try one's luck

try one's luck (at sth) (try to see if you can do or win something; to attempt to achieve something where success requires luck although you know that you might not succeed ) — попытать счастья в чем-л.; рискнуть, попробовать

Example 1: I'm going to try my luck at the slot machines.

Example 2: My great-grandfather came to California to try his luck at finding gold. (McGraw-Hill Dict)