Over the thousands of years that the Jewish people have been observing the day of Yom Kippur, the manner in which we observe it has gone through changes. At its inception there was one procedure that was the centrepiece for the day. The Kohen Gadol (High Priest), the only man who performed services on the day, took two identical goats and designated one as a sacrifice in the Bet HaMikdash, and the other was cast off a cliff far away in the desert. This was done to communally commit to casting-away vices and self-destructive behaviours with the aim at rehabilitation. Yet, the way in which the goats were designated was peculiar. They were not simply chosen, rather, a lot was cast to determine the fate of each goat.
This peculiarity might easily be written off as a simple way of making a decision, but things get even more peculiar when we begin to see lotteries popping up all around Yom Kippur. The famous haftara read on the day, the Book of Yona, has a lottery at the heart of the story. While we all know that Jonah is swallowed by a great fish in the ocean, we are not as familiar with how he was tossed into the sea in the first place:
And each man said to his fellow, let’s cast lots and discover for whom this evil has [come] to us. They cast lots and the lot fell on Yona. (1:7-8)
Even the daily lotteries that were used to determine which kohen would carry out a particular part of the service in the Temple, are oddly inserted in none other than tractate Yoma which is predominantly about Yom Kippur!
Chance seems to play a significant role on Yom Kippur, but why? Perhaps it is because chance is what affords us opportunity in life. Although people often say that it is choice not chance that determines our destiny, it is chance that provides the choice in the first place. When we give someone a chance, we are banking on the openness of the world and its possibilities to allow desirable outcomes that may not have been achieved previously, or that are not anticipated. One can fail time and again, but when we have chances, we assume that failure need not always be the outcome. It is the randomness of the world — the chance — that gives us the chance to do better.
On Kippur we acknowledge that our lives are filled with opportunities, and we have the ability to respond to the chances that life gives us. In knowing and embracing the world’s lack of predictability, we acknowledge that the road ahead is open to us, and, regardless of what might have come before, it does not determine how events and actions must proceed going forward. Each new day brings us a bundle of fresh opportunities at life, and on Yom Kippur, G-d asks us to step away from our regular, routine world of cause and effect, and spend 25 hours in the world of possibilities. It is in that world that new beginnings, untapped options, recreation and rejuvenation are born. Yom Kippur is the Day that G-d gives us the expansive gift of chance.
Gemar Hatima Toba,
 Vayikra, 16:5-10. Also described in Musaf of Kippur, Day of Atonement Mahzor, Vol. III pg.171.
 Chapter 2