Bhaga is a Vedic god. Not much is known about him except that he was one of the 12 solar gods, the Adityas, and he was associated with marriage and prosperity. Bhaga refers to female genitalia and so the source of life and pleasure. It gives rise to two words: bhaaga, or share, and bhaagya, or fate.
The two words are closely related to each other. For in Hindu belief, fate is the share of fortune we are supposed to get in life. Thus some people are born in wealth, some in poverty. Some lose wealth in their lifetime, some gain. Pandavas spent most of their lives in the forest while the Kauravas spent all their lives in palaces. Sita married a prince but spent all her life away from the palace, and him.
What is fair share in life? Imagine a mother feeding her two sons. How should she divide the food? Equally? Or as per need? Who decides the need? Does the elder get more? Does the weaker get more? Does the hungrier get more? Does the obedient get more? Does the favourite get more? Does the smarter get more? And if there was a daughter, would she get less? What is the correct formula of distribution?