The gin game is a metaphor for life.
Fonsia's gardening metaphorically represents that she desires to plant something and make it grow. She wants to give Weller a chance. She wants a relationship to sprout and grow between them. This is demonstrated when she repeatedly acquiesces to his request to play Gin, even though she knows that when he plays, he is likely to erupt into a rage. She tries and tries and tries, with no success. Weller is so stubborn and set in his ways that she cannot change him.
The Gin Game