Cost of a Conversation
What a multi-turn chat costs once every turn re-sends the whole transcript, and how much of the bill is history you have already paid for.
Turn 1 sends 920 input tokens; turn 20 sends 9,850. Re-sent history is 82.9% of everything you pay for on the input side.
- Input tokens billed, total
- 107,700
- — of which is re-sent history
- 89,300
- Output tokens billed
- 7,000
- Input cost
- $0.32
- Output cost
- $0.10
- First turn, input tokens
- 920
- Final turn, input tokens
- 9,850
- If history were never re-sent
- $0.16
- History multiplier
- 2.67×
Why a long chat costs more than it looks
The cost of a conversation is not the number of turns times the cost of a turn. Because the transcript is re-sent on every request, turn twenty pays for turns one through nineteen again. Summed across the conversation the history term is a triangular number: it grows with the square of the turn count while the output cost grows linearly. Doubling the length of a chat roughly quadruples its input bill.
That is the whole reason the last turn of a long session feels expensive and slow at the same time. It is also why the cheapest intervention in a chat product is almost never a cheaper model — it is a shorter system prompt, because the system prompt is multiplied by every turn, or a trimmed history, because the history is multiplied by everything after it.
The three levers, in order
Prompt caching attacks the repeated prefix directly and is usually the largest single win in a chat workload, since the prefix is the part that repeats by definition. Trimming or summarising history caps the quadratic term at a constant and changes the shape of the curve rather than its slope. Shortening replies helps twice: output tokens are typically billed at a multiple of input tokens, and every reply also becomes input on every subsequent turn. The third is the one people forget, and it is the only one that compounds.