chance (one's) arm
slang To do something risky in pursuit of a desired outcome. Primarily heard in UK, Australia. I think he's chancing his arm by dumping his life savings into yet another bizarre money-making scheme.
chance your arm
BRITISHIf you chance your arm, you do something risky or daring in order to get something you want. Sport is about going out and giving it your best shot, chancing your arm for glory. Instead of going on the dole I chanced my arm on a business.
chance your arm (or luck)
undertake something although it may be dangerous or unsuccessful; take a risk. British informalˌchance your ˈarm
(British English, informal) take a risk (especially when you are unlikely to succeed): He knew he wasn’t likely to win the contest, but decided to chance his arm anyway.