to give it a shot(Я отослал заявление на удачу. I sent in an application on the off chance I'd get the job.; рассчитывая на везение, удачу; без уверенности в успехе предпринимаемых действий counting on luck, good fortune; to take something on with little hope of success)
take one's chances(But, those additions will cost substantially more from an American-made knife, or I will have to take my chances with something made in China.4uzhoj)