risk (something) on (someone or something)
To expose oneself to the chance of losing something by betting or relying on someone or something. My father once risked his entire life savings on the outcome of a horse race. We're risking a lot on you, Tom—don't make us regret our decision to put you in charge of this project.
risk something on someone or something
to chance losing something on someone or something. I wouldn't risk any money on him. He's a poor credit risk. Don't risk your life on his being there to help you.