“试试运气”常见的英文表达有：try one's luck 或 have a shot at luck。
try one's luck 是最为常用和地道的表达，例如：
I think I'll try my luck at the lottery this time.（我想这次我试试买彩票碰碰运气。）
He decided to try his luck in the big city.（他决定到大城市去碰碰运气。）
have a shot at luck 表达意思相近，但使用频率稍低一些，例如：
Why not have a shot at luck in the new business venture? （为什么不在新的商业冒险中试试运气呢？ ）