Retrieval-Augmented Generation (RAG) has become the standard way to ground large language models in external knowledge, yet most systems retrieve a fixed number of passages for every question regardless of its difficulty. This wastes computation on easy questions, starves hard ones, and gives no signal for when a generated answer can be trusted. With a growing share of question answering systems built on top of commercial language model APIs, a method that can decide how much to retrieve, and how far to trust its own answers, without retraining the underlying model, is of clear practical value. This paper presents AB-RAG (Adaptive Budgeted Retrieval-Augmented Generation), a training-free and backbone-agnostic framework that generates an answer, estimates its confidence from a combination of three signals, and then decides whether to stop or to retrieve more evidence, subject to a fixed retrieval budget. The estimator combines the model's own certainty, the agreement between the answer and the evidence, and the variance of the retrieval scores. For models that expose token probabilities the certainty signal is read directly; for closed APIs it is approximated by self-consistency, so the method works without access to model internals. Across three backbones and two datasets, the central result is that the confidence estimate reliably separates correct from incorrect answers on every backbone, reaching a clean split of 57.6% against 0% Exact Match between high- and low-confidence answers on a factoid dataset. The adaptive policy improves accuracy on capable backbones, and the study reports its negative and nuanced findings honestly, including a confidence signal that proved unsuitable for short answers and a retrieval signal whose sign was found and corrected through measurement. The entire study was carried out on a single consumer laptop with only a few dollars of API spend.

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