$100 for 10,000 Chats: A Model-Buying Receipt

01 / A $100 receipt, not a claim about live prices

Choosing between Claude Sonnet 5.5 and GPT-6.1 Sol for a chatbot starts with a receipt, not a leaderboard. The useful question is simple: what will your actual conversations cost, and how often will each model complete the job without another attempt?

Here is a concrete budget: 10,000 chatbot turns, averaging 2,000 input tokens and 400 output tokens per turn. At an illustrative $3 per million input tokens and $10 per million output tokens, the bill is $100. Those rates are budgeting assumptions, not current quotes for either model. Check current pricing before choosing; this example does not establish which model is cheaper.

02 / The 10,000-turn receipt has two main lines

A turn means one user request followed by one model response. Input includes everything sent with that request: instructions, conversation history, retrieved documents, and the latest message. Count that full payload, not just the sentence the user typed.

• ■ Input quantity: 10,000 turns × 2,000 tokens = 20 million tokens.
• ■ Input charge: 20 million × $3 per million = $60.
• ■ Output quantity: 10,000 turns × 400 tokens = 4 million tokens.
• ■ Output charge: 4 million × $10 per million = $40.
• ■ Total illustrative token bill: $100, or $0.01 per turn.

This first receipt assumes no caching and no retries. It excludes your application hosting, database, retrieval service, and human support costs. Keeping those outside the model receipt makes the comparison easier to audit, but they still belong in your business budget.

03 / Use the same receipt for both model quotes

For this workload, the uncached token-cost formula is 20 × input rate + 4 × output rate, with both rates expressed in dollars per million tokens. Substitute the current Claude Sonnet 5.5 rates, then the current GPT-6.1 Sol rates. That produces a comparable estimate without pretending either model has the illustrative pricing above.

The sensitivity is useful before you even fetch a quote. Every $1 difference in the input rate changes this monthly receipt by $20. Every $1 difference in the output rate changes it by $4. For this particular workload, input pricing has five times the leverage of an equal-sized output-rate difference.

Response length can reverse that emphasis. If average output rises from 400 to 800 tokens, output volume becomes 8 million tokens. At the illustrative $10 output rate, that line increases from $40 to $80, taking the total to $140. Concise answers are a budget control when they still satisfy the user.

04 / Retries and cached history need separate receipt lines

Suppose 1,000 of those 10,000 turns require one additional generation with the same average token counts. That adds 2 million input tokens and 400,000 output tokens: another $10 at the illustrative rates. The receipt becomes $110. This is a scenario, not a measured retry rate for either model.

Caching needs its own calculation. Separate ordinary input, cache writes, cache reads, and output according to the applicable billing rules. CheapRelay bills real tokens, including cache reads and writes, so cached context should not be treated as free. Use recorded usage rather than estimating savings from repeated text alone.

05 / Buy the cheaper successful conversation, not the cheaper attempt

Run both models against the same representative questions, histories, instructions, and response limits. Record billed tokens, repeat attempts, and whether each answer meets your chatbot’s requirements. Include difficult cases such as missing account information or requests that require escalation. Do not assume either model wins those cases without testing.

CheapRelay offers pay-as-you-go access with no monthly fee or subscription, making a bounded comparison practical. Sign up for CheapRelay and set a small test budget before routing production conversations.

Your decision rule is total measured spend divided by successfully completed conversations. Keep quality requirements fixed. If both candidates satisfy them, choose the lower receipt; if one needs more retries, include those charges before calling it cheaper.