Estimate the daily bill for the reasoning tier behind a 30% router split

First find how many requests hit the reasoning tier: 200,000 times 30% equals 60,000 calls per day. Next find how many output-billed tokens each call uses. With reasoning models, the hidden thinking tokens are billed at the same rate as the visible output tokens. So 5,000 thinking + 500 visible = 5,500 output-billed tokens per call. Multiply: 60,000 calls times 5,500 tokens equals 330 million tokens per day on the reasoning tier. Price it: at $10 per million tokens, that is 330 times $10, or $3,300 per day. The key observation is the structure of the bill. About 91% of that $3,300 comes from the thinking tokens, which the user never sees. Only $300 comes from the visible answers. So if you want to reduce cost, trimming visible output length is almost useless; you have to trim the thinking budget or route fewer requests to this tier.

**$3,300 per day.** The arithmetic is straightforward but the structure matters. Reasoning calls per day: `200,000 x 0.30 = 60,000`. Output-billed tokens per call: `5,000 + 500 = 5,500`, because hidden thinking bills at the output rate on every major reasoning model. $$\text{daily cost} = 60{,}000 \times 5{,}500 \times \frac{\$10}{10^6} = \$3{,}300$$ **Where the bill lives.** Thinking tokens contribute `60,000 x 5,000 x $10 / 1M = $3,000`. Visible tokens contribute `60,000 x 500 x $10 / 1M = $300`. The hidden trace is over 90% of the bill on the reasoning tier. **Implications for cost work.** Trimming visible output length moves $300, not $3,000. The levers that move real money are the routing percentage (currently 30%), the thinking budget per call, and the model selection (some reasoning models charge differently for hidden tokens, or expose effort levels that scale the trace). Plan capacity and budget conversations around the right variable: per-tier thinking-token consumption, not per-call output length.