I read this quote in an article about risk and chance ("Playing the Cards" by Brooks Haxton):
Einstein said that “the Old One,” his name for the ultimate cosmic power, “does not throw dice.” The logical crux of this statement for an agnostic like Einstein might have involved some gamesmanship. But Einstein’s refusal to accept a way of thinking that devalues the idea of consequence and choice has always struck me as admirable.
Judaism has an understanding with seeming chance, mostly in terms of "throwing lots"; even our ultimate villain, Haman, knew about this bond, and attempted to manipulate the concept for his own ends, even unintentionally naming the resultant holiday, Purim.
On Yom Kippur, two literal scapegoats were brought before the Kohen; a lot was thrown, decreeing which would have a noble end as a sacrifice to Hashem, while the other would be unceremoniously shoved off a cliff.
I found this article on the OU website tying together the two seemingly disparate holidays.
Lots, or dice, are the essence of caprice: no rhyme, no reason. One day, flying high, then slip on a banana peel and down he goes. The subjected one, inexplicably, is tossed into security and grandeur. No matter how one claims control, we are all subject to the seemingly chaotic whimsy of the universe. "Mensch tracht und Gott lacht."
It is in lots that many cultures see the divine, the order that is emitted from turmoil. It is when we throw the dice that we abdicate from our ability to choose, placing the outcome in the hands of a higher power. It is not that we ignore God when we employ the anarchy of lots; we remove our biases by abiding by a decision from the truly unprejudiced. We throw together a dizzying array of variables, give a shake, and toss out a simple solution. Is that not where we see the Eibishter most clearly?
We can choose to see only chance. Or we can choose to see only "the Old One."