"Broken my duck"? Is this a common idiom/phrase?

Solution 1:

This might help, it's a fairly common'ish phrase in the UK.

In summary it's a cricket related term. In cricket a "Duck" is where a player has been dismissed from play without scoring a point. "Breaking one's duck" is the occasion where a you break a run of ducks.

breaking your duck - boards.ie

Outside of cricket the term is often used to describe having done something for the first time.

Solution 2:

To break one's duck means the person has done something for the first time. The phrase comes not from duck as an animal, but from a duck in cricket, which is a batsman's dismissal for a score of zero. Therefore, when one breaks his duck, they score the first point.