When switching models mid-session pays off
A cheaper model can make the next call more expensive when it starts with a cold cache. Compare the remaining workflow, including the cold start and the handoff.
Reviewed
I. Price the cold start
Calculated example. Assume a warm 100,000-token prefix on GPT-6 Astra, 2,000 new cache-write input tokens and 1,000 billed output tokens per call. GPT-5.6 Sol starts cold, then reuses its growing prefix. Quality and billed token counts are held equal.
| Model | Input | Cache read | Cache write | Output |
|---|---|---|---|---|
| GPT-6 Astra | $10 | $1 | $12.50 | $50 |
| GPT-5.6 Sol | $4 | $0.40 | $5 | $20 |
Count each input token once at its applicable rate. Cache reads and writes are assumed in this trace; actual cache hits depend on prefix reuse and cache availability.[3]
The next warm Astra call costs $0.175. The first cold Sol call costs $0.530, a $0.355 premium over staying. A warm Sol call with the same prefix would cost $0.070, so Sol's one-time cold-start surcharge relative to its own warm cost is $0.460.
II. Count the calls still ahead
For fixed per-call costs, let a be the warm source cost, b the warm target cost, F the cold-start surcharge and H the additional handoff cost.
Stay = N × a
Switch = N × b + F + H
Switch when N × (a − b) > F + H.For a > b, the first saving integer is floor((F + H) / (a − b)) + 1. At equality, both choices cost the same.
This trace adds input each call. Within its first 86 calls, the totals are Astra(N) = 0.175N + 0.001N(N − 1) and Sol(N) = 0.4 × Astra(N) + 0.460.
| Remaining calls | Stay | Switch | Saving |
|---|---|---|---|
| 1 | $0.1750 | $0.5300 | −$0.3550 |
| 4 | $0.7120 | $0.7448 | −$0.0328 |
| 5 | $0.8950 | $0.8180 | $0.0770 |
| 10 | $1.8400 | $1.1960 | $0.6440 |
| 30 | $6.1200 | $2.9080 | $3.2120 |
Adding an assumed $0.20 handoff cost moves the first saving call from five to seven.
III. Measure the complete handoff
Use the same acceptance criteria for both workflows. Measure retries, output quality and review effort. Equal quality is an assumption in the calculation and needs verification on your workload.
Technical note · pricing boundaries and cache misses
Both model pages specify full-request multipliers above 272,000 input tokens: 2× input-side rates and 1.5× output. The quadratic expression above applies within the unscaled range; a longer trace must apply the higher rates to the entire affected request.[1][2]
Repeated misses add cost on each affected request. Use measured cache-read, cache-write and ordinary-input counts, and include billed reasoning output. Carry over decisions, files, failed attempts and acceptance checks; count the token cost of creating and reading that handoff. Account separately for latency, tool charges and human effort.
Recalculate with current rates and your remaining task horizon before switching. The rate snapshot and cache assumptions above make this example reproducible.
Sources
Sources checked 2026-09-21.