton University Press

Einstein's remark regarding "God does not play dice with the universe" was not a statement about god--it was instead regarding quantum mechanics and is representative of the lack of knowledge surrounding the subject at the time.

Einstein was in fact an atheist (http://www.stcloud.msus.edu/~lesikar/einstein/index.html). Theists often try to use the dice quotation as a means to introduce belief, stating "One of the greatest thinkers of our time was a believer, why aren't you?" It's always a great opportunity to point out their use of the argumentum ad verecundiam (appeal to authority) fallacy and ask why they have to use such blatantly illogical and underhanded tactics.

God does play dice, but only at Las Vegas, though it has been alegged that he goes to Atlantic City and Tunica on his offweeks. He does not play in black holes, as Stephen Hawking has suggested, as this would result in the loss of his dice. The statement that God's dice are loaded has not yet been proven, as God is currently unavailable for comment.

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