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No, because these ones affect the consumer chat products and not the API or Claude Code.

(Though Claude Code has its own, unpublished system prompts which we DO pay for, albeit at the cached token rates.)

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Technically these do count against your token usage if you happen to use claude.ai web chat alongside Claude Code - both use the same allowance. Makes me appreciate OpenAI/ChatGPT giving you unlimited chat that doesn't drain your Codex allowance.
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Yeah, Claude chat does show little in-app messages occasionally warning that Opus or Fable will burn through your rates faster.
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So YES if you're using Cowork or Chat
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No, because they are cached, the inference cost is paid once per model, does not scale linearly per user or use.
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