A prompt is priced per call. A conversation is priced per turn.

A 2,000-token prompt over 30 turns bills 327,000 input tokens while the final context — the thing you can actually see — is only 20,000. Every turn re-sends the whole history, so the bill is a sum of a series: N × (fixed + in) + traffic × N(N−1)/2. A budget built from the per-call price times the turn count is wrong by 2.35× at 30 turns and more at 50.

The engine is free and needs no account, and it calls nothing: every figure is arithmetic on the token counts you paste. A few-shot example is a per-call cost, not a one-off — eight examples at 250 tokens is 2,000 tokens on every single call, $21,900 a year at 10,000 calls a day, for the setup half of the prompt. The window is not the input budget: it holds input AND output, so a 200k window with a 64k maximum output leaves 136,000 for input — 224 turns fit where planning against the model card promised 330. And a cache breakpoint covers a PREFIX, so a 40-token timestamp at the top of a 2,000-token prompt makes all of it uncacheable while the same line at the bottom leaves 98% cached — and nothing reports it, because the cached=yes is accepted and quietly ignored. Below one call per TTL, caching costs exactly 25% more than not caching. Every lane ships a worked example that costs nothing. Writing the report needs credits.