Agent session cost grows with the square of the turns, and the docs price the fix at 10%

The figure on the card was a 5x output-to-input token premium. It is not in the material in front of me: Anthropic's pricing page sets out multipliers for prompt caching, for US-only inference geography, and for marketplace billing in Consumption Units, but it states no output-to-input ratio and defers to claude.com/pricing for current per-model rates ^[1][2]. So treat the 5x as unverified here, and work with the number the same page does commit to: a cache hit costs 10 percent of the standard input price ^[3].

That percentage matters because of how a session accumulates. The context window holds the entire conversation, including every message, every file read, and every command output ^[4], and old conversation costs tokens on every message ^[5]. Turn N therefore re-bills roughly everything from turns 1 through N-1. Per-turn input grows linearly with turn count, so cumulative input over N turns scales as N(N+1)/2 ^[6]. Twenty turns is not twice the cost of ten turns; it is closer to four times ^[7].

An output premium, whatever its size, applies only to the new tokens generated each turn. The quadratic term sits entirely on the input side, which is the side caching discounts. At 10 percent for a read, that accumulated-history term drops by roughly a factor of ten ^[8]. The write premium is 1.25x for the 5-minute duration and 2x for the 1-hour, so caching pays back after one read or two reads respectively ^[9].

The reported spend is consistent with a long tail rather than a high average: about $13 per developer per active day across enterprise deployments, $150 to $250 per developer per month, and under $30 per active day for 90 percent of users ^[10], which puts the 90th percentile at roughly 2.3 times the mean ^[11].

What moves the curve is resetting and delegating, not shorter prompts. /clear starts a new session and the next session's total starts at $0, as of v2.1.211 ^[12]; /compact swaps the conversation for a structured summary ^[13]; /autocompact with a token count such as 500k moves the automatic pass earlier ^[14]; and a subagent does the large reads in its own context window, returning only a summary and a small metadata trailer ^[15].