after consulting the enneagram I figure that Billy falls under category 3.

characteristics of a 3-type:
Basic Fear: Of being worthless
Basic Desire: To feel valuable and worthwhile

The performer

Billy needs to be admired, being admired is often more important than being respected, which makes him somewhat shameless while still respectably ambitious...perhaps. This, along with Billy's adaptability make him an expert performer, whether performing on stage or in the wooing of older women, namely Annie. Billy's image is malleable, he wants to fit the situation, to control and use circumstances for personal success.

The question: when Billy shows frustration, is it at the prospect of losing Annie or simply of losing in general?