A standard model answers in one pass: the first token of the reply follows the prompt directly. A reasoning model first writes to itself - decomposing the problem, checking a step, revising - and only then writes the reply. The intermediate text is usually hidden from the user but it is real generation: it takes time and it is billed, typically at the output rate, and it can run to thousands of tokens for a hard problem.
The gain is real and uneven. On mathematics, planning, multi-step analysis, debugging and anything with dependent constraints, reasoning models score markedly higher on the composite indexes and in practice. On retrieval, summarisation, formatting, classification and short answers they are no better and several times more expensive, and their latency can turn an interactive feature into a waiting screen. Vendors expose an effort setting - how much to think - which is the main lever once the model is chosen.
The cost arithmetic matters because reasoning models are the most common way an AI bill doubles without a decision. A model whose list price matches a standard model's costs several times more per request once the hidden tokens are counted; the per-million figures in a catalogue understate the difference. Price a representative request, not a token, when comparing.
A router's job with reasoning models is restraint. Complexity is one of the signals it extracts, and the verbs - why, prove, diagnose, compare, step by step - are others; a rule can reserve reasoning models for requests that score high on them and send everything else to a standard model that meets the quality floor. Outcomes then correct the threshold in both directions: a standard model that fails hard requests loses them, a reasoning model that adds nothing on easy ones loses those.
