This is the kind of problem where it helps to have someone to talk about your ideas with. Catherine, Ruyi, Elle and Ebony from Annesley College, Adelaide, Australia worked in pairs and decided that although Bipin was taking a risk, he should choose to play again. Here's one of their reasons:

Bipin should play again because he has a four in nine chance of getting a red ball (this doubles his money). He has a three in nine chance of getting a yellow ball (this makes him lose all of his money) and a two in nine chance of getting a blue ball (this gives him another chance of drawing another ball).

This means that he has a greater chance of doubling his money. (Catherine)