take a flyer (on something)
To take a chance, risk, or gamble (on something). Primarily heard in US. I'm just grateful that this team took a flyer on me and gave me a shot at the big times. The economy is too unstable for us to take a flyer on some unproven investment at the moment. We're not just taking a flyer with this plan—we've researched every angle very thoroughly, and we're confident this is the best approach to take.
take a flyer (on something)
tv. to take a chance on something. Fred is too wise an investor to take a flyer on some story stock like that.