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It seems God does play dice with the universe in part. From our point of view things seem random because we're only seeing the end result of probability and information. We're only seeing one Poker hand so to speak because of things like decoherence.
As an example of the fallacy of looking at results and conjecturing backwards on what the probability of such occurring was, grab a set of playing cards and deal them out face up, one at a time. When the first card is dealt, the probability of it being whatever it is, is 52-1, the probability of the second card being whatever it is is then 51-1, giving a combined probability of 2652-1. Once you have got through the deck, the probability of you having dealt those cards in that order is a staggering one in 8x1067, which is pretty much "nearly zero", yet you just managed to do it!