Behavioral scientists have classically documented aversion to algorithmic decision aids, from simple linear models to AI. Sentiment, however, is changing and possibly accelerating AI helper usage. AI assistance is, arguably, most valuable when humans must make complex choices. We argue that classic experimental methods used to study heuristics and biases are insufficient for studying complex choices made with AI helpers. We adapted an experimental paradigm designed for studying complex choices in such contexts. We show that framing and anchoring effects impact how people work with an AI helper and are predictive of choice outcomes. The evidence suggests that some participants, particularly those in a loss frame, put too much faith in the AI helper and experienced worse choice outcomes by doing so. The paradigm also generates computational modeling-friendly data allowing future studies of human-AI decision making.